Pressure and Temperature

Gases -- basics

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

H₂(g) + 2O₂(g) 2H₂O(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 reatants' 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.

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/in² (psi) = 1.033 kg/cm². The SI unit is 101,325 newtons/m² = 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.

The kinetic molecular theory of gases (we will cover this in some detail in a later section) gives us an important result that we need now. This theory is a model for gases from which we can obtain equations for the average velocity of gases and, most important for our needs now, an equation relating the average kinetic energy of the gases to the temperature of the gases. Remember that the kinetic energy is given by

KE = 0.5 * m * v² where m is the mass of the particle and v is the velocity of the particle.

This model gives this relationship between KE and T:

T = 2*KE_av/(3k)

where KE_av is the average kinetic energy and k is Boltzmann's constant (1.38066 x 10^-23J/K where J is joules and K is Kelvin). Remember that whenever we indicate temperature with a capital T, the units are Kelvin. Joules is the SI unit for energy. This relationship between KE and T allows us to better understand what temperature is in that it is a measure of the velocity of the molecules. The equation itself is not an exact equation for it is based upon a model for the motion of gases which is not exact. However the understanding of T as a measure of velocity of molecular motion transcends the model.

So now we have a bit of a molecular understanding of pressure (a measure of the force of the molecules hitting the sides of a container) and temperature (a measure of the velocity of the molecules).

Now take a practice quiz to help you understand if you understand the basic concepts.

You must use your real name when it asks for a name.

The test will only submit when you have answers all of the questions correctly.

If you are not taking this course for credit please do not answer all the questions correctly for I don't want to be flooded with email answers to the tests.

Ready to continue? Then go to the next section.