Question

A sample of gas occupies a volume of 54.0 mL. As it expands, it does 137.1 J of work on its surroundings at a constant pressure of 783 torr. What is the final volume of the gas?

Answer 1

The relation between Pressure, Work and Volume is given by,

w=-PdeltaV

Where deltaV = Vfinal - Vinitial

Negative sign will be used for work as it is done by the system since the gas is expanding.

We will change the values into requisite unit so that Volume can be obtained in L.

w =137.1J = 137.1/101.3L.atm = 1.353L.atm (1L.atm=101.3J)

w = -1.353L.atm

P = 783 torr = 783/760atm = 1.03atm (1 atm = 760torr)

So,

-1.353L.atm = -1.03atm.deltaV

DeltaV = 1.31L

Vfinal - Vinitial = 1.31L

Vinitial = 54mL = 0.054L

Vfinal = 1.31L + 0.054L = 1.364L = 1364mL

Final volume = 1364mL