# A sample of gas has a volume of 250 cm^3 at 28.5 °C and 95.9 kPa. What volume will the gas occupy at STP?

Nov 10, 2015

The volume of the gas at STP will be $\text{0.217 L}$.

#### Explanation:

$\text{STP=273.15 K and 100 kPa}$

Use the equation from the combined gas law, $\frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2$.

Given/Known
${P}_{1} = \text{95.9 kPa}$
${V}_{1} = \text{250 cm"^3"=250 mL"xx(1 "L")/(1000 "mL")="0.250 L}$
${T}_{1} = \text{28.5"^"o""C"+273.15="301.7 K}$
${P}_{2} = \text{100 kPa}$
${T}_{2} = \text{273.15 K}$

Unknown
${V}_{2}$

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

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

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

$\text{V"_2=((95.9 "kPa") * (0.250"L") * (273.15"K"))/((301.7"K")*(100"kPa"))="0.217 L}$