A sample 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