# A rigid cylinder with a movable piston contains 500 liters of a gas at 30.0 C with a pressure of 1.00 atmosphere. What is the volume of the gas in the cylinder at STP?

Jun 7, 2017

The volume of gas in the cylinder is 456 L.

#### Explanation:

This is an example of a Combined Gas Laws problem.

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \frac{{p}_{1} {V}_{1}}{T} _ 1 = \frac{{p}_{2} {V}_{2}}{T} _ 2 \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

We can rearrange this formula to get

V_2 = V_1 × p_1/p_2 × T_2/T_1

STP is defined as 1 bar and 0 °C.

We should therefore convert your original pressure of 1.00 atm to bars.

p_1 = 1.00 color(red)(cancel(color(black)("atm"))) × "1.013 bar"/(1 color(red)(cancel(color(black)("atm")))) = "1.013 bar"

${p}_{1} = \text{1.013 bar"; V_1 = "500 L"; T_1 = "(30.0 + 273.15) K" = "303.15 K}$
${p}_{2} = \text{1 bar"; color(white)(mm)V_2 = "?";color(white)(mml) T_2 = "(0 +273.15) K" = "273.15 K}$
V_2 = V_1 × p_1/p_2 × T_2/T_1 = "500 L" × (1.013 color(red)(cancel(color(black)("bar"))))/(1 color(red)(cancel(color(black)("bar")))) × (273.15 color(red)(cancel(color(black)("K"))))/(303.15 color(red)(cancel(color(black)("K")))) = "456 L"