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\[m{{L}^{-1}}\]).

Answer:

  \[{{n}_{B}}(NaOH)=\frac{{{w}_{B}}}{{{m}_{B}}}=\frac{4}{40}=0.1\] \[{{n}_{A}}({{H}_{2}}O)=\frac{{{w}_{A}}}{{{m}_{A}}}=\frac{36}{18}=2\] \[{{x}_{B}}=\frac{{{n}_{B}}}{{{n}_{A}}+{{n}_{B}}}=\frac{0.1}{2+0.1}=\frac{0.1}{2.1}=0.0476\] \[{{x}_{A}}=(1-0.0476)=0.9524\] 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:                 \[M=\frac{{{w}_{B}}\times 1000}{{{m}_{B}}\times V}=\frac{4\times 1000}{40\times 40}=2.5\]