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Molarity

If 5 mol of l...

Question

If 5 mol of liquid A and 10 mol of liquid B are mixed to form an ideal solution then the total pressure of solution will be (Pa=200 mmHg and Pb=400 mmHg )

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Solution

The number of moles of liquid A $n_{a}$ =5
The number of moles of liquid B $n_{b}$ = 10
Hence the Mole fraction of liquid A $X_{a} = \frac{n_{a}}{n_{a} + n_{b}} = \frac{5}{10 + 5} = \frac{5}{15} = \frac{1}{3}$
Hence the Mole fraction of liquid B $X_{b} = \frac{n_{b}}{n_{a} + n_{b}} = \frac{10}{10 + 5} = \frac{10}{15} = \frac{2}{3}$
The vapour pressure of liquid A is Pa=200 mmHg
The vapour pressure of liquid B is Pb=400 mmHg
The pressure of solution $P_{T}$ will be calculated as:

$P_{T} = X_{a} P_{a} + X_{b} P_{b}$
$= \frac{1}{3} \times 200 + \frac{2}{3} 400$
$= \frac{200}{3} + \frac{800}{3}$
$= \frac{1000}{3} = 333.33 m m H g$

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