Question

4.000 x 10^3 L of propane gas is held in a tank at 25 °C. The tank has a moveable diaphragm to keep the pressure constant at 200 kPa. If the temperature falls to -5 °C on a cold winter day, what volume will the gas occupy?

Answer 1

1) list your givens and convert if necessary

P₁ = 200 kPa

V₁ = 4.000 × $10^{3}$ L

T₁ = 298.15 K

P₂ = 200 kPa

V₂ = ?

T₂ = 268.15 K

2) rearrange formula

$\frac{P_{1}V_{1}}{T_{1}}=\frac{P_{2}V_{2}}{T_{2}}\\\\V_{2}=\frac{T_{2}P_{1}V_{1}}{P_{2}T_{1}}$

3) solve

$V_{2}=\frac{(268.15\ K)(200\ kPa)(4.000\ x\ 10^{3} L)}{(200\ kPa)(298.15\ K)}$

V₂ = 3597.518028 L (round as you wish)