Base unit definitions: Mole Unit of amount of substance (mole) Abbreviations : CGPM, CIPM, BIPM Following the discovery of the fundamental laws of chemistry, units called, for example, "gram-atom" and "gram-molecule," were used to specify amounts of chemical elements or compounds. These units had a direct connection with "atomic weights" and "molecular weights," which were in fact relative masses. "Atomic weights" were originally referred to the atomic weight of oxygen, by general agreement taken as 16. But whereas physicists separated isotopes in the mass spectrograph and attributed the value 16 to one of the isotopes of oxygen, chemists attributed that same value to the (slightly variable) mixture of isotopes 16, 17, and 18, which was for them the naturally occurring element oxygen. Finally, an agreement between the International Union of Pure and Applied Physics (IUPAP) and the International Union of Pure and Applied Chemistry (IUPAC) brought this duality to an end in 1959/60.

Physicists and chemists have ever since agreed to assign the value 12, exactly, to the "atomic weight," correctly the relative atomic mass, of the isotope of carbon with mass number 12 (carbon 12, 12C). The unified scale thus obtained gives values of relative atomic mass. It remained to define the unit of amount of substance by fixing the corresponding mass of carbon 12; by international agreement, this mass has been fixed at 0.012 kg, and the unit of the quantity "amount of substance" was given the name mole (symbol mol). Following proposals of IUPAP, IUPAC, and the International Organization for Standardization (ISO), the CIPM gave in 1967, and confirmed in 1969, a definition of the mole, eventually adopted by the 14th CGPM (1971): 1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol." 2.

When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. At its 1980 meeting, the CIPM approved the 1980 proposal by the Consultive Committee on Units of the CIPM specifying that in this definition, it is understood that unbound atoms of carbon 12, at rest and in their ground state, are referred to. si units - Why is the mole/"amount of substance" a dimensional quantity? - Physics Stack Exchange up vote 33 down vote favorite 11 According to the BIPM and Wikipedia, "amount of substance" (as measured in moles) is one of the base quantities in our system of weights and measures. Why? I get why the mole is useful as a unit. In fact, my question isn't really about the mole at all; I just mention it because what little information I could find generally talked about moles, not about "amount of substance". Nor am I asking about why it's chosen as a base quantity and not a derived quantity. I get that any particular choice of bases is more or less arbitrary.

I don't understand why it's a dimensional quantity at all. It is, after all, just a count of things; every student is taught to think of it as "like 'a dozen', only more sciencey". Can't we just call it a dimensionless number? No, says SI; molar mass doesn't just have dimensions of $\mathsf{M}$, it has dimensions of $\mathsf{M}\cdot\mathsf{N}^{-1}$; and Avogadro's number isn't just a number, it's got units of "per mole" (or dimensions of $\mathsf{N}^{-1}$). Contrast this with an "actual" dimensionless quantity, plane angle (and its unit the radian). Now, you might say that it's dimensionless because radians are defined as arc length over radius, and so plane angle is just $\mathsf{L}\cdot\mathsf{L}^{-1}$; cancel out and you have no dimensions. That strikes me as arbitrary.

We could just as easily argue that arc length is "really" a quantity of $\mathsf{a}\cdot \mathsf{L}$ (where $\mathsf{a}$ is plane angle), because it's the measurement of a quantity that subtends $\mathsf{a}$ at distance $\mathsf{L}$. But this isn't needed; plane angle isn't even a derived quantity, it's a non-quantity. Plane angle is accepted as dimensionless. Why isn't amount of substance? As I said, I've found very little on this question. From the Wikipedia article on the mole , I found a PDF of an interesting IUPAC article on atomic weight . It acknowledges the argument (as does the Wikipedia article), but dismisses it out of hand by saying (essentially) "of course counting things is a way of measuring things, so of course we need a unit of measurement for it". Other than that, Wikipedia (as far as I can tell) touches on eliminating the mole only in the context of eliminating other units (as for example in natural systems of units).

The Unified Code for Units of Measure blithely cuts moles from the base units as being "just a count of things", but doesn't go into why SI says it is necessary. Is there any official rationale for the inclusion of "amount of substance" as a dimension? Failing that, can anyone provide, or point me to, some good reasons why it's so special? EDIT: Thank you all for your input. The more I've thought about it, the more I've come to feel that there's no reason why "count of stuff" shouldn't be a dimension (it's clearly different from, say, a dimensionless number included as a scale factor), and that my unease with the idea comes from simple habit: in any case not involving moles, it tends to get left out. Really, I'm now more wondering why angles are considered dimensionless... Reading before coming here: Consultative Committee for Amount of Substance (CCQM) (I thought maybe a committee with this name would be in charge of explaining why amount of substance is needed, but no; it seems they just deal with standardising it) up vote 16 down vote accepted So, here's the thing.

The chemistry that underlies molar mass ratios dates back at least to 1805. We've known that if you divide by a certain "relative mass" number you can get whole-number ratios for atoms in a pile of stuff, for that long. It took us about 60 more years to get a handle on how large atoms were with the estimations of Loschmidt, who worked out that atoms are much smaller than the wavelengths of visible light -- too small to ever "see". This gave a rough count of how many atoms there were in a confined space, too -- but we weren't able to connect these two different quantities (atomic relative masses, count of atoms) together to figure out the mass of a single atom until some work done by Einstein on diffusion in Brownian motion (1905) and some concrete numbers could finally be rolled in with Millikan's oil-drop experiment (1910).

So due to history and convenience, the chemists are basically at the level of saying, "okay, we have N grams of this stuff, our mass spectrometer says that it's M grams per mole, so we've got N/M moles, that includes N/M moles of nitrogen and 15 N/M moles of hydrogen due to the known atomic composition, ..." and so on. You never have to add the uncertainty in Avogadro's number to these calculations; the "size" of a mole isn't important. It's only important when you start to want to know things that are "beyond" historical chemistry approaches, like counting actual numbers of atoms. With all that said, you'll be heart-warmed to know that there is a unit revision being considered by the SI organization, and one of the proposals is to fix the number of atoms in 1 mole.

But of course they will still use as a guideline that "1 mole of carbon-12 has exactly 12 grams of mass"; it will just transition from what is now "exactly" to what will be "almost exactly." up vote -1 down vote The number of atoms or molecules is not dimensionless, it is the way we "count" the matter. Here are some examples to illustrate the fundamental importance of the amount of substance: While $E = m c^2$, you will not extract the same total energy if your fission process is done with 1 atom or with 1 mole of $^{235}U$. Consider the other basic law $PV=nRT$: the amount of substance will determine the volume of your gaz at fixed pressure and temperature. The amount of substance is also important in interface physics in processes were the number of molecules may change. For example, evaporation imply a variation of the amount of substance and you must take it into account to describe accurately the evaporation rate. Chemistry International -- Newsmagazine for IUPAC by Ian Mills and Martin Milton The International System of Units, the SI, is built upon seven base quantities and seven base units, as summarized in the table below.

Although most of these are familiar to all scientists, the quantity “amount of substance” and its unit “mole” are less familiar and are mainly used by chemists. 1 In the chemistry community, the unit “mole” is familiar, but the name of the corresponding quantity “amount of substance” is not so familiar, and the concept is still a source of difficulty for many students. This article reviews and clarifies these two concepts 2 and discusses the definition of the unit “mole” and its possible revision. Base quantity cd Amount of Substance Amount of substance, symbol n, is a quantity that measures the size of an ensemble of entities. It appears in thermodynamic relations, such as the ideal gas law, and in stoichiometric relations between reacting molecules, as in the Law of Multiple Proportions. Familiar equations involving n are thus pV = nRT for an ideal gas, and the equation c = n/V (2) for the amount-of-substance concentration (usually called simply the concentration, the molar concentration, or the amount concentration) of a solution. Here, V is the volume of a solution containing the amount of solute n.

Another important relation is that between amount of substance n and mass m for a pure sample n = m/M (3) where M is the mass per amount of substance, usually called the “molar mass.” Similarly, amount concentration c (SI unit mol/dm3) may be related to mass concentration ρ (SI unit g/dm3) by the equation c = ρ/M (4) An important application of the quantity n in chemistry is to the way in which molecules react in a titration (or more generally in any chemical reaction); molecules (or ions or entities) of X always react with molecules (or ions or entities) of Y in a simple ratio, such as 1:1, or 1:2, or 2:1, and so forth. This is the most fundamental concept of chemical reactions. Thus, the ratio of volumes of solutions of X and Y that react together in a titration are given by (5) where the quantity (nX/nY) is a simple rational fraction. Hence, the concentration of an unknown solution may be determined from the concentration of a standard solution by measuring the volumes in a titration. This is the law of multiple proportions.

It is difficult to give formal definitions for quantities, particularly base quantities, such as length, mass, time, temperature, and amount of substance. The most useful definitions of quantities are in terms of the equations that relate them to other quantities, and, in this way, derived quantities are defined in terms of base quantities. But defining the base quantities is more difficult. The best formal definition of “amount of substance” is as follows: Amount of substance is a quantity proportional to the number of entities N in a sample. The proportionality constant is the same for all substances and is the reciprocal of the Avogadro constant NA. The entities may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. The quantity amount of substance, n, is thus an alternative to using the quantity number of entities, N. They are related by the equation n = N/NA (6) where NA is the Avogadro constant, a fundamental constant whose value is related to the unit of amount of substance n. Because the number of entities N is a dimensionless number, the dimension of NA is the reciprocal of the dimension of n and is thus (amount of substance)-1.

One might reasonably ask why we need the quantity amount of substance n at all. Why not simply use number of entities N in its place? There are three reasons for preferring the use of n rather than N: First, equations, such as Equation 3, can be used to determine molar mass M, or amounts in terms of moles, without knowing the value of the Avogadro constant. The atomic weights of atoms in the periodic table were known long before the value of the Avogadro constant was known with similar accuracy. Even today, the value of the Avogadro constant is known only to about a part in 107, whereas many atomic weights are known to about a part in 109 or better. A second reason is practical: The number of entities is generally of the order 1023, whereas n is generally a number of order 1 when expressed in moles. Thus, for example, in a chemistry laboratory, the concentration of solutions is typically quoted in moles per litre, with numbers in the general order of magnitude 1. It would be inconvenient to quote concentrations in molecules per litre, with numbers of the order 1023.

Thus we find bottles labeled “0.1 M NaOH,” where M is read as “molar” and is an accepted shorthand for the unit mol/L = mol/dm3. The quantity amount of substance may be seen as a device used to handle the same quantitative information with much smaller numbers. A third motivation for introducing the quantity amount of substance with the mole as a base unit is that it extends the power of dimensional analysis in chemistry, and to equations involving chemical quantities. This follows from the fact that n is a base quantity with its own dimension, whereas N is dimensionless. The Mole The mole, with symbol mol, is the SI unit for the quantity amount of substance. It is currently defined as follows: 3 The mole is that amount of substance that contains the same number of elementary entities as there are atoms in 12 g of carbon 12. When the mole is used, the entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

It follows that the numerical value of the Avogadro constant, denoted {NA}, expressed in the unit mol-1, is simply the number of atoms in 12 g of carbon 12, so that the value of the Avogadro constant is directly related to the definition of the mole. The present best estimate of the Avogadro constant is 4 NA = 6.022 141 79 (30) x 1023 mol-1 [ur = 5 x 10-8] (7) where the number in square brackets is the relative standard uncertainty. The effect of this definition is that the molar mass of carbon 12, M(12C), is exactly 12 g/mol, and the molar mass of any atom or molecule X is determined from its atomic or molecular weight by simply multiplying by the unit g/mol, without the need to know the value of the Avogadro constant.

This is summarized in the relations M(12C) = Ar(12C) g/mol = 12 g/mol (8) M(X) = Ar(X) g/mol (9) Here, Ar(X) is the recommended symbol for the molecular weight of the entity X. The atomic or molecular weight of an entity is actually the relative atomic or molecular mass, relative to the value for the carbon 12 atom taken as exactly 12. The names “atomic weight” and “molecular weight” are universally used and have been officially sanctioned by IUPAC, although they are actually dimensionless quantities and are not either masses or weights. The Names “Mole” and “Amount Of Substance” The name “mole” has been—and still is—the cause of some confusion. Its origin has been discussed in several publications. 5 The terms “Kilogrammemolekuel” and “g-Molekel” were used by German scientists in the 1880s and 1890s. The term “gramme-molecule” was first used in English in 1893 in an article in the Encyclopedia Britannica.

As the term implies, one gram molecular weight of a substance X is that amount in a mass equal to the molecular weight expressed in grams. These terms proved too awkward for everyday use, and the shortening of the term “g-Molekel” to “Mol” was first recorded in 1898 by Nernst. 6 The term “mole” appears in English for the first time in the translation of Ostwald’s Principles of Inorganic Chemistry, published in 1902, in which Ostwald associated the term with a standard number of molecules. Thus, one gram molecule of X became one mole of X.

The development of mass spectrometry and the discovery of isotopes in the early twentieth century led to the transition of atomic weights from a basis of either 16 for the naturally occurring mix of oxygen isotopes (used in chemistry) or 16 for the 16O isotope (used in physics), and eventually to the use of 12 for 12C, adopted in 1961 and described as the “unified atomic mass scale.” During this period, it was recognized that the quantity for which the mole was a unit itself deserved recognition as a quantity, and it was given the name “amount of substance.” The International Committee for Weights and Measures (Comité International des Poids et Mesures, CIPM), with the support of IUPAC, the International Union of Pure and Applied Physics (IUPAP), and the International Organization for Standardization (ISO), adopted “amount of substance” as a base quantity and “mole” as a base unit in 1971.

7 It must be admitted that the name “amount of substance” is not well chosen; the word “amount” has a common dictionary meaning, and the additional words “of substance” seem inadequate to imply chemists’ more special meaning for this name. It was the original intention that the words “of substance” should be replaced by the specification of the entity whenever possible, so that one would say (for example) “amount of benzene, C6H6” or “amount of hydrogen ions, H+.” Note the importance of specifying the molecular formula of the entity. For example, “amount of sulphur” might refer to an entity S, or S2, or S8 without further specification of the molecular formula. Yet in practice, many people say “amount of substance of benzene,” or even “amount of substance of substance benzene,” which is long winded and seems like a tautology in addition to being ambiguous. Other names have been suggested for the quantity n. A possible name might be “chemical amount,” because this quantity has to do with chemistry.

The name “chemical amount” for n would then naturally extend to the name “chemical concentration” for c (compare with the name “mass concentration” for C), and when there is no confusion, the adjective “chemical” might be dropped—leading to the names that are usually used today in such phrases as “an amount of three moles,” or “a concentration of 0.1 mol/dm3.” The name “enplethy” has also been suggested for amount of substance; see the discussion on page 4 of the new edition of the IUPAC Green Book. 8 Another name for n, which is the name that most chemists use, is simply “number of moles.” However, this name is problematic because it confuses the name of the quantity with the name of the unit. For this reason, we would not regard “number of kilograms” as an acceptable synonym for “mass” nor “number of kelvins” as an acceptable synonym for “temperature.” A clear understanding requires that we always distinguish between quantities and units.

Thus, mass is a quantity, for which kilogram (or gram, or milligram) is a unit; similarly, we wish to say that amount of substance is a quantity, for which mole (or millimole, or micromole) is a unit. Setting aside the difficulties with the name “amount of substance,” it is important to realize that in the system of quantities and units that is now universally adopted in chemistry, amount of substance n is regarded as a base quantity with its own dimension, whereas—in contrast—number of entities N is regarded as a dimensionless quantity. A Possible New Definition for the Mole The current definition of the seven base units of the SI is given in the SI Brochure. 3 However, proposals are under discussion to adopt new definitions for four of the base units. This follows from our desire to define each of the base units in relation to one of the fundamental constants of physics, or the properties of a simple atom, because we believe these to be the most stable and reliable constants of nature available. Specifically, new definitions are being considered for the kilogram, ampere, kelvin, and mole. This is the subject known as quantum metrology, and the proposals are discussed in detail elsewhere.

9 However, the proposed new definition of the mole is particularly relevant to this discussion, and the suggestion is that it should simply specify the number of entities in a mole. This new definition might then read as follows: The mole is that amount of substance of a system that contains exactly 6.022 141 79 x 1023 specified elementary entities, which may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. The effect of this new definition would be to fix the value of the Avogadro constant to be 6.022 141 79 x 1023 mol-1 exactly. The number would be chosen to be the best estimate of the numerical value of the Avogadro constant at the time the new definition is adopted, thus ensuring continuity in the value of the mole. This new definition would be conceptually simpler than the current definition, which is chosen to fix the molar mass of carbon 12 rather than the number of entities in a mole.

Also, the new definition would no longer be dependent on the kilogram, so that uncertainties in realizing the definition of the kilogram would no longer be transmitted to the mole, as they are at present. The Molar Mass Constant Mu Many of the relations between the quantities discussed here can be simplified by introducing the molar mass constant Mu, defined as one twelfth of the molar mass of the carbon 12 atom. This is the natural analog on the macroscopic scale of the unified atomic mass constant mu on the atomic scale, defined as one-twelfth of the mass of a carbon 12 atom. The quantity mu is often used as a unit of atomic mass, denoted either u (for “unified”) or Da (for “dalton,” a name for this unit that is widely used in the biosciences for expressing the mass of biomolecules with many thousands of atoms).

Thus, we have Mu = M(12C) / 12 BIPM - mole Unit of amount of substance (mole) SI Brochure, Section 2.1.1.6 Following the discovery of the fundamental laws of chemistry, units called, for example, "gram-atom" and "gram-molecule", were used to specify amounts of chemical elements or compounds. These units had a direct connection with "atomic weights" and "molecular weights", which are in fact relative masses. "Atomic weights" were originally referred to the atomic weight of oxygen, by general agreement taken as 16. But whereas physicists separated the isotopes in a mass spectrometer and attributed the value 16 to one of the isotopes of oxygen, chemists attributed the same value to the (slightly variable) mixture of isotopes 16, 17 and 18, which was for them the naturally occurring element oxygen. Finally an agreement between the International Union of Pure and Applied Physics (IUPAP) and the International Union of Pure and Applied Chemistry (IUPAC) brought this duality to an end in 1959/60.

Physicists and chemists have ever since agreed to assign the value 12, exactly, to the so-called atomic weight of the isotope of carbon with mass number 12 (carbon 12, 12C), correctly called the relative atomic mass Ar(12C). The unified scale thus obtained gives the relative atomic and molecular masses, also known as the atomic and molecular weights, respectively. The quantity used by chemists to specify the amount of chemical elements or compounds is now called "amount of substance". Amount of substance is defined to be proportional to the number of specified elementary entities in a sample, the proportionality constant being a universal constant which is the same for all samples. The unit of amount of substance is called the mole, symbol mol, and the mole is defined by specifying the mass of carbon 12 that constitutes one mole of carbon 12 atoms. By international agreement this was fixed at 0.012 kg, i.e. 12 g. Following proposals by the IUPAP, the IUPAC, and the ISO, the CIPM gave a definition of the mole in 1967 and confirmed it in 1969.

This was adopted by the 14th CGPM (1971, Resolution 3 ): The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol". When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. It follows that the molar mass of carbon 12 is exactly 12 grams per mole, M(12C) = Volume and Density 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. Volume and Density Density and volume are two common measurements in chemistry. Learning Objective Describe the relationship between density and volume Key Points The volume of a substance is related to the quantity of the substance present at a defined temperature and pressure .

The volume of a substance can be measured in volumetric glassware, such as the volumetric flask and the graduated cylinder. Density indicates how much of a substance occupies a specific volume at a defined temperature and pressure. The density of a substance can be used to define the substance. Water is unusual because when water freezes, its solid form (ice) is less dense than liquid water, and thus floats on top of liquid water. Terms Full Text Volume and Density The properties of a material may be described in many ways. Any amount of any substance will have a volume. If you have two containers of water that are different sizes, they each hold a different amount, or volume, of water. The unit for volume is a unit derived from the SI unit of length and is not a fundamental SI measurement. If two water samples have different volumes, they still share a common measurement: the density. Density is another measurement derived from SI basic units. The density of a material is defined as its mass per unit volume. In this example, each volume of water is different and therefore has a specific and unique mass.

The mass of water is expressed in grams (g) or kilograms (kg), and the volume is measured in liters (L), cubic centimeters (cm3), or milliliters (mL). Density is calculated by the dividing the mass by the volume, so that density is measured as units of mass/volume, often g/mL. If both water samples are at the same temperature, their densities should be identical, regardless of the samples' volume. Measurement Tools The measuring cup is a common household utensil used for measuring the volumes of liquids. If you have ever cooked in a kitchen, you have probably seen some sort of measuring cup, which allows the user to measure liquid volumes with reasonable accuracy . The measuring cup expresses liquid volume in the standard SI units of liters and milliliters. Most American measuring cups also measure liquid in the older system of cups and ounces. Volumetric Glassware Scientists who work in a laboratory must be familiar with typical laboratory glassware, often called volumetric glassware. These may include beakers, a volumetric flask, an Erlenmeyer flask, and a graduated cylinder. Each of these containers is used in a laboratory setting to measure liquid volumes for different purposes.

Glassware, such as these beakers, is commonly used in a laboratory setting to conveniently measure and separate different volumes of liquids. Density of Water Different substances have different densities, so density is often used as a method to identify a material. Comparing the densities of two materials can also predict how substances will interact. Water is used as the common standard to substances, and it has a density of 1000 kg/m3 at Standard Temperature and Pressure (called STP). Using Water as a Density Comparison When an object is placed in water, the object's relative density determines whether it floats or sinks. If the object has a lower density than water, it will float to the top of the water. An object with a higher density will sink. For example, cork has a density of 240 kg/m3, so it will float. Air has a density of approximately 1.2 kg/m3, so it rises immediately to the top of a water column. The metals sodium (970 kg/m3) and potassium (860 kg/m3) will both float on water, while lead (11,340 kg/m3) will sink. Is the crown made of pure gold?

An ancient Greek king needs to know if he's been cheated by a goldsmith. He summons Archimedes, who decides to use density to determine the metal. But how can he determine the volume of the crown? Liquids tend to form layers when added to water. The sugar alcohol glycerol (1,261 kg/m3) will sink into the water and form a separate layer until it is thoroughly mixed (glycerol is soluble in water). Vegetable oil (approx. 900 kg/m3) will float on water, and no matter how vigorously mixed, will always return as a layer on the water surface (oil is not soluble in water). The Variable Density of Water Water itself is a complicated and unique molecule . Even if the pressure is consistent, water's density will change based on the temperature. Recall that the three basic forms of matter are solid, liquid and gas (ignore plasma for the time being). As a rule of thumb, almost all materials are more dense in their solid or crystalline form than in their liquid form; place the solid form of almost any material on the surface of its liquid form, and it will sink.

Water, on the other hand, does something very special: ice (the solid form of water) floats on liquid water. Look carefully at the relationship between water's temperature and its density. Beginning at 100 °C, the density of water steadily increases, as far as 4 °C. At that point, the density trend reverses. At 0 °C, water freezes to ice and floats. This table lists the densities of water at different temperatures and constant pressure. The implications of this simple fact are enormous: when a lake freezes, ice crusts at the surface and insulates the liquid below from freezing , while at the same time allowing the colder water (with a temp of approx. 4 °C and a high density) to sink to the bottom. If ice did not float, it would sink to the bottom, allowing more ice to form and sink, until the lake froze solid! Scuba divers and swimmers often encounter these water temperature gradients, and they might even encounter a water layer at the very bottom of a lake with a temperature of approximately 4 °C. That's just about as cold as the lake will get at the bottom; as soon as the water gets colder, the liquid water becomes less dense and rises.

S. I. Units S. I. Units S. I. Units Quantities and Units In science a Quantity is expressed as the product of a number and a unit. A number without units often has no meaning to a scientist. A set of standard (agreed upon) units are essential not only in science, but also in commerce. The most widely accepted system of measurement in the sciences is the International System , otherwise known as S.I. Units. S.I. stands for Le Systéme International. This is also called the metric system, with which you may already be familiar. The metric system is easy to learn and use because subdivisions and multiples of base units employ only factors of 10. Prefices indicate the size of the unit relative to a base unit. Prefix p 10-12 The SI system defines seven base quantities, from which all other scientific quantities can be derived. These base quantities are length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity. All other quantities can be derived from these base quantities using the equations of physics and chemistry. Let's look at the base units for some base and derived quantities. SI Base Quantities The SI base unit for length is the meter.

The abbreviated symbol for meters is m . A meter is slighly longer than a yard (i.e., 1 m = 39.37 inches). Mass The SI base unit for mass is the kilogram. The abbreviated symbol for the kilogram is kg . 1 kg weighs approximately 2.2 pounds. The choice of the kilogram instead of the gram as the base unit for mass is only for historical reasons. Time The SI base unit for time is the second. The abbreviated symbol for the second is s . Electric Current The SI base unit for electric current is the ampere. The abbreviated symbol for the ampere is A . Amount of Substance The SI base unit for amount of substance is the mole. The abbreviated symbol for the mole is mol . We will learn more about the mole later in this course. Luminous Intensity The SI base unit for luminous intensity is the candela. The abbreviated symbol for the candela is cd . Thermodynamic Temperature The SI base unit for temperature is the Kelvin. The abbreviated symbol for the Kelvin is K . The coldest temperature theoretically possible is 0 K. You simply cannot go any lower. In fact, it is experimentally impossible to even reach 0 K.

For historical reasons it is also common to define temperature in terms of its difference from a reference temperature T0=273.15 K, the freezing point of water. This is called the Celsius temperature, and the abbreviated symbol for Celsius is °C . It is related to the Thermodynamic Temperature by the equation T(in Celsius) = T(in Kelvin) - 273.15 K On the Celsius scale the freezing point of water is set at 0 °C, and the boiling point is 100 °C. Thus, the coldest temperature theoretically possible is -273.15 °C. Warning: Celsius and fahrenheit scales are not absolute scales and their conversion is ambiguous. Without additional information one cannot know if a value in celsius or fahrenheit should be interpreted as an absolute temperature or a temperature difference. That is, for any calculation involving ΔT you can use celsius and fahrenheit without problems, such as the heat calculated from a heat capacity and a temperature change, q = C ΔT. On the other hand, celsius and fahrenheit are not appropriate in any calculation requiring an absolute temperature, such as the ideal gas law, P V = n R T.

In any case, the safest approach is to convert all temperatures into kelvin or rankines before using them in a calculation. If your final answer needs to be in celsius or fahrenheit, then perform this conversion at the end of your calculation. To give you some other reference points: System English-metric Conversions - Two and Three Dimensions: Volume Determination by Dimensions of Objects Using the Metric System: Density Density is a derived quantity and has the dimensions of mass/length3, and is defined as the mass per unit volume. density = mass/volume The S.I. units for density are kg/m3, but these are not very convenient units for everyday use. More common units are g/cm3 for solids g/ml for liquids g/L for gases If we know the mass and volume of a sample, then we can calculate its density. A cube of lead 3.00 cm on a side has a mass of 305.0 g. What is the density of lead? To answer this question we need to put the mass and volume of the sample into the equation above. The mass of lead is given at 305.0 g.

Although we are not given the volume directly, we do know that the sample is a cube (i.e., all sides of equal length), and that length of a side is 3.00 cm . The volume of this cube would be Volume = ( 3.00 cm)3 = 27.0 cm3. Thus, the density of the cube of lead is density = mass/volume = 305.0 g / 27.0 cm3 = 11.3 g/cm3. Notice that the density is the same no matter the size or shape of the sample. Density Given Mass and Volume: Density of Object from Dimensions and Mass: Volume Given Density and Mass: Dimensions of Objects from Density and Mass: Mass Given Density and Volume: Mass of An Object Given Dimensions and Density: Comparison of Mass, Volume and Density: Density of Atomic Nuclei:

Question: Physics. What is the SI unit for amount of substance?
Answer: Mole