Calculating Work with Moles of Gas

Question

How much work is done by 0.86 moles of gas that has an initial volume of 10 L and expands under the following conditions: 32 Celsius and 1.3 atm.

Answer 1

What do we know?:

Initial volume = 10 L

Temperature = 32ºC + 273 = 305K

Pressure = 1.3 atm

Moles = 0.86

Since work (w) = -P∆V, we need to find ∆V which means we must find the final volume

PV = nRT

V = nRT/P = (0.86)(0.0821)(305)/1.3 = 16.6 L

∆V = 16.6 L - 10 L = 6.6 L

w = -P∆V = -1.3 atm x 6.6 L = - 8.58 L-atm = - 8.6 joules of work done by the system