Chapter 16, Problem 91A

Interpretation Introduction

Interpretation: The molar mass of the unknown solute with the mass of $5.76\text{g}$ dissolved in $750\text{g}$ of benzene is to be calculated.

Concept introduction: Depression in freezing point is a term associated with the decrease in the value of the freezing point of solvents by the addition of solute molecules.

The formula used for calculating the depression in the freezing point is,

  $\Delta T_f=K_{f}m$

Here, $\Delta T_f$ is the freezing point depression, $K_f$ is the molal freezing point depression constant, and $m$ is molality.

The molecular mass can be calculated as,

  $Molecularmass=\frac{Givenmass}{numberofmoles}$   ...... (1)

The expression for molality is as follows:

  $m=\frac{\text{moles of solute}}{\text{Mass of solvent(kg)}}$   ...... (2)

Answer to Problem 91A

The molecular mass of the unknown solute with the mass of $5.76\text{g}$ dissolved in $750\text{g}$ of benzene is $85.5\text{g/mol}$ .

Explanation of Solution

The depression of the freezing point is $0.46°C$ .

The mass of the solvent is $750\text{g}$ .

Convert $\text{g}$ to $\text{kg}$ .

  $\begin{array}{c}750.0\text{g}=750\times \frac{1\text{kg}}{1000\text{g}}\\ =0.75\text{kg}\end{array}$

The molal freezing point depression constant of benzene is $5.12°{\text{Ckgmol}}^{-1}$ .

So,

Substitute $5.12°{\text{Ckgmol}}^{-1}$ for $K_f$ and $0.46°C$ for $\Delta T_f$ in the equation of freezing point depression.

  $\begin{array}{c}\Delta T_f=K_{f}m\\ m=\frac{0.46}{5.12}\\ =0.089\text{m}\end{array}$

The number of moles of the unknown solute can be calculated by using the formula of molality.

Number of moles of solute is,

Substitute $0.089$ for $m$ and $\text{0}\text{.75}\text{kg}$ for the mass of solvent in equation (2).

  $\begin{array}{c}\text{Number}\text{of}\text{moles}=\frac{0.089}{0.75}\\ =0.0673\text{mol}\end{array}$

Substitute, $5.76$ for a given mass and $\text{0}\text{.0673}$ for the number of moles in equation (1).

  $\frac{5.76}{\text{0}\text{.0673}}=85.5g/mol$

So, the molecular mass of the unknown solute is $85.5g/mol$ .

Conclusion

The molecular mass of the unknown solute dissolved in $750\text{g}$ of benzene is $85.5g/mol$ .