Question

A gas occupies 5 L at20 °C and 1 atm. What is its volume at 2 atm and 27 °C?

Answer 1

The volume will be 2.6 L.

This looks like a case where we can use the combined gas laws:

`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`

NTP is 1 atm and 20 °C, so

`p_1 = "1 atm"; V_1 = 5color(white)(l) "L"; T_1 = (20 + 273.15) K = 293.15 K"`
`p_2 = "2 atm";V_2 = ?; color(white)(m)T_2 = (27 + 273.15) K = 300.15 K"`

∴ `V_2 = 5 color(white)(l)"L" × (1 color(red)(cancel(color(black)("atm"))))/(2 color(red)(cancel(color(black)("atm")))) × (300.15 color(red)(cancel(color(black)("K"))))/(293.15 color(red)(cancel(color(black)("K")))) = "2.6 L"`