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

Answer:

#V_2=1.07L#

Explanation:

The relationship between work (#w#), pressure (#P#) and volume (#V#) 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.