A sample of gas occupies a volume of 50.0 milliliters in a cylinder with a movable piston. The pressure of the sample is 0.90 atmosphere and the temperature is 298 K. What is the volume of the sample at STP?

Dec 19, 2015

The new volume is 41 mL.

Explanation:

Use the combined gas law $\frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2$.
$\text{STP=273.15 K and 1 atm}$

Given/Known
${P}_{1} = \text{0.90 atm}$
${V}_{1} = \text{50.0 mL}$
${T}_{1} = \text{298 K}$
${P}_{2} = \text{1 atm}$
${T}_{2} = \text{273.15 K}$

Unknown
${V}_{2}$

Solution
Rearrange the equation to isolate ${V}_{2}$ and solve.

$\frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2$

${V}_{2} = \frac{{P}_{1} {V}_{1} {T}_{2}}{{T}_{1} {P}_{2}}$

V_2=(0.90cancel"atm"xx50.0"mL"xx273.15cancel"K")/(298cancel"K"xx1cancel"atm")="41 mL"