# Introductory Chemistry Online/Physical and Chemical Properties of Matter
## 2.1 Pure Substances and Mixtures

In Chapter 1, we learned that atoms are composed of electrons, protons and neutrons and that the number of protons in the nucleus of an atom (the atomic number) defines the identity of that element. For example, an atom with six protons in its nucleus is a carbon atom; seven protons makes it nitrogen; eight protons makes it oxygen, and so on. The periodic table organizes these elements by atomic number and there are currently over 116 known elements.
Because there are clearly more than 116 different types of substances in the world around us, we can see that most substances that we encounter are not pure elements, but are composed of different elements combined together. In chemistry, we refer to these as compounds, which we define as a substance that results from the combination of two or more elements in a constant ratio. For example, water is a compound composed of two hydrogen atoms bonded to one oxygen atom. We can show the ratio of hydrogen to oxygen in this compound by using subscripts on the chemical symbols for each element. Thus, water (two hydrogens and one oxygen) can be written as H$_2$O. This shorthand notation for water is called a chemical formula. For any compound, the chemical formula tells us the elements that are present and the ratio of the elements to each other. Later we will see that water is a member of a special sub-type of compound, called a molecular compound. In a molecule, the atoms are not only bonded together in a constant ratio, but they are bonded in a specific geometric arrangement as well (Figure 2.1). In the following chapter, we will look more closely at how elements are bonded together in compounds, but first we will examine some of the properties of chemical substances.
When we speak of a pure substance, we are speaking of something that contains only one kind of matter. This can either be one single element or one single compound, but every sample of this substance that you examine must contain exactly the same thing with a fixed, definite set of properties. If we take two or more pure substances and mix them together, we refer to this as a mixture. Mixtures can always be separated again into component pure substances,because bonding among the atoms of the constituent substances does not occur in a mixture. Whereas a compound may have very different properties from the elements that compose it, in mixtures the substances keep their individual properties. For example sodium is a soft shiny metal and chlorine is a pungent green gas. These two elements can combine to form the compound, sodium chloride (table salt) which is a white, crystalline solid having none of the properties of either sodium or chlorine. If, however, you mixed table salt with ground pepper, you would still be able to see the individual grains of each of them and, if you were patient, you could take tweezers and carefully separate them back into pure salt and pure pepper.(Figure 2.2)
Mixtures fall into two types, based on the uniformity of their composition. The first, called a heterogeneous mixture, is distinguished by the fact that different samples of the mixture may have a different composition. For example, if you open a container of mixed nuts and pull out a series of small samples and examine them, the exact ratio of peanuts-to-almonds in the samples will always be slightly different, no matter how carefully you mix them. Common examples of heterogeneous mixtures include dirt, gravel and vegetable soup.(Figure 2.3)
In a homogeneous mixture, on the other hand, any sample that you examine will have exactly the same composition as any other sample. Within chemistry, the most common type of homogeneous mixture is a solution which is one substance dissolved completely within another. Think of a solution of pure sugar dissolved in pure water (Figure 2.4). Any sample of the solution that you examine will have exactly the same ratio of sugar-to-water, which means that it is a homogeneous mixture. Even in a homogeneous mixture, the properties of the components are generally recognizable. Thus, sugar-water tastes sweet (like sugar) and is wet (like water). Unlike a compound, which has a fixed, definite ratio, in a mixture one can vary the amounts of each component. For example, when you add a little sugar to one cup of tea and a lot of sugar to another, each cup will contain a homogeneous mixture of tea and sugar but they will have a different taste. If you add so much sugar that some does not dissolve and stays on the bottom, however, the mixture is no longer homogeneous, it is heterogeneous;you could easily separate the two components.
Exercise 2.1 Distinguishing Substances & Mixtures

## The States of Matter

As described in Section 2.1, a molecule of water is composed of two atoms of hydrogen bonded to one atom of oxygen(H$_2$O). All water molecules are exactly the same (same ratio of elements, same geometric bonding pattern), but we encounter water in three different forms in the world around us. At low temperature, water exists as a solid (ice). As the temperature increases, water exists as a liquid, and at high temperature, as water vapor, a gas. An example in which these three states (or phases) exist simultaneously is shown in Figure 2.5. These three forms of water represent the three states of matter: solids, liquids and gases. States of matter are examples of physical properties of a substance. Other physical properties include appearance (shiny, dull, smooth, rough), odor, electrical conductivity, thermal conductivity, hardness and density, to name just a few. We will discuss density in more detail in the next section, but first let’s examine the states of matter and how they differ on an atomic level.
If ice, liquid water and water vapor all consist of identical molecules, then what accounts for the difference in their properties? So far, we have talked about molecules as if they were standing still, but in fact, they are always moving. In chemistry, we often explain the states of matter in terms of the kinetic molecular theory (KMT). The word kinetic refers to motion and the kinetic molecular theory suggests that atoms and molecules are always in motion. The energy associated with this motion is termed kinetic energy. The amount of kinetic energy that a particle has is a direct function of temperature, and it is the kinetic energy of the water molecules under different conditions that determines the different properties of the three states of water as shown in Figure 2.5.
Atoms and molecules move in different ways under different conditions because of the forces attracting them to each other, called intermolecular forces. Intermolecular forces is a general term describing the fact that all atoms, and molecules share a certain inherent attraction for each other. These attractive forces are much weaker than the bonds that hold molecules together, but in a large cluster of atoms or molecules the sum of all of these attractive forces can be quite significant.
Now, consider a group of molecules or atoms clustered together and held in place by these attractive forces. At low temperature, the molecules or atoms will remain stuck together in a lump of defined shape and structure, like water in the form of an ice cube. This is referred to as the solid phase. At the atomic level, the molecules or atoms in a solid are closely packed, and although they are still all rapidly moving, their movements are so small that they can be thought of as vibrating about a fixed position. As an analogy here, think of a handful of small magnets stuck together in a solid mass (Figure 2.6). Solids and liquids are the most tightly packed states of matter. Because of the intermolecular forces, solids have a defined shape, which is independent of the container in which they are placed.
As energy is added to the system, usually in the form of heat, the individual molecules or atoms acquire enough energy to overcome some of the attractive intermolecular forces between them so that neighboring particles are free to move past or slide over one another. This state of matter is called the liquid phase. As in a solid, in a liquid, the attractive forces are strong enough to hold the molecules or atoms close together so they are not easily compressed and have a definite volume. Unlike in a solid, however, the particles will flow (slide over each other) so that they can assume the shape of their container, as shown in Figure 2.7.
Finally, if enough energy is put into the system, the individual molecules or atoms acquire enough energy to totally break all of the attractive forces between them and they are free to separate and rapidly move throughout the entire volume of their container. This is called the gas phase and atoms or molecules in the gas phase will totally fill whatever container they occupy, taking on the shape and volume of their container. Because there is so much space between the particles in a gas, a gas is highly compressible, which means that the molecules can be forced closer together to fit in a much smaller space (Figure 2.8). We are all familiar with cylinders of compressed gas, where the compressibility of gasses is exploited to allow a large amount of gas to be transported in a very small space. Figure 2.9 shows a simple graphic representation of the atomic states in solids, liquids and gasses.
Returning to our example of water, at low temperature, water exists as the solid, ice. As the solid is warmed, the water molecules acquire enough energy to overcome the strongest of the attractive forces between them and the ice melts to form liquid water. This transition from the solid phase to the liquid phase happens at a fixed temperature for each substance called the melting point. The melting point of a solid is one of the physical properties of that solid. If we remove energy from the liquid molecules they will slow down enough for the attractive forces to take hold again and a solid will form. The temperature that this happens is called the freezing point and is the same temperature as the melting point.
As more energy is put into the system, the water heats up, the molecules begin moving faster and faster until there is finally enough energy in the system to totally overcome the attractive forces. When this happens, the water molecules are free to fly away from each other, fill whatever container they are occupying and become a gas. The transition from the liquid phase to the gas phase happens at a fixed temperature for each substance and is called the boiling point. Like the melting point, the boiling point is another physical property of a liquid.
Phase transitions for a typical substance can be shown using simple diagram showing the physical states, separated by transitions for melting and boiling points. For example, if you are told that a pure substance is 15˚ C above its boiling point, you can use the diagram to plot the temperature relative to the boiling point. Because you are above the boiling point, the substance will exist in the gas phase.
Example 2.1 The Physical State of a Substance
There are, however, some exceptions to the rules for changes of state that we have just established,. For example, ice is a solid and the molecules in the interior are held together tightly by intermolecular forces. Surface molecules, however, are exposed and they have the opportunity to absorb energy from the environment (think of a patch of snow on a bright sunny day). If some of these surface molecules absorb enough energy, they can break the attractive forces that are holding them and escape as a gas (water vapor) without ever going through the liquid phase. The transition from a solid directly into a gas is called sublimation. The reverse process, a direct transition from a gas to a solid, is called deposition. Perhaps the most common example of a solid that does not melt, but only sublimes, is dry ice (solid carbon dioxide;CO$_2$), shown in Figure 2.10. This property of dry ice is what makes it a good refrigerant for shipping perishables. It is quite cold, keeping things well frozen, but does not melt into a messy liquid as it warms during shipment.
Just like surface molecules in solids can move directly into the gas phase, surface molecules in liquids also absorb energy from the environment and move into the gas phase, even though the liquid itself is below the boiling point. This is the process of vaporization (evaporation). The reverse process, a transition from a gas to a liquid, is called condensation. Liquid substances undergo vaporization and the space above any liquid has molecules of that substance in the gas state. This is called the vapor pressure of the liquid, and vapor pressure (at a given temperature) is another of the physical properties of liquid substances.
Summarizing what we know about the different states of matter:
In a gas:
* the molecules or atoms are highly separated, making a gas highly compressible,
* attractive forces between the particles are minimal, allowing the gas to take on the shape and volume of its container.
In a liquid:
* the molecules or atoms are closely spaced, making a liquid much less compressible than a gas,
* attractive forces between the particles are intermediate, allowing the molecules or atoms to move past, or slide over one another,
* liquids have a definite volume, but will take on the shape of their container.
In a solid:
* the attractive forces are strong, keeping the atoms or molecules in relatively fixed positions,
* the neighboring atoms or molecules are close together, making the solid not compressible and giving it a definite shape that is independent of the shape and size of its container.
Exercise 2.2 States of Matter

## 2.3 Density, Proportionality and Dimensional Analysis

In the previous section, we have learned about the states of matter. The physical state of a substance at under a defined set of conditions (like temperature and pressure) is an intensive property of a substance. An intensive property is defined as a property that is inherent to the substance and is not dependent on the sample size. Density, the mass-to-volume ratio of a substance, is another example of an intensive property.(Figure 2.11)
If you picked up equal sized samples of aluminum and gold, you would immediately notice that one was much heavier than the other. The atomic mass of gold is over seven times greater than the atomic mass of aluminum, so although the two samples are the same size, the lump of gold is significantly more massive than the equally sized lump of aluminum. We can say that gold is more dense than aluminum.
Making this a quantitative measurement, one cubic centimeter of gold has a mass of 19.3 grams (remember that a cubic centimeter is the volume of a cube that is exactly one cm on each side, and it has the units of cm$^3$[http://askthenerd.com/COL/images/2.12.html ;see Figure 2.12]. We defined density as the mass-to-volume ratio of a substance. For gold, the mass is 19.3 grams and the volume is 1 cm$^3$. The mass-to-volume ratio of gold is $\left(^{19.3{\text{ g}}}\!\!\diagup \!\!_{{\text{1 cm}}^{\text{3}}}\;\right)$, and the density (d) of gold is written as d = 19.3 g/cm$^3$.
Returning to our block of aluminum;experimentally, one cubic centimeter of aluminum has a mass of 2.70 grams. The mass-to-volume ratio of aluminum is $\left(^{2.{\text{70 g}}}\!\!\diagup \!\!_{{\text{1 cm}}^{\text{3}}}\;\right)$, and the density of aluminum is therefore 2.70 g/cm$^3$, about 7 times less than that of gold.
Density is a physical property that can be measured for all substances, solids, liquids and gasses. For solids and liquids, density is often reported using the units of g/cm$^3$. Densities of gasses, which are significantly lower than the densities of solids and liquids, are often given using units grams/liter (g/L, remembering from Section 1.4 that a liter is defined as 1000 cm$^3$). Table 2.1 gives the densities of some common solids, liquids and gasses.
The definition of density that we used previously was the mass-to-volume ratio of a substance. This is also stated as “mass per unit volume”. The word per in this context implies that a mathematical relationship exists between mass and volume. In this case, the relationship is the ratio of mass-to-volume. Whenever two factors can be related by a ratio or fraction we can use unit analysis to solve problems relating those factors. For density, the ratio is mass-to-volume. If a sample of iron has a mass of 23.4 grams and a volume of 3.00 cm$^3$, the density of iron can be calculated as:
d = $\left(^{\text{mass}}\!\!\diagup \!\!_{\text{volume}}\;\right)$
d = $\left(^{2{\text{3}}{\text{.4 g}}}\!\!\diagup \!\!_{{\text{3}}{\text{.00 cm}}^{\text{3}}}\;\right)$ or, d = 7.80 g/cm$^3$
In this calculation, our two experimental numbers are 23.4 and 3.00. Each of these numbers has three significant figures (remember, the trailing zeros in 3.00 are significant because the number has a decimal point). Our answer must therefore also be accurate to three significant figures, or 7.80.
Exercise 2.3 Density Calculations
Example 2.3 Calculating the Density of a Solid:Converting Length to find Volume.
Example 2.4 Calculating Density of a Solid:Converting Mass and Volume.
Example 2.5 Calculating the Density of a Solid:Converting Mass.

## 2.4 Chemical Properties, Physical Changes and Chemical Changes

A lump of gold can be hammered into a very thin sheet of gold foil (it is the most malleable of all of the elements). Nonetheless, the gold in the foil sheet is still just elemental gold;nothing has changed except the physical appearance of the sample. The same is true if you take any solid pure substance and melt it, or convert it to a gas. The atomic or molecular structure of the substance has not changed, it simply has a different physical appearance. Changes in outward appearances that do not alter the chemical nature of the substance and make no new substance are called physical changes. Pure carbon, in the form of a briquette, can be smashed to a fine powder without changing the fact that it is still just elemental carbon (thus, this is a physical change), but if pure carbon is heated in the presence of oxygen, something else happens. The carbon slowly disappears (often in flames) and the carbon atoms now appear as a compound with oxygen with the formula CO$_2$. Carbon dioxide is a totally different substance than either the carbon or the oxygen that we started with. For example, carbon is a black solid and carbon dioxide is a colorless gas. You know that a chemical change has occurred when the chemical composition of the material changes and a new substance is produced.(Figure 2.13)
Just like we defined a set of physical properties for substances, we can also define a set of chemical properties. Chemical properties are simply the set of chemical changes that are possible for that substance. For the element magnesium (Mg), we could say that chemical properties include:
* the reaction with oxygen to form MgO,
* the reaction with hydrochloric acid to form MgCl$_2$ and hydrogen gas (H$_2$),
* the reaction with solid carbon dioxide (dry ice) to form MgO and carbon.
Chemical changes can almost always be detected with one of our physical senses. Thus, when magnesium reacts with oxygen (burns in air) a bright white flame is produced, heat is evolved and the shiny metallic magnesium is converted to a crumbly white powder (MgO; (Figure 2.14a). In the reaction with hydrochloric acid (the molecule HCl dissolved in water), the solid metallic magnesium disappears, bubbles of hydrogen gas (H$_2$) are evolved, heat is produced, and a clear solution containing MgCl$_2$ is formed (Figure 2.14b). In the reaction with solid carbon dioxide (dry ice), a bright white flame is produced, heat is evolved and the shiny metallic magnesium is converted to a crumbly white powder and solid carbon (Figure 2.14c). In general, when you are trying to identify a chemical change, look for evidence of heat or light, the evolution of a gas, a change in color or the formation of new solid products from otherwise clear solutions.
Exercise 2.4 Chemical and Physical Changes

## 2.5 Conservation of Mass and Chemical Changes

When substances undergo chemical changes their physical state is usually dramatically altered. Despite this dramatic change, however, no matter is lost or created. We can show this with the reaction of magnesium metal with oxygen to form magnesium oxide (Figure 2.14). Instead of burning the magnesium metal openly in the air, if you were to seal the magnesium and air together in a glass vessel, weigh it, heat it to promote reaction, and then weigh the vessel again, you would find that there was no change in total mass. The mass of the product, magnesium oxide, would exactly equal the masses of the substances that reacted (oxygen gas and magnesium metal).
This is analogous to an experiment performed by the French chemist, Lavoisier, in the 1770s in which he heated metallic tin (Sn) with air in a closed vessel. This, and other experiments of the time, provided the data that led to the law of mass conservation. Formally, the law states, there is no detectable change in the total mass of materials when they react chemically to form new materials.
Basically, what the conservation law says is that whenever a chemical change occurs, the total mass of the substances reacting must equal the total mass of the substances that are produced. Sometimes this is stated as mass is conserved or mass is neither created nor destroyed in a chemical reaction. For example, when charcoal is burned in oxygen, the mass of the (charcoal + oxygen) must equal the mass of the (carbon dioxide, water vapor and ash) that is produced. The conservation of mass is one of the fundamental principles on which modern chemistry is based.

## Study Points

* A compound is defined as a substance that results from the combination of two or more elements in a constant ratio. In a compound such as water, we show the ratio of the elements (hydrogen and oxygen) by using subscripts on the chemical symbols for each element. Thus, water (two hydrogens and one oxygen) is written using the chemical formula H$_2$O. In a molecule, the atoms are not only bonded together in a constant ratio, but they are also bonded in a specific geometric arrangement.
* A pure substance contains only one kind of matter;it can be a single element or a single chemical compound. Two or more pure substances mixed together constitute a mixture;you can always separate a mixture by simple physical means.
* A heterogeneous mixture is not uniform and different samples of the mixture will have a different compositions. A homogeneous mixture, is uniform and any sample that you examine will have exactly the same composition as any other sample. Within chemistry, the most common type of homogeneous mixture is a solution.
* Any pure substance, under appropriate conditions, can exist in three different states: solids, liquids and gases. States of matter are examples of physical properties of a substance. Other physical properties include appearance (shiny, dull, smooth, rough), odor, electrical conductivity, thermal conductivity, hardness and density, etc.
* Solids have both a definite shape and volume. Liquids have a definite volume, but take on the shape of their container. Gasses have neither a definite shape nor volume, and both of these are defined by the shape and volume of their container.
* The kinetic molecular theory (KMT) is generally used to explain physical states of matter. The KMT suggests that atoms and molecules are always in motion and are loosely bound to each other by attractive called intermolecular forces. In a solid, the kinetic energy (energy of motion) associated with the atoms or molecules is insufficient to break these forces and the particles are essentially fixed in place, adjacent to each other. In a liquid, there is enough kinetic energy to break some of the attractive forces, allowing the particles to “slip and slide” next to each other, but there is not enough energy to allow them to escape. In a gas, there is sufficient kinetic energy to totally overcome the forces and the particles have no interactions with each other.
* A change of state from a solid to a liquid occurs at a defined temperature (which) called the melting point (or freezing point);this temperature is a unique physical property of the substance. The transition from a liquid to a gas, likewise, occurs at the boiling point. A direct transition from a solid to a gas is called sublimation.
* An intensive property is defined as a property that is inherent to the substance and is not dependent on the sample size. Density, the ratio of mass-to-volume for a substance, is a classic example of an intensive property.
* Density is calculated by taking the mass of a sample of a substance, and dividing that by the volume of that sample. Density for solids is typically expressed using units of grams per cubic centimeter (g cm$^{-3}$);liquids as grams per milliliter (g mL$^{-1}$) and gasses as grams per liter (g L$^{-1}$), although any mixture of mass and volume units may be used. Remember, a mL has the same volume as a cm$^3$, and a L is simply 1000 mL.
* Physical changes are changes in outward appearances that do not alter the chemical nature of the substance and produce no new substance. When a chemical change occurs, a new substance is produced. Just like physical properties describe the appearance or intensive properties of a substance, chemical properties describe the set of chemical changes that are possible for that substance.
* The law of mass conservation (conservation of mass) simply states, that there is no detectable change in the total mass of materials when they react chemically (undergo a chemical change) to form new substances.

## Supplementary Problems

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