• # question_answer 78)   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 1g$m{{L}^{-1}}$).

${{n}_{B}}(NaOH)=\frac{{{w}_{B}}}{{{m}_{B}}}=\frac{4}{40}=0.1$ ${{n}_{A}}({{H}_{2}}O)=\frac{{{w}_{A}}}{{{m}_{A}}}=\frac{36}{18}=2$ ${{x}_{B}}=\frac{{{n}_{B}}}{{{n}_{A}}+{{n}_{B}}}=\frac{0.1}{2+0.1}=\frac{0.1}{2.1}=0.0476$ ${{x}_{A}}=(1-0.0476)=0.9524$ Volume of solution = $\frac{\text{Mass}\,\text{of}\,\text{solution}}{\text{Density}\,\text{of}\,\text{solutions}}$ $=\frac{(4+36)}{1}=40mL$ Molarity of solution can be calculated as:                 $M=\frac{{{w}_{B}}\times 1000}{{{m}_{B}}\times V}=\frac{4\times 1000}{40\times 40}=2.5$