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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 equal number of moles are:

PA=3PB

PA=2PB

2PA=3PB

3PA=2PB

Solution:

The correct option is A
2PA=3PB
Given that
VA=2VB
Z = compressibility factor
PV = ZnRT
P = pressure
V = volume
Z = compressibility factor
n = number of moles
R = gas constant
T = temperature
For gas A:
PA VA = nA ZARA T
For gas B:
PB VB = nB ZBRB T
Given that nA = nB and TA = TB
Then PA VA = PB VB (ZA/ZB)
Since VA = 2VB and ZA = 3ZB
PA (2VB) = PB VB (3)
2PA = 3PB