Ncert Exercises & Solutions

If 4 g of NaOH dissolves in 36 g of $H_{2} O$ , calculate the mole fraction of each component in the solution. Also, determine the molarity of solution (specific gravity of solution is 1 g mL^-1).

Number of moles of NaOH,

n_{NaOH} = \frac{4}{40} = 0.1 mol {∵ n = \frac{Mass (g)}{Molar mass (g {mol}^{- 1})}}

Similarly, n_{H_{2} O} = \frac{36}{18} = 2 mol

Mole fraction of NaOH,

X_{NaOH} = \frac{moles of NaOH}{moles of NaOH + moles of H_{2} O}

X_{NaOH} = \frac{0.1}{0.1 + 2} = 0.0476

Similarly,

X_{H_{2} O} = \frac{n_{H_{2} O}}{n_{NaOH} + n_{H_{2} O}}

= \frac{2}{0.1 + 2} = 0.9524

Total mass of solution = mass of solute + mass of solvent

= 4 + 36 = 40 g

Volume of solution = \frac{Mass of solution}{specific gravity} = \frac{40 g}{1 g {mL}^{- 1}} = 40 mL

Molarity = \frac{Moles of solute \times 1000}{Volume of solution (mL)}

= \frac{0.1 \times 1000}{40} = 2.5 M

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