An aqueous solution of sodium chloride is marked $10$ % $(\frac{w}{w})$ on the bottle. The density of the solution is $1.071 g m l^{- 1} .$ What is its molality and molarity? Also, What is the mole fraction of each component in the solution?

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Solution

$100 g$ solution contains $10 g N a C l$

$w = 10 g, m_{N a C l} = 58.5$ , Volume of solution $= \frac{100}{1.071 \times 1000} l i t r e$

$w_{H_{2} O} = 100 - 10 = 90 g$

Molarity = $\frac{W t . o f s o l u t e}{m o l . w t . o f s o l u t e \times V_{i n L}} = \frac{10 \times 1.071 \times 1000}{58.5 \times 100} = 1.83 M$

Molality $= \frac{W t . o f s o l u t e}{m o l . w t . o f s o l u t e \times w e i g h t o f s o l v e n t i n K g} = \frac{10 \times 1000}{5.85 \times 90} = 1.90 m$

Mole fraction of $N a C l = \frac{w / m}{w / m + W / M} = \frac{10 / 58.5}{10 / 58.5 + 90 / 18} = 0.03$

Mole fraction of $H_{2} O = 1 - 0.03 = 0.97$

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