# If 4 g of NaOH dissolves in 36g of H2O, calculate the mole fraction of each component in the solution. Also, determine the molarity

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If 4 g of NaOH dissolves in 36g of H2O, 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 )

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$X_{NaOH} =\frac{n_{NaOH}}{n_{NaOH}+n{H_2O}}$

$\frac{\frac{W_{NaOH}}{M_{NaOH}}}{\frac{W_{NaOH}}{M_{NaOH}}+\frac{W_{H_2O}}{M_{H_2O}}}$

$\frac{\frac{4}{40}}{\frac{4}{40}+\frac{36}{18}}$

$\frac{\frac{1}{10}}{\frac{1}{10}+2}$ = $\frac{\frac{1}{10}}{\frac{21}{10}}$ = $\frac{1}{10}$ x $\frac{10}{21}$ = $\frac{1}{21}$

= 0.047

$\because$ xNaOH + xH2O = 1

$\therefore$ xH2O = 1 - 0.047 = 0.953

Mass of solution = 36 + 4 = 40g

Volume of solution = Mass x Specific gravity

= 40 x 1 = 40 ml

M = $\frac{W_B}{M_B}$ x $\frac{1000}{40}$ = 2.5 M
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