A mixture of two gases A and B in the mol ratio 2 : 3 is kept in a 2 L vessel. A second 3 L vessel has the same two gases in the mol ratio 3 : 5. Both gas mixtures have the same temperature and same total pressure. They are allowed to intermix and the final temperature and total pressure are the same as the initial values, the final volume being 5 litres. Given that the molar masses are MA and MB, what is the mean molar mass of the final mixture?

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A mixture of two gases A and B in the mol ratio 2 : 3 is kept in a 2 L vessel. A second 3 L vessel has the same two gases in the mol ratio 3 : 5. Both gas mixtures have the same temperature and same total pressure. They are allowed to intermix and the final temperature and total pressure are the same as the initial values, the final volume being 5 litres. Given that the molar masses are M_A and M_B, what is the mean molar mass of the final mixture?

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

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

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

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

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$\frac{n_{A}}{n_{B}} = \frac{2}{3}$ $\frac{n_{A'}}{n_{B'}} = \frac{3}{5}$

nA = 2/3 n_B n_A’ = 3/5 n_B’

Put the value of n_A, n_B’, n_A’ and n_B’ and get.

mean molar mass $\frac{(n_{A} + n_{A'}) m_{A} + (n_{B} + n_{B'}) m_{B}}{(n_{A} + n_{B} + n_{A'} + n_{B'})}$

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