JEE Main · 2019 · 12 Jan 2019 · Shift 1 · States of Matter

The volume of gas A has is twice than that of gas B. The compressibility factor of gas

A

is thrice that that of gas

B

at same temperature. The pressure of gases for equal per moles are

(A) $3 P_{A} = 2 P_{B}$
(B) $2 P_{A} = 3 P_{B}$ ✓ Correct
(C) $P_{A} = 3 P_{B}$
(D) $P_{A} = 2 P_{B}$

Answer: (B)

Solution

From

Z = \frac{P V}{n R T}

we have

P = \frac{Z n R T}{V}

, so at the same temperature and for equal moles

P \propto \frac{Z}{V}

. Gas

A

has twice the volume of

B

and three times its compressibility factor, so

\frac{P _{A}}{P _{B}} = \frac{Z _{A}}{Z _{B}} \cdot \frac{V _{B}}{V _{A}} = 3 \times \frac{1}{2} = \frac{3}{2}

. That is the same statement as

2 P_{A} = 3 P_{B}

JEE Main · 2019 · 12 Jan 2019 · Shift 1 · Single correct option

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