What is the volume of the gas in the following problem?
I have an unknown volume of gas at a pressure of 0.5 atm and a temperature of 325 K. If I raise the pressure to 1.2 atm, decrease the temperature to 320 K, and measure the final volume to be 48 liters, what was the initial volume of the gas?
The ideal gas law can be used to find the initial volume of the gas. This law provides the relation between volume V, pressure P, temperature T and the amount of substance n as P*V = n*R*T, with R being the gas constant.
The information we have gives the initial pressure as 0.5 atm, initial temperature as 325 K, the final pressure as 1.2 atm, final temperature as 320 K and final volume as 48 L. Let the initial volume of the gas be V. Substitute these values in the gas equation
0.5*V = n*R*325
=> 0.5*V/325 = n*R
and 48*1.2 = n*R*320
=> 48*1.2/320 = n*R
Equate the terms that are equal to n*R as that is a constant here.
0.5*V/325 = 48*1.2/320
=> V = 48*1.2*325/320*0.5
=> V = 117 L
The initial volume of the gas was 117 L.