Question

Find out the mole fraction of solute in an aqueous solution of $30\%\mathrm{NaOH}$.

Answer 1

Mole fraction$\left({\mathrm{x}}_{\mathrm{i}}\right)$:

1. It is defined as the ratio of the number of moles of solute to the total number of moles in the mixture.
2. $x_i=\frac{n_i}{n_{total}}=\frac{molesofsolute}{totalmolesofmixture.}$

Part-$1$: Calculating the mass of the components of the mixture.

1. As it is mentioned aqueous solution so there is water present in the mixture.
2. $30\%\mathrm{NaOH}$ means in $100\mathrm{g}$ solution $30\mathrm{g}\mathrm{NaOH}$ is present.
3. The amount of water $=100-30=70\mathrm{g}$

Part-$2$: Calculating the number of moles$\left(n\right)$

1. $n_{NaOH}=\frac{30}{40}=0.75mol$
2. $n_{H_{2}O}=\frac{70}{18}=3.88mol.$
3. Total number of moles $=3.88+0.75=4.63mol$

Part-$3$: Calculating mole fraction:

$x_{NaOH}=\frac{n_{NaOH}}{n_{NaOH}+n_{H_{2}O}}=\frac{0.75}{4.63}=0.162$