The volume of gas A is twice than that of gas B . The...

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 same temperature. What are the pressures of the gases for equal number of moles?

Options

A $2{P}_{A} = 3{P}_{B}$
B ${P}_{A} = 2{P}_{B}$
C $3{P}_{A} = 2{P}_{B}$
D ${P}_{A} = 3{P}_{B}$

Correct answer

A. $2{P}_{A} = 3{P}_{B}$

Step-by-step solution

PV = ZnRT

{V}_{A} = 2{V}_{B}

and

{Z}_{A} = 3{Z}_{B}

P = \dfrac{ZnRT}{V}

\dfrac{{P}_{A}}{{P}_{B}} = \dfrac{{Z}_{A}{V}_{B}}{{Z}_{B}{V}_{A}} = \dfrac{3{Z}_{B} \times {V}_{B}}{{Z}_{B} \times 2{V}_{B}} = \dfrac{3}{2}

2{P}_{A} = 3{P}_{B}

At constant

T

and moles;

P ∝ \dfrac{Z}{V}

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