A sample of gas occupies a volume of 70.9 mL. As it expands, it does 118.9 J of work on its surroundings at a constant pressure of 783 torr. What is the final volume of the gas?

1 Answer
Oct 1, 2016

V_2=1.07LV2=1.07L

Explanation:

The relationship between work (ww), pressure (PP) and volume (VV) is the following:

w=-PDeltaV

where, DeltaV=V_2-V_1

since the gas is expanding, then the work is done by the system and it is of a negative value .

Note that work, in this case, should be expressed in L*atm.

1L*atm=101.3J therefore,
w=118.9cancel(J)xx(1L*atm)/(101.3cancel(J))=1.174L*atm

Since work is done by the system: w=-1.174L*atm

Pressure should then be expressed in atm:

P=783cancel("torr")xx(1atm)/(760cancel("torr"))=1.03atm

Thus, replacing every term in its value in the expression w=-PDeltaV we get:

cancel(-)1.174L*cancel(atm)=cancel(-)1.03cancel(atm)xxDeltaV

=>DeltaV=(1.174)/(1.03)=1.14L

Note that DeltaV=V_2-0.0709L=1.14L

=>V_2=1.14L+0.0709L=1.21L

Here is a video that further explains this topic:

Thermochemistry | The Nature of Energy.