# 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?

Oct 1, 2016

${V}_{2} = 1.07 L$

#### Explanation:

The relationship between work ($w$), pressure ($P$) and volume ($V$) is the following:

$w = - P \Delta V$

where, $\Delta V = {V}_{2} - {V}_{1}$

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 $L \cdot a t m$.

$1 L \cdot a t m = 101.3 J$ therefore,
$w = 118.9 \cancel{J} \times \frac{1 L \cdot a t m}{101.3 \cancel{J}} = 1.174 L \cdot a t m$

Since work is done by the system: $w = - 1.174 L \cdot a t m$

Pressure should then be expressed in $a t m$:

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

Thus, replacing every term in its value in the expression $w = - P \Delta V$ we get:

$\cancel{-} 1.174 L \cdot \cancel{a t m} = \cancel{-} 1.03 \cancel{a t m} \times \Delta V$

$\implies \Delta V = \frac{1.174}{1.03} = 1.14 L$

Note that $\Delta V = {V}_{2} - 0.0709 L = 1.14 L$

$\implies {V}_{2} = 1.14 L + 0.0709 L = 1.21 L$

Here is a video that further explains this topic:

Thermochemistry | The Nature of Energy.