Avogadro's Law: Volume and Amount About Watch and Favorite Watch Watching this resources will notify you when proposed changes or new versions are created so you can keep track of improvements that have been made. Favorite Favoriting this resource allows you to save it in the “My Resources” tab of your account. There, you can easily access this resource later when you’re ready to customize it or assign it to your students. Avogadro's Law: Volume and Amount Avogadro's Law states that at the same temperature and pressure, equal volumes of different gases contain an equal number of particles. Learning Objective State Avogadro's Law and its underlying assumptions Key Points The number of molecules or atoms in a specific volume of ideal gas is independent of size or the gas' molar mass . Avogadro's Law is stated mathematically as follows: $\frac{V}{n} = k$ , where V is the volume of the gas, n is the number of moles of the gas, and k is a proportionality constant. Volume ratios must be related to the relative numbers of molecules that react; this relationship was crucial in establishing the formulas of simple molecules at a time when the distinction between atoms and molecules was not clearly understood.

Term Full Text Definition of Avogadro's Law Avogadro's Law (sometimes referred to as Avogadro's hypothesis or Avogadro's principle) is a gas law; it states that under the same pressure and temperature conditions, equal volumes of all gases contain the same number of molecules. The law is named after Amedeo Avogadro who, in 1811, hypothesized that two given samples of an ideal gas—of the same volume and at the same temperature and pressure—contain the same number of molecules; thus, the number of molecules or atoms in a specific volume of ideal gas is independent of their size or the molar mass of the gas. For example, 1.00 L of N2 gas and 1.00 L of Cl2 gas contain the same number of molecules at Standard Temperature and Pressure (STP). Avogadro's Law is stated mathematically as: $\frac{V}{n} = k$ V is the volume of the gas, n is the number of moles of the gas, and k is a proportionality constant.

As an example, equal volumes of molecular hydrogen and nitrogen contain the same number of molecules and observe ideal gas behavior when they are at the same temperature and pressure. In practice, real gases show small deviations from the ideal behavior and do not adhere to the law perfectly; the law is still a useful approximation for scientists, however. The model contains gas molecules under constant pressure. The barrier moves when the volume of gas expands or contracts. Run the model and select different numbers of molecules from the drop-down menu. What is the relationship between the number of molecules and the volume of a gas? (Note: Although the atoms in this model are in a flat plane, volume is calculated using 0.1 nm as the depth of the container.) Significance of Avogadro's Law Discovering that the volume of a gas was directly proportional to the number of particles it contained was crucial in establishing the formulas for simple molecules at a time (around 1811) when the distinction between atoms and molecules was not clearly understood. In particular, the existence of diatomic molecules of elements such as H2, O2, and Cl2 was not recognized until the results of experiments involving gas volumes was interpreted.

Early chemists calculated the molecular weight of oxygen using the incorrect formula HO for water. This lead to the molecular weight of oxygen being miscalculated as 8, rather than 16. However, when chemists found that an assumed reaction of H + Cl $\rightarrow$ HCl yielded twice the volume of HCl, they realized hydrogen and chlorine were diatomic molecules. The chemists revised their reaction equation to be H2 + Cl2 $\rightarrow$ When chemists revisited their water experiment and their hypothesis that $HO \rightarrow H + O$ , they discovered that the volume of hydrogen gas consumed was twice that of oxygen. By Avogadro's Law, this meant that hydrogen and oxygen were combining in a 2:1 ratio. This discovery led to the correct molecular formula for water (H2O) and the correct reaction $2H_2O \rightarrow 2H_2 + O_2$ Gas Laws Gas Laws Contact Webmaster Gas Laws Gases behave differently from the other two commonly studied states of matter, solids and liquids, so we have different methods for treating and understanding how gases behave under certain conditions. Gases, unlike solids and liquids, have neither fixed volume nor shape.

They are molded entirely by the container in which they are held. We have three variables by which we measure gases: pressure , volume, and temperature. Pressure is measured as force per area. The standard SI unit for pressure is the pascal (Pa). However, atmospheres (atm) and several other units are commonly used. The table below shows the conversions between these units. Units of Pressure 1 N*m-2 = 1 kg*m-1*s-2 1 atmosphere (atm) 1 bar 105 Pa Volume is related between all gases by Avogadro's hypothesis, which states: Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. From this, we derive the molar volume of a gas (volume/moles of gas). This value, at 1 atm, and 0° C is shown below.

Vm = = 22.4 L at 0°C and 1 atm Where: Vm = molar volume, in liters, the volume that one mole of gas occupies under those conditions V=volume in liters n=moles of gas An equation that chemists call the Ideal Gas Law, shown below, relates the volume, temperature, and pressure of a gas, considering the amount of gas present. PV = nRT T=temperature in Kelvins R is the molar gas constant, where R=0.082058 L atm mol-1 K-1. The Ideal Gas Law assumes several factors about the molecules of gas. The volume of the molecules is considered negligible compared to the volume of the container in which they are held. We also assume that gas molecules move randomly, and collide in completely elastic collisions. Attractive and repulsive forces between the molecules are therefore considered negligible. Example Problem: A gas exerts a pressure of 0.892 atm in a 5.00 L container at 15°C. The density of the gas is 1.22 g/L. What is the molecular mass of the gas?

Answer: = 1.22 g/L x = Molecular Weight = 32.3 g/mol We can also use the Ideal Gas Law to quantitatively determine how changing the pressure, temperature, volume, and number of moles of substance affects the system. Because the gas constant, R, is the same for all gases in any situation, if you solve for R in the Ideal Gas Law and then set two Gas Laws equal to one another, you have the Combined Gas Law: P1V1 values with a subscript of "1" refer to initial conditions values with a subscript of "2" refer to final conditions If you know the initial conditions of a system and want to determine the new pressure after you increase the volume while keeping the numbers of moles and the temperature the same, plug in all of the values you know and then simply solve for the unknown value. Example Problem: A 25.0 mL sample of gas is enclosed in a flask at 22°C. If the flask was placed in an ice bath at 0°C, what would the new gas volume be if the pressure is held constant?

Answer: Because the pressure and the number of moles are held constant, we do not need to represent them in the equation because their values will cancel. So the combined gas law equation becomes: V1 273 K V2 = 23.1 mL We can apply the Ideal Gas Law to solve several problems. Thus far, we have considered only gases of one substance, pure gases. We also understand what happens when several substances are mixed in one container. According to Dalton's law of partial pressures , we know that the total pressure exerted on a container by several different gases, is equal to the sum of the pressures exerted on the container by each gas. Pt = P1 + P2 + P3 + ... P1=partial pressure of gas "1" P2=partial pressure of gas "2" and so on Using the Ideal Gas Law, and comparing the pressure of one gas to the total pressure, we solve for the mole fraction . P1 Where: X1 = mole fraction of gas "1" And discover that the partial pressure of each the gas in the mixture is equal to the total pressure multiplied by the mole fraction.

P1 = nt Pt = X1Pt Example Problem: A 10.73 g sample of PCl5 is placed in a 4.00 L flask at 200°C. a) What is the initial pressure of the flask before any reaction takes place? b) PCl5 dissociates according to the equation: PCl5(g) --> PCl3(g) + Cl2(g). If half of the total number of moles of PCl5(g) dissociates and the observed pressure is 1.25 atm, what is the partial pressure of Cl2(g)?

Answer: a) 10.73 g PCl5 x 1 mol 208.5 g = 0.05146 mol PCl5 PV = nRT T = 273 + 200 = 473 P(4.00) = (.05146)(.0821)(473) P = 0.4996 atm b) PCl5 → PCl3 + Cl2 Start: .05146 mol 0 mol 0 mol Change: -.02573 mol +.02573 mol +.02573 mol Final: .02573 mol .02573 mol .02573 mol XCl2 = .07719 mol PCl2 = .4167 atm As we stated earlier, the shape of a gas is determined entirely by the container in which the gas is held. Sometimes, however, the container may have small holes, or leaks. Molecules will flow out of these leaks, in a process called effusion .

Because massive molecules travel slower than lighter molecules, the rate of effusion is specific to each particular gas. We use Graham's law to represent the relationship between rates of effusion for two different molecules. This relationship is equal to the square-root of the inverse of the molecular masses of the two substances. r1 r1=rate of effusion in molecules per unit time of gas "1" r2=rate of effusion in molecules per unit time of gas "2" u1=molecular mass of gas "1" u2=molecular mass of gas "2" Previously, we considered only ideal gases, those that fit the assumptions of the ideal gas law. Gases, however, are never perfectly in the ideal state. All atoms of every gas have mass and volume. When pressure is low and temperature is low, gases behave similarly to gases in the ideal state. When pressure and temperature increase, gases deviate farther from the ideal state. We have to assume new standards, and consider new variables to account for these changes. A common equation used to better represent a gas that is not near ideal conditions is the van der Waals equation, seen below.

P + Where the van der Waals constants are: a accounts for molecular attraction b accounts for volume of molecules The table below shows values for a and b of several different compounds and elements. Species 0.11974 Practice Ideal Gas Law Problem: 2.00 g of hydrogen gas and 19.2 g of oxygen gas are placed in a 100.0 L container. These gases react to form H2O(g). The temperature is 38°C at the end of the reaction. a) What is the pressure at the conclusion of the reaction? b) If the temperature was raised to 77° C, what would the new pressure be in the same container? Ideal gas law solution . Practice Pressure Problem: 1 mole of oxygen gas and 2 moles of ammonia are placed in a container and allowed to react at 850°C according to the equation: 4 NH3(g) + 5 O2(g) --> 4 NO(g) + 6 H2O(g) a) If the total pressure in the container is 5.00 atm, what are the partial pressures for the three gases remaining?

b) Using Graham's Law, what is the ratio of the effusion rates of NH3(g) to O2(g)? General Chemistry/Gases - Wikibooks, open books for an open world General Chemistry/Gases 3.2 Pressure and Collisions Characteristics of Gases[ edit ] Gases have a number of special characteristics that differentiate them from other states of matter. Here is a list of characteristics of gases: Characteristics of Gases Gases have neither definite shape nor definite volume. They expand to the size of their container. Gases are fluid, and flow easily. Gases have low density, unless compressed. Being made of tiny particles in a large, open space, gases are very compressible. Gases diffuse (mix and spread out) and effuse (travel through small holes). Standard Temperature and Pressure[ edit ] Wikipedia has related information at Standard conditions for temperature and pressure Standard Temperature and Pressure, or STP, is 0 °C and 1 atmosphere of pressure. Expressed in other units, STP is 273 K and 760 torr. The Kelvin and torr are useful units of temperature and pressure respectively that we will discuss later in the following sections.

Avogadro's Law[ edit ] Amedeo Avogadro, the Italian chemist. Avogadro's Law is named after him and his discoveries about the behavior of gases Wikipedia has related information at Avogadro's Law Avogadro's Law states that equal volumes of gases at the same temperature and pressure contain the same number of molecules. So both one mole of Xenon at STP (131.3 grams) and one mole of helium at STP (4.00 grams) take up 22.4 liters. Even 1 mole of air, which is a mixture of several gases, takes up 22.4 liters of volume. 22.4 L is the standard molar volume of a gas. [Avogadro's Law] s t {\displaystyle {\frac {p_{1}\cdot V_{1}}{T_{1}\cdot n_{1}}}={\frac {p_{2}\cdot V_{2}}{T_{2}\cdot n_{2}}}=const} where: p is the pressure of the gas T is the temperature of the gas has the same value for all gases, independent of the size or mass of the gas molecules.

Pressure[ edit ] Gases exert pressure on their containers and all other objects. Pressure is measured as force per unit area. A barometer is a device that measures pressure. There are a number of different units to measure pressure: torr, equal to millimeters of mercury (mm Hg): if a glass cylinder with no gas in it is placed in a dish of liquid mercury, the mercury will rise in the cylinder to a certain number of millimeters. atmosphere (atm), the pressure of air at sea level. pascal (Pa), equal to one newton (N) per square meter. A newton is the force necessary to accelerate one kilogram by one meter per second squared. You should know that 1 atm = 760 torr = 101.3 kPa. Wikipedia has related information at Ideal gas Gases are complicated things composed a large numbers of tiny particles zipping around at high speeds. There are a number of complex forces governing the interactions between molecules in the gas, which in turn affect the qualities of the gas as a whole. To get around these various complexities and to simplify our study, we will talk about ideal gases.

An ideal gas is a simplified model of a gas that follows several strict rules and satisfies several limiting assumptions. Ideal gases can be perfectly modeled and predicted with a handful of equations. Ideal gases follow, among others, these important rules: Rules of Ideal Gases The molecules that make up a gas are point masses, meaning they have no volume. Gas particles are spread out with very great distance between each molecule. Thus, intermolecular forces are essentially zero, meaning they neither attract nor repel each other. If collisions do occur between gas particles, these collisions are elastic, meaning there is no loss of kinetic (motion) energy. Gas molecules are in continuous random motion. Temperature is directly proportionate to kinetic energy. Note: Ideal gases never truly exist (because the nature of gases is so complicated), but gases are often close enough to an ideal gas that the equations still hold fairly accurate. Ideal Gas Law[ edit ] Ideal gases can be completely described using the ideal gas law: [Ideal Gas Law] Real Gases[ edit ] All real gases (or non-ideal gases) deviate from the ideal gas laws that we discussed above. These deviations can occur for several reasons: Real molecules have mass and volume.

They are too big and no longer behave like ideal point masses Low volumes and high pressures cause molecules to be close enough for intermolecular forces. Polar molecules exaggerate the problem. Low temperature means low kinetic energy. At lower temperatures, intermolecular forces become significant and cannot be ignored like they are in ideal gasses Other complicated factors may prevent ideal behavior. When these issues are present, gas molecules attract each other, and may even condense into a liquid. Gases act most like ideal gases when the molecules have low mass (small volume), are not polar, and are at high temperature and low pressure. Noble gases like Xenon or Argon act the most like ideal gases because they are mostly electrical neutral and non-interactive. Kinetic Molecular Theory[ edit ] This theory describes why gases exhibit their properties. It only applies accurately to ideal gases. Because there is no such thing as an ideal gas, the Kinetic Molecular Theory can only approximate gas behavior. It is still very useful to chemists. Wikipedia has related information at Kinetic theory The Kinetic Molecular Theory explains the pressure, temperature, kinetic energy, and speed of gases and their molecules. See Wikipedia for the exact equations of the Kinetic Molecular Theory, as well as detailed explanations.

What is most important is understanding the general concepts, not the specific equations. Kinetic Energy and Temperature[ edit ] Kinetic energy is the mechanical, or movement, energy. It is given by the equation: K {\displaystyle v_{rms}} is the average velocity Explained with words, kinetic energy is dependent on the product of a particle's mass and its velocity squared. The more kinetic energy, the faster a particle moves. Conversely, the faster a particle moves, the more kinetic energy it has. The Kinetic Molecular Theory states that kinetic energy and temperature are directly proportionate. Thus, a double in temperature will result in a double in kinetic energy and an increase in velocity by a factor of 1.4 (the square root of 2, see the KE equation). This means that the higher the temperature of a gas, the faster the individual particles in that gas are moving. A hotter gas has more kinetic energy than a colder gas. If two gases are at the same temperature, they will have the same kinetic energy. The lighter-massed gas will have a higher average speed for its particles at the same energy level. It is important to know that gas temperature must be measured in kelvin.

Zero degrees Celsius is 273 kelvin. One Celsius degree is equal to one kelvin, but the kelvin scale has water's freezing point at 273 and boiling point at 373. It is necessary to use kelvin because temperatures must always be positive when using the Kinetic Molecular Theory. Question for the reader A gas's temperature is increased from 20 °C to 40° C. What factor does its kinetic energy increase? Velocity? Keep in mind that gases are all about averages. For a temperature increase, there will be an average increase in the kinetic energy of the particles in that gas. Even in a very hot gas there will be some particles moving very slowly. However, the average will be high. Pressure and Collisions[ edit ] Pressure exists because the gas molecules are in continuous random motion, and they will constantly strike the walls of their container. Pressure will increase as the speed of the molecules increases, due to greater forces of collision. Pressure will also increase as the mass of the molecules increase. A small, slow molecule has less momentum than a large, fast molecule, which explains their difference in pressure. Question for the reader There are two jars of ideal gas, for example.

In Jar A there is nitrogen gas (N2). In Jar B there is methane gas (CH4). Both jars are at the same temperature. Which will have greater pressure? Question for the reader Now, Jars A and B both have propane gas (C3H8). Jar A is at 300 K and Jar B is at 500 K. Which will have greater pressure? Gas Laws Gas Laws One of the most amazing things about gases is that, despite wide differences in chemical properties, all the gases more or less obey the gas laws. The gas laws deal with how gases behave with respect to pressure, volume, temperature, and amount. Pressure Gases are the only state of matter that can be compressed very tightly or expanded to fill a very large space. Pressure is force per unit area, calculated by dividing the force by the area on which the force acts. The earth's gravity acts on air molecules to create a force, that of the air pushing on the earth. This is called atmospheric pressure. The units of pressure that are used are pascal (Pa), standard atmosphere (atm), and torr. 1 atm is the average pressure at sea level. It is normally used as a standard unit of pressure.

The SI unit though, is the pascal. 101,325 pascals equals 1 atm. For laboratory work the atmosphere is very large. A more convient unit is the torr. 760 torr equals 1 atm. A torr is the same unit as the mmHg (millimeter of mercury). It is the pressure that is needed to raise a tube of mercury 1 millimeter. The Gas Laws: Pressure Volume Temperature Relationships Boyle's Law: The Pressure-Volume Law Boyle's law or the pressure-volume law states that the volume of a given amount of gas held at constant temperature varies inversely with the applied pressure when the temperature and mass are constant. Another way to describing it is saying that their products are constant. PV = C When pressure goes up, volume goes down. When volume goes up, pressure goes down. From the equation above, this can be derived: P1V1 = P2V2 = P3V3 etc. This equation states that the product of the initial volume and pressure is equal to the product of the volume and pressure after a change in one of them under constant temperature.

For example, if the initial volume was 500 mL at a pressure of 760 torr, when the volume is compressed to 450 mL, what is the pressure? Plug in the values: (760 torr)(500 mL) = P2(450 mL) 760 torr x 500 mL/450 mL = P2 844 torr = P2 The pressure is 844 torr after compression. Charles' Law: The Temperature-Volume Law This law states that the volume of a given amount of gas held at constant pressure is directly proportional to the Kelvin temperature. V Same as before, a constant can be put in: V / T = C As the volume goes up, the temperature also goes up, and vice-versa. Also same as before, initial and final volumes and temperatures under constant pressure can be calculated. V1 / T1 = V2 / T2 = V3 / T3 etc. Gay-Lussac's Law: The Pressure Temperature Law This law states that the pressure of a given amount of gas held at constant volume is directly proportional to the Kelvin temperature.

P Same as before, a constant can be put in: P / T = C As the pressure goes up, the temperature also goes up, and vice-versa. Also same as before, initial and final volumes and temperatures under constant pressure can be calculated. P1 / T1 = P2 / T2 = P3 / T3 etc. Avogadro's Law: The Volume Amount Law Amedeo Avogadro (1776-1856) Gives the relationship between volume and amount when pressure and temperature are held constant. Remember amount is measured in moles. Also, since volume is one of the variables, that means the container holding the gas is flexible in some way and can expand or contract. If the amount of gas in a container is increased, the volume increases. If the amount of gas in a container is decreased, the volume decreases.

V FW = gRT / PV ; V = (0.1000 g)(0.0821 L-atm / mole-K)(295.3 K) / (0.0928 atm)(0.256 L) = 102 g / mole FW of CHF2 = 51.0 g / mole ; 102 / 51.0 = 2 ; C2H2F4 If the equation above is rearranged further, g / V = P x FW / RT = density you get an expression of the density of the gas as a function of T and FW. EXAMPLE 3: Compare the density of He and air (average FW = 28 g/mole) at 25.0 oC and 1.00 atm.

dHe = (4.003 g / mole)(1.00 atm) / (0.0821 L-atm / mole-K)(298 K) = 0.164 g / L dair = (28.0 g / mole)(1.00 atm) / (0.0821 L-atm / mole-K)(298 K) = 1.14 g / L EXAMPLE 4: Compare the density of air at 25.0 oC and air at 1807 oC and 1.00 atm.

dHe = (28.0 g / mole)(1.00 atm) / (0.0821 L-atm / mole-K)(298 K) = 1.14 g / L dair = (28.0 g / mole)(1.00 atm) / (0.0821 L-atm / mole-K)(2080 K) = 0.164 g / L Partial Pressures Dalton's Law of Partial Pressures states that the total pressure of a mixture of nonreacting gases is the sum of their individual partial pressures. Ptotal = Pa + Pb + Pc + ... Ptotal = naRT / V + nbRT / V + ncRT / V + ... or Ptotal = (na+ nb+ nc+ ... )RT / V The pressure in a flask containing a mixture of 1 mole of 0.20 mole O2 and 0.80 mole N2 would be the same as the same flask holding 1 mole of O2. Partial pressures are useful when gases are collected by bubbling through water (displacement).

The gas collected is saturated in water vapor which contibutes to the total number of moles of gas in the container. EXAMPLE 5: A sample of H2 was prepared in the laboratory by the reaction: Mg(s) + 2 HCl(aq) MgCl2(aq) + H2(g) 456 mL of gas was collected at 22.0 oC. The total pressure in the flask was 742 torr. How many moles of H2 were collected? The vapor pressure of H2O at 22.0 oC is 19.8 torr. nH2 = PH2V / RT ; nH2 = (0.9503 atm)(0.456 L) / (0.0821 L-atm / mole-K)(295 K) = 0.0179 mole H2. Non-Ideal Gases Johannes Diderik van der Waals (1837-1923) The ideal gas equation (PV=nRT) provides a valuable model of the relations between volume, pressure, temperature and number of particles in a gas.

As an ideal model it serves as a reference for the behavior of real gases. The ideal gas equation makes some simplifying assumptions which are obviously not quite true. Real molecules do have volume and do attract each other. All gases depart from ideal behavior under conditions of low temperature (when liquefaction begins) and high pressure (molecules are more crowed so the volume of the molecule becomes important). Refinements to the ideal gas equation can be made to correct for these deviations. In 1873 J. D. van der Waals proposed his equation, known as the van der Waals equation. As there are attractive forces between molecules, the pressure is lower than the ideal value. To account for this the pressure term is augmented by an attractive force term a/V2. Likewise real molecules have a volume. The volume of the molecules is represented by the term b. The term b is a function of a spherical diameter d known as the van der Waals diameter.

The van der Waals equation for n moles of gas is: The values for a and b, below, are determined empirically: Equal Numbers in Equal Volumes: Avogadro Elements and Atoms: Chapter 9 Equal Numbers in Equal Volumes: Avogadro Amedeo Avogadro (1776-1856; see portrait at the Edgar Fahs Smith collection, University of Pennsylvania) was an Italian chemist and physicist best known for today for Avogadro's law and Avogadro's number. Avogadro did not discover or determine Avogadro's number; its determination occured late in the 19th century and early in the 20th and it was named in his honor. [ Perrin 1908 ] It is the number of atoms in 1 gram of hydrogen, or equivalently the number of atoms in one mole: 6.022x1023 . This chapter includes Avogadro's law, that equal volumes of gas contain equal numbers of particles, presented as a hypothesis. Combined with Dalton's atomic hypothesis ( chapter 7 ), the law explains Gay-Lussac's observations about combining volumes of gases ( chapter 8 ).

Avogadro's ideas removed an important obstacle to the determination of atomic weights by allowing molecular formulas to be determined independently of mass measurements, at least for volatile compounds. I should say that his ideas would have removed that obstacle if they were adopted by other chemists; however, they were not widely accepted for about 50 years, until Stanislao Cannizzaro made them the foundation of a logical and coherent system [ Cannizzaro 1858 ]. from Essay on a Manner of Determining the Relative Masses of the Elementary Molecules of Bodies, and the Proportions in Which They Enter into These Compounds Journal de Physique 73, 58-78 (1811), as translated in Alembic Club Reprint No. 4 , (Edinburgh, 1890) I. M. Gay-Lussac has shown in an interesting Memoir (Mémoires de la Société d'Arcueil, Tome II.) that gases always unite in a very simple proportion by volume, and that when the result of the union is a gas, its volume also is very simply related to those of its components.

But the quantitative proportions of substances in compounds seem only to depend on the relative number of molecules which combine, and on the number of composite molecules which result. [1] It must then be admitted that very simple relations also exist between the volumes of gaseous substances and the numbers of simple or compound molecules which form them. The first hypothesis to present itself in this connection, and apparently even the only admissible one, is the supposition that the number of integral molecules in any gases [sic] is always the same for equal volumes, or always proportional to the volumes. [2] Indeed, if we were to suppose that the number of molecules contained in a given volume were different for different gases, it would scarcely be possible to conceive that the law regulating the distance of molecules could give in all cases relations as simple as those which the facts just detailed compel us to acknowledge between the volume and the number of molecules.

[3] On the other hand, it is very well conceivable that the molecules of gases being at such a distance that their mutual attraction cannot be exercised, their varying attraction for caloric may be limited to condensing the atmosphere formed by this fluid having any greater extent in the one case than in the other, and, consequently, without the distance between the molecules varying; or, in other words, without the number of molecules contained in a given volume being different. Dalton, it is true, has proposed a hypothesis directly opposed to this, namely that the quantity of caloric is always the same for the molecules of all bodies whatsoever in the gaseous state, and that the greater or less attraction for caloric only results in producing a greater or less condensation of this quantity around the molecules, and thus varying the distance between the molecules themselves.

[3a] But in our present ignorance of the manner in which this attraction of the molecules for caloric is exerted, there is nothing to decide us à priori in favour of the one of these hypotheses rather than the other; and we should rather be inclined to adopt a neutral hypothesis, which would make the distance between the molecules and the quantities of caloric vary according to unknown laws, were it not that the hypothesis we have just proposed is based on that simplicity of relation between the volumes of gases on combination, which would appear to be otherwise inexplicable. [4] Setting out from this hypothesis, it is apparent that we have the means of determining very easily the relative masses of the molecules of substances obtainable in the gaseous state, and the relative number of these molecules in compounds; for the ratios of the masses of the molecules are then the same as those of the densities of the different gases at equal temperature and pressure, and the relative number of molecules in a compound is given at once by the ratio of the volumes of the gases that form it.

[5] For example, since the numbers 1.10359 and 0.07321 express the densities of the two gases oxygen and hydrogen compared to that of atmospheric air as unity, and the ratio of the two numbers consequently represents the ratio between the masses of equal volumes of these two gases, it will also represent on our hypothesis the ratio of the masses of their molecules. Thus the mass of the molecule of oxygen will be about 15 times that of the molecule of hydrogen, or, more exactly as 15.074 to 1. In the same way the mass of the molecule of nitrogen will be to that of hydrogen as 0.96913 to 0.07321, that is, as 13, or more exactly 13.238, to 1. On the other hand, since we know that the ratio of the volumes of hydrogen and oxygen in the formation of water is 2 to 1, it follows that water results from the union of each molecule of oxygen with two molecules of hydrogen. [6] Similarly, according to the proportions by volume established by M.

Gay-Lussac for the elements of ammonia, nitrous oxide, nitrous gas , and nitric acid , ammonia will result from the union of one molecule of nitrogen with three of hydrogen, nitrous oxide from one molecule of oxygen with two of nitrogen, nitrous gas from one molecule of nitrogen with one of oxygen, and nitric acid from one of nitrogen with two of oxygen. [7] II. There is a consideration which appears at first sight to be opposed to the admission of our hypothesis with respect to compound substances. It seems that a molecule composed of two or more elementary molecules should have its mass equal to the sum of the masses of these molecules; and that in particular, if in a compound one molecule of one substance unites with two or more molecules of another substance, the number of compound molecules should remain the same as the number of molecules of the first substance. Accordingly, on our hypothesis, when a gas combines with two or more times its volume of another gas, the resulting compound, if gaseous, must have a volume equal to that of the first of these gases. Now, in general, this is not actually the case. [8] For instance, the volume of water in the gaseous state is, as M.

Gay-Lussac has shown, twice as great as the volume of oxygen which enters into it, or, what comes to the same thing, equal to that of the hydrogen instead of being equal to that of the oxygen.

[9] But a means of explaining facts of this type in conformity with our hypothesis presents itself naturally enough; we suppose, namely, that the constituent molecules of any simple gas whatever (i.e., the molecules which are at such a distance from each other that they cannot exercise their mutual action) are not formed of a solitary elementary molecule, but are made up of a certain number of these molecules united by attraction to form a single one; [10] and further, that when molecules of another substance unite with the former to form a compound molecule, the integral molecule which should result splits itself into two or more parts (or integral molecules) composed of half, quarter, &c., the number of elementary molecules going to form the constituent molecule of the first substance, combined with half, quarter, &c., the number of constituent molecules of the second substance that ought to enter into combination with one constituent molecule of the first substance (or, what comes to the same thing, combined with a number equal to this last of half-molecules, quarter-molecules, &c., of the second substance); so that the number of integral molecules of the compound becomes double, quadruple, &c., what it would have been if there had been no splitting up, and exactly what

 is necessary to satisfy the volume of the resulting gas.

[11] Thus, for example, the integral molecule of water will be composed of a half-molecule of oxygen with one molecule, or what is the same thing, two half-molecules of hydrogen. On reviewing the various compound gases most generally known, I only find examples of duplication of the volume relatively to the volume of that one of the constituents which combines with one or more volumes in the other. We have already seen this for water. In the same way, we know that the volume of ammonia gas is twice that of the nitrogen which enters into it. M. Gay-Lussac has also shown that the volume of nitrous oxide is equal to that of the nitrogen which forms part of it, and consequently is twice that of the oxygen. Finally, nitrous gas, which contains equal volumes of nitrogen and oxygen, has a volume equal to the sum of the two constituent gases, that is to say, double that of each of them. [12] Thus in all these cases there must be a division of the molecule into two; but it is possible that in other cases the division might be into four, eight, &c.

The possibility of this division of compound molecules might have been conjectured à priori; for otherwise the integral molecules of bodies composed of several substances with a relatively large number of molecules, would come to have a mass excessive in comparison with the molecules of simple substances. We might therefore imagine that nature had some means of bringing them back to the order of the latter, and the facts have pointed out to us the existence of such means. [13] Besides, there is another consideration which would seem to make us admit in some cases the division in question; for how could one otherwise conceive a real combination between two gaseous substances uniting in equal volumes without condensation, such as takes place in the formation of nitrous gas? Supposing the molecules to remain at such a distance that the mutual attraction of those of each gas could not be exercised, we cannot imagine that a new attraction could take place between the molecules of one gas and those of the other. But on the hypothesis of division of the molecule, it is easy to see that the combination really reduces two different molecules to one, and that there would be contraction by the whole volume of one of the gases if each compound molecule did not split up into two molecules of the same nature. M.

Gay-Lussac clearly saw that, according to the facts, the diminution of volume on the combination of gases cannot represent the approximation of their elementary molecules. [14] The division of molecules on combination explains to us how these two things may be made independent of each other. III. Dalton, on arbitrary suppositions as to the most likely relative number of molecules in compounds , has endeavoured to fix ratios between the masses of the molecules of simple substances. [15] Our hypothesis, supposing it well-founded, puts us in a position to confirm or rectify his results from precise data, and, above all, to assign the magnitude of compound molecules according to the volumes of the gaseous compounds, which depend partly on the division of molecules entirely unexpected by this physicist. Thus Dalton supposes that water is formed by the union of hydrogen and oxygen, molecule to molecule. [16] From this, and from the ratio by weight of the two components, it would follow that the mass of the molecule of oxygen would be to that of hydrogen as 71/2 to 1 nearly, or, according to Dalton's evaluation, as 6 to 1.

This ratio on our hypothesis is, as we saw, twice as great, namely, as 15 to 1. As for the molecule of water, its mass ought to be roughly expressed by 15+2=17 (taking for unity that of hydrogen), if there were no division of the molecule into two; but on account of this division it is reduced to half, 81/2, or more exactly 8.537, as may also be found by dividing the density of aqueous vapour 0.625 (Gay-Lussac) by the density of hydrogen 0.0732. [17] This mass differs from 7, that assigned to it by Dalton, by the difference in the values for the composition of water; so that in this respect Dalton's result is approximately correct from the combination of two compensating errors,--the error in the mass of the molecule of oxygen, and his neglect of the division of the molecule. [18] Dalton supposes that in nitrous gas the combination of nitrogen and oxygen is molecule to molecule: we have seen on our hypothesis that this is actually the same.

Thus Dalton would have found the same molecular mass for nitrogen as we have, always supposing that of hydrogen to be unity, if he had not set out from a different value for that of oxygen, and if he had taken precisely the same value for the quantities of the elements in nitrous gas by weight. But supposing the molecule of oxygen to be less than half what we find, he has been obliged to make that of nitrogen also equal to less than half the value we have assigned to it, viz., 5 instead of 13. [19] As regards the molecule of nitrous gas itself, his neglect of the division of the molecule again makes his result approach ours; he has made it 6+5=11, whilst according to us it is about , or more exactly , as we also find by dividing 1.03636, the density of nitrous gas according to Gay-Lussac, by 0.07321. Dalton has likewise fixed in the same manner as the facts has given us, the relative number of molecules in nitrous oxide and in nitric acid, and in the first case the same circumstance has rectified his result for the magnitude of the molecule.

He makes it 6 + 2x5 = 16, whilst according to our method it should be , a number which is also obtained by dividing 1.52092, Gay-Lussac's value for the density of nitrous oxide, by the density of hydrogen. In the case of ammonia, Dalton's supposition as to the relative number of molecules in its composition is on our hypothesis entirely at fault. He supposes nitrogen and hydrogen to be united in it molecule to molecule, whereas we have seen that one molecule of nitrogen unites with three molecules of hydrogen. According to him the molecule of ammonia would be 5+1=6; according to us it should be , or more exactly 8.119, as may also be deduced directly from the density of ammonia gas. The division of the molecule, which does not enter into Dalton's calculations, partly corrects in this case also the error which would result from his other suppositions. All the compounds we have just discussed are produced by the union of one molecule of one of the components with one or more molecules of the other.

In nitrous acid we have another compound of two of the substances already spoken of, in which the terms of the ratio between the number of molecules both differ from unity. From Gay-Lussac's experiments (Société d'Arcueil, same volume) it appears that this acid is formed from 1 part by volume of oxygen and 3 of nitrous gas [20] , or, what comes to the same thing, of 3 parts of nitrogen and 5 of oxygen; hence it would follow, on our hypothesis, that its molecule should be composed of 3 molecules of nitrogen and 5 of oxygen, leaving the possibility of division out of account. But this mode of combination can be referred to the preceding simpler forms by considering it as the result of the union of 1 molecule of oxygen with 3 of nitrous gas, i.e. with 3 molecules, each composed of a half-molecule of oxygen and a half-molecule of nitrogen, which thus already included the division of some of the molecules of oxygen which enter into that of nitrous acid.

Supposing there to be no other division, the mass of this last molecule would be 57.542, that of hydrogen being taken as unity, and the density of nitrous acid gas would be 4.21267, the density of air being taken as unity. But it is probable that there is at least another division into two, and consequently a reduction of the density to half: we must wait until this density has been determined by experiment. [21] ... [22] VIII. It will have been in general remarked on reading this Memoir that there are many points of agreement between our special results and those of Dalton, although we set out from a general principle, and Dalton has only been guided by considerations of detail. [23] This agreement is an argument in favour of our hypothesis, which is at bottom merely Dalton's system furnished with a new means of precision from the connection we have found between it and the general fact established by M. Gay-Lussac. Dalton's system supposes that compounds are made in general in fixed proportions, and this is what experiment shows with regard to the more stable compounds and those most interesting to the chemist.

It would appear that it is only combinations of this sort that can take place amongst gases, on account of the enormous size of the molecules which would result from ratios expressed by larger numbers, in spite of the division of the molecules, which is in all probability confined within narrow limits. We perceive that the close packing of the molecules in solids and liquids, which only leaves between the integral molecules distances of the same order as those between the elementary molecules, can give rise to more complicated ratios, and even to combinations in all proportions; but these compounds will be so to speak of a different type from those with which we have been concerned, and this distinction may serve to reconcile M. Berthollet's ideas as to compounds with the theory of fixed proportions. [24] Notes [1] Avogadro uses the term molecule and never atom. His molecules are similar conceptually to Dalton's atoms, the smallest piece of matter which retained its identity as a particular substance ( chapter 7, note 5 ). Sometimes he modifies the word, as in composite molecule or (below) elementary molecule. An "elementary molecule" is what a modern chemist would call an atom.

A "composite molecule" is what a modern chemist would call a molecule (i.e., two or more atoms bound together). [2] This is Avogadro's law, presented as a hypothesis. In modern terms, it states that equal volumes of gas contain equal numbers of molecules. [3] Why might one think that equal volumes of gas contain equal numbers of molecules? For one thing, it is the simplest explanation of Gay-Lussac's observations that gases combine in simple ratios by volume. For if atoms combine in simple ratios by volume (as Dalton believed), and if equal volumes of gas contain equal numbers of molecules, then it would follow that gases would combine in simple ratios by volume.The close relationship between Gay-Lussac's observations and Dalton's ideas was not sufficient, however, to convince Dalton either of Gay-Lussac's observations or of Avogadro's hypothesis.

(See chapter 8, note 42 .) In fact, the hypothesis of equal volumes containing equal numbers of molecules had already occured to Dalton, but he rejected it: "At the time I formed the theory of mixed gases, I had a confused idea, as many have, I suppose, at this time, that the particles of elastic fluids are all of the same size; that a given volume of oxygenous gas contains just as many particles as the same volume of hydrogenous; ..." [Dalton 1808, p. 188]. The reasons Dalton rejected the hypothesis had to do with caloric supposed to be associated with gaseous particles. [3a] Note that Avogadro has already referred to the work of two of his contemporaries. Scientists typically build upon, criticise, and modify the work of their predecessors and contemporaries. In this sense, they do not work alone. Often the interaction among scientists and their ideas is international. Here the Italian (or, more accurately, Piedmontese, as Italy was not yet unified) Avogadro refers to work of the English Dalton and the French Gay-Lussac.

[4] Avogadro accepts the conventional wisdom of his time that molecules in a gas are coated with caloric (heat), which overcomes the forces of cohesion apparent in solids and liquids. Dalton pictures this caloric [Dalton 1808] as a mechanical spacer keeping molecules apart, the distance of separation determined by a substance's affinity to caloric. Avogadro maintains that not enough is known about caloric to decide the question; therefore, Dalton's picture should not be an obstacle to Avogadro's hypothesis. [5] Avogadro recognized that if his hypothesis was correct, it provided the basis for determining the relative atomic and molecular weights of gases and the formulas of gaseous compounds. If equal volumes of gas contain equal numbers of molecules, then their densities (mass per unit volume) are proportional to their molecular weights (mass per molecule). Ratios of gas densities, then, are equal to ratios of molecular weights. "The relative number of molecules [atoms] in a compound" is nothing more than the compound's formula, a list of the atoms in the compound and their relative numbers. Already Avogadro has begun to give some evidence for his hypothesis (previous paragraph) and to sketch out its implications.

[6] That is, the formula for water is H2O; compare to Dalton's assumed formula, HO. [7] That is, the formula for ammonia is NH3; compare to Dalton's assumed formula, NH. "Nitrous gas" is known today as nitric oxide, NO; "nitric acid" is known today as nitrogen dioxide, NO2. Dalton got right the formulas for the three compounds of nitrogen with oxygen. [8] Gay-Lussac presented some examples of these apparent paradoxes. See notes 39 and 40 of the previous chapter. [9] For example, Gay-Lussac reported that one part oxygen reacts with two parts hydrogen to give two parts water by volume. Why two parts of water, Avogadro asks: after all, if water is H2O, shouldn't the two particles of hydrogen attach to the one particle of oxygen to make one particle of water? [10] In modern terminology, Avogadro supposes that any gaseous element ("simple gas") exists not as single atoms ("solitary elementary molecule") but as molecules composed of more than one atom. This hypothesis turned out to be correct, but it was not widely accepted at the time.

Indeed, there were some good reasons for skepticism. Some scientists were not convinced of the atomic hypothesis in the first place [Brock & Knight 1967, Knight 1967]; they naturally were not convinced that gaseous elements existed as pairs of atoms bound together. In addition, many scientists who thought the atomic hypothesis did make sense (including Dalton) saw the idea of diatomic gases as nonsense. These scientists believed (correctly) that gases were made up of widely separated particles. It did not make sense that these particles would form pairs and that these pairs would then stay apart from other pairs: if atoms of the same kind were attracted to each other, they would all cluster together to form a solid or liquid; if they repelled each other (as they were believed to do when they were attached to caloric), then no pairs would form. Thus, the hypothesis of composite molecules for gaseous elements was one which had no direct evidence in its favor, while it had a considerable quantity of scientific opinion against it. The only point in its favor at the time was that it (in conjunction with the hypothesis of equal volumes of gas containing equal numbers of molecules) explained the available data.

Thus the notion of composite molecules was a classic case of an ad hoc hypothesis, one which was not intimately connected with the rest of the theory in which it appeared and which was introduced only to make the rest of the theory work. [11] Many commentators have remarked that Avogadro's writing in this paper is not always clear. Leonard Nash, for example, writes [Nash 1957], "The French text suffers from occasional obscurity, which must have confused Avogadro's contemporaries even as it does us." Perhaps the obscurity arises (as Nash hints) because Avogadro was not writing in his native Italian; perhaps because the ideas were not entirely clear in his mind. Perhaps the lack of clarity in Avogadro's prose contributed to the difficulty his ideas experienced in becoming established. What Avogadro is suggesting here may best be illustrated by example. Suppose, he says, that hydrogen and oxygen gases consist not of a single atom but of two atoms bound together. Using modern notation, we would say that these elements have formulas of H2 and O2 rather than H and O respectively.

Now suppose that when they react in the observed proportions of two parts hydrogen to one part oxygen, they form a larger molecule which then splits up to give two molecules of water as the ultimate products: 2 H2 + O2 --> [H4O2] --> 2 H2O . Today, we recognize Avogadro's two suppositions or hypotheses as correct: equal volumes of gas contain equal numbers of molecules, and many gaseous elements exist as diatomic molecules. In fact, by the end of the 19th century, when argon was discovered, the idea of a monatomic gas was shocking. (See chapter 14, note 52 .) The actual mechanism of water formation does not involve the formation and then splitting of a double molecule of water, H4O2, though. Avogadro recognizes that he cannot tell if the original molecules of hydrogen and oxygen contained two atoms or four atoms or some other even number of atoms.

For example, he recognized that if hydrogen and oxygen had the formulas H4 and O4, the reaction 2 H4 + O4 --> [H8O4] --> 2 H4O2 would still explain the data: hydrogen and oxygen would still combine in a ratio of 2 to 1; water would still have the ratio of two hydrogen to one oxygen; and the volume of water produced would be the same as the volume of hydrogen, not oxygen. Indeed, André-Marie Ampère proposed a hypothesis quite similar to Avogadro's except that it explicitly proposes tetratomic (4-atom) molecules [Ampère 1814]. In the absence of any additional information, however, the notion of diatomic molecules is more attractive than that of tetratomic molecules because it is simpler. [12] The reactions mentioned here are: N2 + 3 H2 --> 2 NH3 , 2 N2 + O2 --> 2 N2O , N2 + O2 --> 2 NO . [13] Avogadro seems to suggest that there is some sort of natural tendency to keep molecules from getting very large or complicated.

He would be surprised, then, by the knowledge chemists have built up about macromolecules (molecules consisting of hundreds or thousands of atoms). Both natural and artificial macromolecules abound. DNA (which carries the genetic code of living things) and hemoglobin (a protein which transports oxygen in the blood) are two examples of natural macromolecules of tremendous biological importance. Most modern plastics are examples of synthetic macromolecules. [14] That is, the diminution of volume in these reactions is much less than can be explained if the only thing going on was the atoms getting close together ("approximation") by attraction. [15] See chapter 7, note 18 . [16] Here and below, Avogadro means one molecule of each reactant by "molecule to molecule." [17] Recall that Avogadro proposed that a ratio of gas densities would be equal to a ratio of molecular weights. Here and in the remainder of this section, he compares the molecular weight of water based on gas densities to that based on his improved formulas. This is an attempt to compare different ways of measuring the same quantity.

In fact, the two ways of getting at the molecular weight of water are not quite independent; still, comparing the results shows that Avogadro's methods are at least self-consistent. [18] To summarize Avogadro's conclusions on water and its constituents: take the mass of H2 to be 1; then that of O2 is 15, and that of H2O is 81/2. Contrast this to Dalton's conclusions, which take the mass of H to be 1, that of O as 7, and that of HO as 8. A modern chemist would say that if the mass of H is taken to be 1, the mass of O is 16 and that of H2O is 18. The differences among these three sets of values stem from several sources. First, all use different analyses for the ratio of combining weights of hydrogen and oxygen in water (1:7 for Dalton, 1:7.5 for Avogadro; 1:8 today). These numbers represent the results of experiments which became progressively more accurate. They do not depend on the atomic hypothesis or Avogadro's hypotheses.

Avogadro's figures differ from Dalton's, besides the difference due to accuracy of the analysis, because Avogadro recognizes that water has two atoms of hydrogen for every atom of oxygen. Finally, Avogadro's numbers differ from modern numbers, besides the difference due to the accuracy of the analysis, because Avogadro in essence chooses H2 (the hydrogen molecule) as unity, while the modern system's basis is tantamount to taking the hydrogen atom as unity. [19] Actually, Dalton's assignment of 5 for nitrogen appears to be based on an analysis of ammonia, not of nitrous gas (NO). See chapter 7, note 20 for the uneasy coexistence of data on ammonia and on NO in Dalton's work. [20] This "nitrous acid" must be nitrous anhydride, N2O3. The reaction actually involves four times as much "nitrous gas" as oxygen, not three as stated: 4 NO + O2 --> 2 N2O3 . Nitrogen forms several compounds with oxygen, including NO, N2O3, NO2, N2O4, and N2O5, and frequently these gases appear in mixtures.

Therefore it is not surprising that Gay-Lussac's report was erroneous. [21] Avogadro suspects that the product of this reaction divides not just in two, as was the case in the examples he has already given, but in half again. Apparently Avogadro thought that such a large molecule was unlikely to be stable. (See footnote 13 above.) [22] I have omitted sections IV-VII of this paper. --CJG [23] Dalton, on the contrary, considered that his atomic hypothesis was general, and that conclusions drawn on the combining ratios of gases were restricted to gases. (Cf. chapter 8, note 40 .) I must agree with Dalton, with two provisos: Avogadro's ideas can be extended to volatile compounds which are not gases at room temperature; more important, Avogadro corrects a serious flaw in Dalton's system. [24] See previous chapter, note 6 regarding the question of definite proportions and variable proportions. Avogadro attempts to make a distinction between situations in which definite proportions apply and those in which variable proportions are permitted; however, it is not the modern distinction between compounds and mixtures ( chapter 8, note 40 ).

Reference Annales de chimie et de physique 90, 45- (1814); translated in Philosophical Magazine 45, 41-43, 109-116, 188-193, 344-349 (1815) , (Edinburgh, 1890); annotated excerpts above. W. H. Brock & D. M. Knight, "The Atomic Debates" in W. H. Brock, ed., The Atomic Debates (Leicester: Leicester U. Press, 1967), pp. 1-30. Stanislao Cannizzaro, 7, 321-366 (1858); translated as Alembic Club Reprints Fundamental laws of chemical reactions and chemical equations Fundamental laws of chemical reactions and chemical equations 1. The law of conservation of mass (Lavoisier, 18th century): Lavoisier was one of the first to carry out quantitatively accurate chemical measurements. He demonstrated that combustion required oxygen, and he demonstrated oxygen's role in the rusting of metals.

His observations led him to deduce the following general law known as the law of conservation of mass: In every chemical transformation, an equal quantity of matter exists before and after the reaction. (Because he was a tax collector and nobleman, Lavoisier was branded a traitor during the French Revolution and beheaded in 1794.) 2. law of definite proportions (Joseph Proust, shortly after Lavoisier): Proust studied metal compounds, including metal oxides, carbonates and sulfides. From the work of Robert Boyle in the 17th century, it was understood that substances that could be broken down into more fundamental components were mixtures or compounds. Substances that could not be further broken down were referred to as elements. Thus, Proust deduced the so-called law of definite proportions: In a given chemical compound, the proportion by mass of the elements that compose it are fixed, independent of the origin of the compound or its mode of preparation. This is basically saying that sodium chloride, for example, is always NaCl, no matter how it is obtained, made, or prepared. There are no ``intermediate'' compounds. 3.

The law of multiple proportions: (John Dalton, shortly after Proust): Studied gases and gaseous mixtures under different external conditions. Building on Proust's work, he noted that mathematically discrete manner in which elements combined to form different compounds. For example, in carbon monoxide (CO), the mass ratio of oxygen to carbon and in carbon dioxide (CO ) . Thus, since the amount of carbon is fixed in each compound, we can look at how the amount of oxygen varies, and we find that . The generalization of this idea is the law of multiple proportions: When two elements form a series of compounds, the masses of one that combine with a fixed mass of the other are in the ratio of (small) integers to each other. This law is obeyed by all gaseous compounds, which is what Dalton studied. Certain solids are exceptions to both this rule and the law of definite proportions. An example is the solid wüstite, which can range from Fe O to Fe O, depending on the mode of preparation. These formulae express the incommensurate compositions possible in this solid.

But, since atoms are essentially indestructible (we have to work hard to get them to fission!), this explains why we do not find compounds such as C H in nature. Dalton's observations led him to propose the notion of the atom as the fundamental and indestructible building blocks of matter. 4. The law of combining volumes (Joseph Gay-Lussac, Amedeo Avagadro, Stanislao Cannizzaro, early 19th century following Dalton): Again, based on studies of gases and how they combine, the law of combining volumes has been attribued to these three. The generalization of the observations is stated as follows: When two gases are allowed to react, such that the gases are at the same temperature and pressure, the volumes of each gas consumed will be in the ratio of small integers. Moreover, the ratio of the volume of each product gas to the volume of either reacting gas will be a ratio of simple integers. Example: 3 volumes of hydrogen + 1 volume of nitrogen 2 volumes of ammonia. Although this is a statement about gases, its implications can be deduced: the coefficients in chemical equations expressions how much of different reactants combine to give products will be integers. 5.

Avogadro's hypothesis (1811): Equal volumes of different gases (at the same temperature and pressure) contain equal numbers of particles. Example: How many particles are in 1 L of O gas, and how many particles are in 1 L of H gas? The density of O is 1.429 g/L, and the density of H gas is 0.0899 g/L. Combining Avogadro's hypothesis with the law of combining volumes allows the statement written above about volumes of hydrogen and nitrogen combining to give ammonia as a statement about definite numbers of molecules rather then volumes. This number could be expressed as moles, or even as individual molecules. The statement then reads: This is an example of a balanced chemical equation. What does it mean to be balanced? It means that the law of conservation of mass is obeyed - equal quantities of hydrogen and nitrogen exist on both sides of the reaction. Furthermore, the coefficients, i.e., the numbers multiplying H , N and NH in the above equation, are expressible as simple integers. When balancing chemical equations, this serves as an important check. Calculate the density of CO2 gas at STP.

-How many L of C3H8(g) at STP would contain the same # of particles as 15L of O2 gas at STP? For the second equation I just don't understand what we're trying to find... Liters of gas at STP, or particles? Help | Socratic This question is talking about the number of particles (molecules) of CO₂ and O₂. For this question, we don't even have to do a calculation. Avogadro's Law tells us that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. If 15 L of O₂ at STP contain a certain number of molecules, then 15 L of C₃H₈ at STP contain the same number of molecules. Was this helpful? Let the contributor know! Yes Ch 19 Unit 19 Gases and The Mole The purpose of this is to give quick reference to information or to use in an emergency (like if your text has accidentally been left under your desk at school). This is NOT intended to replace reading the text with its excellent photographs, diagrams, charts, and tables.

GASES AND THE MOLE In Chapter 18, we examined the effect of temperature and pressure on the volume of a constant mass of gas. The principles hold true for any gas exhibiting ideal behavior. Different gases, however, have molecules and atoms of different masses. In this chapter, we will look at the effect of the number of particles on the other gas variables, particularly volume. We will also find out how to obtain mass measurements of gases at various temperatures and pressures. 19:1 DEVELOPlNG AVOGADRO'S PRlNClPLE Suppose we place two different gases at exactly the same temperature and pressure in separate containers which have exactly the same volume. At a given temperature, all gas molecules will have the same average kinetic energy regardless of size or mass. Massive molecules will travel slowly, lighter molecules will travel more rapidly. However, the average kinetic energy (1/2 mv2) will be the same for all. If the kinetic energies are equal, any difference in pressure exerted by the gases is determined by the number of molecules of each gas. Since we have already said the two gases are at the same pressure, there must be an equal number of molecules in the two containers.

At equal temperatures and equal pressures, equal volumes of gases contain the same number of molecules. This statement is called Avogadro's principle, after Amadeo Avogadro. When he proposed the principle, in 1811, the kinetic theory had not been developed. As we read in Section 5:2, Avogadro developed his principle to explain some of the observations made by Gay-Lussac. Gay-Lussac had observed that two gases always react in such a way that the combining volumes can be expressed in small whole numbers. Proust had previously stated his law of definite proportions. Avogadro knew that one molecule of chlorine always united with one molecule of hydrogen. He also knew that two molecules of hydrogen chloride were formed. He therefore concluded that equal volumes of gases must contain equal numbers of molecules, Avogadro's principle has been verified so often that it is sometimes called a law. 19:2 MOLAR VOLUME One mole of any gas at STP will occupy the same volume as 1 mole of any other gas at STP.

This volume is 22.4 dm3, (22.4 liters/mol) the volume occupied by 1 mole of any gas under standard conditions, is called the molar volume of the gas. The molar volume for all gases at STP is 22.4 L/mol 19:3 lDEAL GAS EQUATlON We are now in a position to combine all four variables concerned with the physical characteristics of gases. These variables are pressure, volume, temperature, and number of particles. Charles' law states that volume varies directly as the absolute temperature. Boyle's law states that volume varies inversely as the pressure. Combining all the above factors gives us the ideal gas equation: PV = nRT The equation PV = nRT is called the ideal gas equation. The value of the new constant R can be obtained by substituting into the equation a set of known values of n, P, V, and T. We know that standard pressure P is 1O1 kPa, molar volume V is 22.4 dm3, standard temperature T is 273 K, and the number of moles n is 1.

So the constant R = 8.31 dm3kPa/molK This value for R is constant and can always be used if the units of the other quantities are not changed. We can determine the number of moles, n, in a quantity of a substance by dividing its mass by its formula mass. Any problem that can be solved by this equation can also be solved by direct application of the gas laws. SUMMARY 1. Avogadro's principle: At equal temperatures and pressures, equal volumes of gases contain equal numbers of molecules. 2. The molar volume of a gas is the volume occupied by 1 mole of the gas at STP; its value is 22.4 dm3 or 22.4 L/mol, for all gases. 3. The ideal gas equation is PV = nRT, where P = pressure, V = volume, n = number of moles, R = a constant, and T = kelvin temperature. 4. The molecular mass of a gas may be determined by using a modified form of the ideal gas equation. 5. A limiting reactant is a reactant which is completely consumed in a reaction. Any remaining reactants are said to be in excess. 6.

In solving problems involving gas volumes, consideration must be given to the change of gas volume with change in pressure and temperature. 7. A gas which expands or is compressed does work or has work done on it. More on Gases & Moles:

Question: Whose Law states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules?
Answer: Avogadro