In this activity you will be introduced to the concepts of the Kinetic Molecular Theory of Gases. So far you know a little about how gases act when subjected to changes in temperature, pressure and volume. Now you will have a chance to learn a little about why they act that way. You will also get a more detailed picture of just what pressure and temperature really are.
Also, you will learn about Dalton’s Law of Partial Pressures. This law says that the pressure of a mixture of gases is simply the sum of the pressures that each gas would exert if it were alone in the container. For instance, in Earth’s atmosphere the major components are oxygen (O_{2} ) and nitrogen (N_{2} ). Ignoring the other minor components for a moment we can say that O_{2} (22% of the atmosphere) has a partial pressure of 0.22 atm and N_{2} has a partial pressure of 0.78 atm. Adding these together you can see that they equal the total pressure of 1 atm.
Pressure  Unit  Symbol  Convert  Example 
torr = mmHg  torr or mmHg  1/760 atm 
used in the lab a column of mercury in a glass tube makes a simple barometer; 1 mm of that column is 1 mmHg or 1 torr 

kiloPascals  kPa 
101.325 kPa = 1 atm 
the SI unit of P 
You may be wondering why you are looking at still more units of pressure. Well, there happen to be a lot of units for pressure (bar, lb/in^{2}, lb/ft^{2}, ton/ft^{2}, millimeters of mercury, etc.) It isn’t helpful to know them all but these two are important because of what they can tell us about the nature of pressure.
First, a word about kPa: The study of physics led to the development of units of force. The unit of force is called the newton (N), named after Isaac Newton, a scientist of some note. Pressure is defined as force divided by the area over which the force acts: P = (force)/(area). Using the standard unit of force, the units of pressure are newtons per square meter (N/m^{2}). These units are commonly called pascals (Pa) after Blaise Pascal, a French mathematician and scientist. That is the origin of the kilopascal (kPa), which is equal to 1,000 pascals. Your text uses the kPa unit for pressure.
Pascals point to a concept of pressure that has some real value. What is causing the force on an area when we talk about gas pressure? That force is due to the collisions between the molecules and atoms of a gas and the sides of their container. As the gas particles strike the sides of the container they exert a force on it depending on how fast they are moving and how often they hit it. The more times they hit it, in a given amount of time, and the harder they hit, the higher the pressure.
Second, the ‘new’ unit introduced above is not really all that new. The mmHg stands for millimeters of mercury (Hg is the chemical symbol for mercury). That is in fact the definition of the torr: 1 torr equals 1 mmHg. This unit was named for the first person (supposedly) to realize that the atmosphere exerts a pressure on everything on Earth: Evangelista Torricelli. More important than that, though, is the fact that he invented the mercury barometer (at right). The barometer is simple but dangerous because mercury is chemically very reactive and is in fact a very strong poison. It works like this: you fill a long glass tube with mercury and cover the open end. Place the open end in a pool of mercury and let the mercury in the tube flow into the pool. On an average day you will find that the height of the column of mercury is about 760 mm (76 cm or about 29.92 in.) A vacuum forms at the top of the closed column of mercury because the mercury is being pulled by gravity out of the tube.
What keeps any mercury in the tube? Atmospheric pressure. The atmosphere pushes down on the pool of mercury with a force per unit area of 101.3 N/m^{2}, or 14.7 pounds per square inch. This is exactly enough pressure to hold up a 76cm tall column of Hg . Consider the power of atmospheric pressure as seen in the cancrushing demonstration and the upsidedown glass of water.
The kinetic theory of gases is based on the following assumptions:
The kinetic energy of any object is directly proportional to the mass and velocity of the object (in case you are interested, KE = ½mv^{2}). So the faster something moves and the more massive it is, the more kinetic energy it has. (Kinetic comes from the Greek for movement.) Gas particles are not very massive but they move incredibly fast at normal temperatures (~1,100 mph). The motion of gas particles can be measured with a thermometer because temperature is proportional to the average kinetic energy of a collection of molecules. So the faster the molecules are flying around, the higher their temperature. Naturally, the faster they fly, the harder they hit things they collide with. It is these collisions which gives rise to pressure as the particles of a gas collide with each other and with other objects. The constant pushing from trillions and trillions of gas particles against objects is what we call gas pressure.
I know after all this reading you are anxious to get on to some problems. So have at it:
When two or more gases mix, and do not chemically react, then the total pressure of the mixture equals the sum of the pressure of each component if it were present alone. In your imagination fill a steel vessel with 1 mol of He. Say the total pressure in the vessel is 10 atm. Add another mole of He but keep the volume and temperature constant. According to PV=nRT the total pressure should now be 20 atm because twice as many moles of gas are in the vessel. Now, how would the pressure have changed if instead of He, you added O_{2}? Just as when you added more He, the pressure doubles.
Mathematically, the idea behind this law can be stated this way: P_{total} = P_{1} + P_{2} + P_{3} + … + P_{n}
This idea has an application that you will use in a lab later in this course. When a gas is collected over water the gas that is being collected accounts for most of the pressure. The rest is due to water vapor. Water molecules are always evaporating and condensing at the surface of water. When the water is in a closed container the pressure of water vapor depends only on the temperature. Here is an excerpt from a data table showing the vapor pressure of water at various temperatures:
The pressures listed are the partial pressures of water that you would have at the temperature shown in a closed container. Say you were to generate O_{2} according to the following chemical equation: 2KClO_{3} > 2KCl + 3O_{2}. This equation describes the decomposition of potassium chlorate into oxygen and potassium chloride. If you set up some lab apparatus as shown in the illustration then you can collect the O_{2} to use for something else. When you collect the gas over water, the pressure inside a 1L capacity jar is equal to the external atmospheric pressure.
That is, the total pressure. So if atmospheric pressure is 101.3 kPa today then that is also the total pressure inside the jar. But what is the pressure of the oxygen? Use Dalton’s Law of Partial Pressures: P_{T} = P_{1} + P_{2} or P_{T} – P_{2} = P_{1}. If the temperature of the system is 25°C then P_{2}, the partial pressure of H_{2}O is 3.169 kPa. So the pressure of O_{2} alone is 98.16 kPa (which is 0.967 atm). And why did we want to know? We wanted to know how much O_{2} was generated in the chemical reaction. So how can you find that out? Use PV=nRT. For the volume use the total amount of oxygen generated, say it was 5.5 L.
PV n = —— RT (0.967 atm)(5.5 L) substituting n = ———————————————————————— = 0.217 mol values: (0.0821 L atm/K mol)(298 K)
And what is a mole? A mole is a unit of chemical measurement for amount of substance. It is directly proportional to the number of atoms or molecules. For now, we will just be using the unit without any discussion of what it means: we will leave that for our discussion of the periodic table.
The mole is useful in the discussion of partial pressures
because of the idea of a mole fraction. Say a container has
equal amounts of two gasses, say He and Ar.
The amount of He in the
container is 50% of the total by volume. Its mole
fraction is 0.5. Similarly, the mole fraction of
Ar is 0.5. Mole fraction can
be calculated using equation 1.
n_{a} X_{a} = —————————————— n_{a} + n_{b} + … n_{n} equation 1
P_{a} = X_{a}P_{T} or P_{b} = X_{b}P_{T} equation 2
V  P  T  V at STP 
20.3 L  98.3 kPa  42.0°C  
21.2 L  97.8 kPa  40.4°C  
19.7 L  100.2 kPa  39.5°C  
20.8 L  99.0 kPa  40.1°C 