Chapter 16, Problem 2STP

Interpretation Introduction

Interpretation: The mole fraction of methanol is to be calculated when 2 moles of methanol is dissolved in $45\text{g}$ of water.

Concept introduction: Mole fraction is a term that can be used to express solutions' concentration.

The formula that can be used for the calculation is,

  $X_a=\frac{n_a}{n_a+n_b}$

Here, $n_a$ are the moles of solvent, $n_b$ are the moles of solute and $X_a$ is mole fraction of solute.

Answer to Problem 2STP

The correct option is (A).

Explanation of Solution

The number of moles of solute can be determined by taking the ratio of the given mass and molecular mass.

Hence, the number of moles of methanol is $n_a=2\text{mol}$ .

The number of moles of water is calculated as:

  $\begin{array}{c}{n}_b=\frac{45}{18}\\ =2.5\text{mol}\end{array}$

Substitute $2$ for $n_a$ and $2.5$ for $n_b$ in the formula of mole fraction to calculate the mole fraction of methanol, $X_a$ .

  $\begin{array}{c}{X}_a=\frac{2}{2+2.5\text{mol}}\\ =0.44\end{array}$

Thus, the correct option is (A).