Question

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?

Answer 1

The volume of gas in the cylinder is 456 L.

Explanation:

This is an example of a Combined Gas Laws problem.

`color(blue)(bar(ul(|color(white)(a/a)(p_1V_1)/T_1 = (p_2V_2)/T_2color(white)(a/a)|)))" "`

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"`

Your data are then:

`p_1 = "1.013 bar"; V_1 = "500 L"; T_1 = "(30.0 + 273.15) K" = "303.15 K"`

`p_2 = "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"`

The volume is 456 L.