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A mixture of two gases A and B in the mole ratio 2 : 3 is kept in a 2 liter vessel. A second 3L vessel has the same two gases in the mole ratio 3 : 5. Both gas mixtures have the same temperature and same total pressure. They are allowed to inter- mix and the final temperature and the total pressure are the same as the initial values, the final volume being 5 liters. Given that the molar masses are $M_{A} and M_{B}$ What is the mean molar mass of the final mixture?

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$\frac{5 M_{A} + 8 M_{B}}{13}$

$\frac{77 M_{A} + 123 M_{B}}{200}$

$\frac{123 M_{A} + 77 M_{B}}{250}$

$\frac{123 M_{A} + 77 M_{B}}{150}$

answer is B.

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Detailed Solution

$Mean molar mass = \frac{(n_{A} + n_{A}^{'}) M_{A} + (n_{B} + n_{B}^{'}) M_{B}}{n_{A} + n_{A}^{'} + n_{B} + n_{B}^{'}} = \frac{77 M_{A} + 123 M_{B}}{200}$

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