MODERN ALCHEMIST

Ideal Gas Law Following the work of Charles and Boyle, the Ideal Gas Law was developed, uniting the variables pressure, volume, and temperature into one equation.

PV = nRT

R is the real gas constant. R must have units matching the units used for the four variables, P, V, n, and T.

^-1

T must have units corresponding to a scale which places zero at the lowest temperature possible, absolute zero. The Kelvin temperature scale will be used.

Two types of problems will be considered. In the first case, volume remains constant, in the second, the pressure remains constant. In all the scenarios, R remains constant. Some variables will be treated as constants, as the situation described does not allow them to change.

Constant volume:

PV = nRT
If the quantity of gas in the system (n) remains constant, and the temperature (T) is increased, the pressure (P) will increase.
One of the first safety rules you need to learn before working in a chemistry lab is "never heat a closed system". If a container is filled with gas (any gas, or mixture of gases), sealed, and then heated it over a Bunsen burner, it will become a bomb that will explode when the pressure exceeds the strength of the container.
PV = nRT
If no temperature change occurs, but more gas is pumped into the system, the pressure will increase.

Constant Pressure:

We are going to build a tube, with gas tight piston in it. This is a big tube, with a 2 meter diameter and a 50 meter height. By measuring the height of the piston, we can determine the volume of gas in the tube. There is an inlet at the bottom of the tube for adding or removing gas from the tube. In addition, the walls of the tube can be heated or cooled to change the temperature of the gas.

PV = nRT
The tube is heated.
Since the piston is free to move, it moves upward until the internal pressure is equal to the external pressure.
PV = nRT
As more gas is added, the piston moves upwards until the internal pressure is equal to the external pressure.

What are the units for the product of pressure multiplied by volume?

                          3         2
 kg      m               m      kg m
---- * ----- * ----- * ----- = -------
          2       2               2 
         s       m               s

^-2


     2
 kg m
------- = N m = J        Joules is the unit for energy.
    2
   s

For some reactions, high pressures are needed concurrent with high temperatures, and so the reaction is carried out in a "bomb", a deviced with safety features designed to withstand high pressure. As a safety feature, a blow value is present which will burst above a certain pressure.

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