Question

The volume of gas A is twice than that of gas B. The compressibility factor of gas A is thrice than that of gas B at the same temperature. The pressures of the gases for an equal number of moles are ______.

Options

• 3P_A = 2P_B

• 2P_A = 3P_B

• P_A = 3P_B

• P_A = 2P_B

Answer 1

The volume of gas A is twice than that of gas B. The compressibility factor of gas A is thrice than that of gas B at the same temperature. The pressures of the gases for an equal number of moles are 2P_A = 3P_B.

Explanation:

Compressibility factor is given by,

Z = `"PV"/"RT"`

∴ `"Z"_"A"/"Z"_"B" = ("P"_"A""V"_"A")/("P"_"B""V"_"B")`

Given Z_A = 3Z_B, V_A = 2V_B

`(3"Z"_"B")/("Z"_"B") = ("P"_"A" xx 2"V"_"B")/("P"_"B" xx "V"_"B")`

⇒ `3 = ("P"_"A")/("P"_"B") xx 2`

2P_A = 3P_B