Asample of an ideal gas at 15.0 atm and 10.0 l is allowed to expand against a constant external pressure of 2.00 atm at a constant temperature. calculate the work in units of kj for the gas expansion.

According to Boyle's law the volume of a gas is inversely proportional to its pressure. Boyle's law follows the equation:  

P1*V1 = P2*V2 P1= 15atm V1= 10L P2= 2atm V2= ?  

(15atm)*(10L)= (2atm) *(V2)  

V2= 75L  

change in volume = final volume - initial volume =  

75L - 10L = 65L  

The work done by an expanding gas can be calculated by the equation:  

w = -(Pressure)*(change in volume)  

The pressure is the amount of pressure under which the gas expands which is 2atm (If the pressure was 15atm, the gas would not expand). So:  

w = -(2atm)*(65L) = -130 L*atm  

Now you have to convert from L*atm to J. Here's how you do it. The conversion factor can be obtained from R values.  

.08206 (L*atm)/(K*mol) and 8.314 J/(K*mol)  

We want J/(L*atm) so divide the R values the denominators cancel:  

(8.314J/(K*mol)) / ((.08206L*atm)/(K*mol)) = 101.3J/(L*atm)  

See how the K*mol cancels.  

w= -130L*atm *(101.3J/(L*atm)) *(kJ/1000J) =  

w= -13.2kJ

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