Chapter Five, Section One | |

**OBJECTIVES**

- Understand the basic differences among the three phases of matter.
- Understand the meaning of pressure.
- Learn the gas laws and how to apply them.

**I. Gases**

As we have been studying chemical reactions, we have been dealing in grams of substances because we have been dealing with liquids or solids. However there is another very important phase of matter: gases. So how do we deal with gaseous reactants and products? How do we calculate the number of grams of water formed from the reaction

H_{2}(g) + 2O_{2}(g) 2H_{2}O(g)

if we have 13.6 liters of O2(g) at 10 C and 755 mm Hg mixed with 34.6 liters of H2(g) at 28 C and 724 mm Hg to produce water?

You know that we need to calculate the number of moles of hydrogen and oxygen that we start with , then use the reactants' mole ratio to determine limiting reagent, and then use the mole ratio to calculate the number of moles of product formed. But how do we calculate the number of moles of the gases used from the data given? We can't with what we know so far. So,

There are four properties which determine the physical behavior of gases:

- the mass of the gas,m
- the volume of the gas,V
- the temperature,T
- the pressure,P

These variables {m,V,T,P} are called *state variables* because the values of these variables will define the *state* of the system. Now what we would really like to have would be an equation of state (a mathematical relation among the state
variables) so that we could calculate the number of moles of gas (from the mass) if we know the values of the state variables like given in the example reaction above. So that is where we will be heading -- obtain an equation of state.

**II. Pressure**

First let's determine what pressure is. Pressure, from your physics, is force/area:

eq 1 ...........P = F/A

Look at a liquid first. If we have a beaker with a liquid of density d in it up to a height of h and a surface area of A then the mass of the liquid is

mass = V*d = A*h*d where the volume is the height times the area.

The weight of the liquid is w = m*g where g is the gravitational constant. So we have the weight is w = A*h*d*g. This weight is the force of the liquid so from above the pressure is

P = F/A = A*h*d*g/A = g*h*d for the liquid at the bottom of the beaker. The higher the height of the liquid in the beaker, the greater the pressure of the liquid on the bottom of the beaker.

Now what about a gas? A gas will fill the container and the molecules are rapidly moving about the container. The pressure is caused by the collisions of the molecules with the sides of the container and will still be given by the formula above (eq 1), but the equation for the force will be quite different.

Units for dealing with gases are that 1 atm = 760 mm Hg = 760 torr = 14.7 lb/in^{2} (psi) = 1.033 kg/cm^{2}. The SI unit is 101,325 newtons/m^{2} = 101,325 Pa (Pascals) = 1.01325 bars = 1013.25 millibars. All of these units are
still used today. Engineers still use the psi units and scientists mainly use atm even though that is not an SI unit.

**III. Gas Laws**

The development of the equation of state that we need took many years due to the lack of equipment needed to make accurate measurements. In 1662 Boyle discovered that at constant T, the volume of a gas was inversely proportional to pressure:

V = constant/P

Then in 1787 Charles discovered that at constant P, the volume of a gas was directly proportional to temperature:

V = constant*T

Combining these two equations we see

V = constant * (T/P)

A standard temperature and pressure is called STP and is T = 0^{0}C = 273.15 K and P = 1 atm.

Gay-Lussac discovered that when gases react with one another they do so by volumes that are in the ratios of small whole numbers.

Work homework problems 13, 17, 19, 25 in the text.

After you have studied this material and practiced some problems, take quiz one. If you score at least 80 on the test then you are ready to continue to the next section.

*Web Author: Dr. Leon L. Combs*
*Copyright ©2001 by Dr. Leon L. Combs - ALL RIGHTS RESERVED*