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?
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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.
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