Question

If I initially have a gas at a pressure of 12 atm, a volume of 23 liters, and a temperature of 200 K, and then l raise the pressure to 14 atm and increase the temperature to 300 K, what is the new volume of the gas?

Answer 1

The new volume of the gas is 30 L.

Explanation:

This is an example of a Combined Gas Laws problem.

`color(blue)(|bar(ul((P_1V_1)/T_1 = (P_2V_2)/T_2|)`

We can rearrange this formula to get

`V_2 = V_1 × P_1/P_2 × T_2/T_1`

Your data are:

`P_1 = "12 atm"; V_1 = "23 L"; T_1 = "200 K"`

`P_2 = "14 atm"; V_2 = "?";color(white)(mll) T_2 = "300 K"`

∴ `V_2 = V_1 × P_1/P_2 × T_2/T_1 = "23 L" × (12 color(red)(cancel(color(black)("atm"))))/(14 color(red)(cancel(color(black)("atm")))) × (300 color(red)(cancel(color(black)("K"))))/(200 color(red)(cancel(color(black)("K")))) = "30 L"`

The volume is 30 L.