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Concentration Terms

A very dilute...

Question

A very dilute saturated solution of a sparingly soluble salt $A_{3} B_{4}$ has a vapour pressure of $20 m m$ of $H g$ at temperature $T$ , while pure water exerts a pressure of $20.126 m m H g$ at the same temperature.
The solubility product constant of $A_{3} B_{4}$ at the same temperature is $5.4 \times 10^{- x}$
value of x is __________.

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Solution

$P_{s} = 20 P^{\circ} = 20.0126$

$\frac{P^{\circ} - P_{s}}{P^{\circ}} = \frac{0.0126}{20} = \frac{n}{n + N} = \frac{n}{N}$

$\frac{m o l e s o f s o l u t e}{m o l e s o f H_{2} O} = 0.0063$

$1 m o l e H_{2} O = 18 g = 18 m L$

$18 m L$ solution $= 0.00063 m o l e$

$1 L$ solution $= \frac{0.00063}{18} \times 1000 = 0.35 m o l e / L$

Let solubility of salt $A_{3} B_{4}$ is $s$ then

$7 s = 0.035$

$s = 0.005 m o l e / L$

$k_{s p} = 3^{3} . 4^{4} (s)^{7} = 27 \times 256 \times (0.005)^{7}$

$k_{s p} = 5.4 \times 10^{- 13}$

$x = 13$

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