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?

Jul 3, 2016

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

${P}_{1} = \text{12 atm"; V_1 = "23 L"; T_1 = "200 K}$
${P}_{2} = \text{14 atm"; V_2 = "?";color(white)(mll) T_2 = "300 K}$
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"