Question

Gas storage containers are sometimes designed to store the gas at a low temperature. This allows more gas to be stored at a lower pressure, and therefore more safely. Consider a rigid (constant volume) gas container that can safely store nH moles of gas at a higher temperature TH = 303 K and pressure PH = 5.13 x 10^6 Pa. Calculate the number of moles of gas, nL, that this container can hold at a lower temperature TL = 124 K and pressure PL = 3.81 x 106 Pa? Give your answer as the ratio, nL/nH, to at least three significant digits.

Answer 1

Universal gas constant = R = 8.314 J/(mol.K)

Volume of the rigid gas container = V

Higher temperature of the gas = T_H = 303 K

Pressure of the gas at the higher temperature = P_H = 5.13 x 10⁶ Pa

Number of moles in the gas container at higher temperature = n_H

By ideal gas law at higher temperature,

P_HV = n_HRT_H

Lower temperature of the gas = T_L = 124 K

Pressure of the gas at the lower temperature = P_L = 3.81 x 10⁶ Pa

Number of moles in the gas container at lower temperature = n_L

By ideal gas law at lower temperature, (Volume remains constant)

P_LV = n_LRT_L

Dividing the two equations,

Ratio of moles of the gas in the cylinder at lower temperature to that at higher temperature = n_L/n_H = 1.81