What was the initial volume of the gas in the following case?
I have an unknown volume of gas held at a temperature of 115 K in a container with a pressure of 60 atm. If increasing the temperature to 222 K and decreasing the pressure to 30 atm causes the volume of the gas to be 29 liters, how many liters of gas did I start with?
When an amount of gas equal to n moles is placed under conditions where the temperature is T and the pressure is P, the relation of the volume occupied by the gas is given by the Ideal Gas Equation as P*V = n*R*T. Here R is a universal constant that remains the same.
As we can write this equation in the form P*V/T = n*R we have a relation with the variables on one side equated to a constant. This allows us to determine changes in any of the three variables P, V and T.
Let the original volume of the gas in the problem be V. We can use the values given to create:
V*60 / 115 = 29*30 / 222
=> V = 29*30*115/ 222*60
=> V = 7.51 L
The original volume of the gas before the pressure was decreased and the temperature increased, was 7.51 L