# A certain sample of gas has a volume of 0.452 L measured at 87°C and 0.620 atm. What is its volume at 1 atm and 0°C?

May 19, 2014

To solve this problem we would use the combined gas law.

The formula for the combined gas law is
$\frac{\left({P}_{i}\right) \left({V}_{i}\right)}{T} _ i = \frac{\left({P}_{f}\right) \left({V}_{f}\right)}{T} _ f$

We begin by identifying the values for each of the variables and identifying the missing value.

${P}_{i}$ = 0.620 atm
${V}_{i}$ = 0.452 L
${T}_{i}$ = 87 C + 273 = 360 K

${P}_{f}$ = 1 atm
${V}_{f}$ = ???
${T}_{f}$ = 0 C + 273 = 273 K

$\frac{\left(0.620 a t m\right) \left(0.452 L\right)}{360 K} = \frac{\left(1 a t m\right) \left(x\right)}{273 K}$

$\frac{\left(273 K\right) \left(0.620 a t m\right) \left(0.452 L\right)}{\left(360 K\right) \left(1 a t m\right)} = \left(x L\right)$

$x L = 0.212 L$