Chapter 17.3, Problem 33LC

Interpretation Introduction

Interpretation: The amount of heat released when a certain amount of $\text{NaOH}$ is dissolved in water.

Concept introduction:

Enthalpy of the solution is defined as the heat change associated with the dissolution of a substance in a solvent resulting in infinite dilution at constant pressure. It is measured in $\text{kJ/mol}$ .

Answer to Problem 33LC

The amount of heat released when $\text{25}\text{.0 g}$ of $\text{NaOH}$ is dissolved in water is $27.81\text{ kJ}$

Explanation of Solution

The dissolution of $\text{NaOH}$ is represented by:

  $\text{NaOH(s)}\to {\text{Na}}^{\text{+}}{\text{(aq) +OH}}^{\text{-}}\text{(aq) }\Delta \text{H= -44}\text{.51 kJ/mol}$

The enthalpy change is negative, which means the reaction is exothermic and the heat is released during the reaction.

It is given that when $\text{1 mol}$ of $\text{NaOH}$ is dissolved, the energy released is $\text{44}\text{.51 kJ}$

Given amount of $\text{NaOH}$ = $\text{25}\text{.0 g}$

Moles of a substance is found by dividing the given amount of substance by the molecular mass of the substance.

  $\begin{array}{l}\text{moles of NaOH}=\frac{\text{given amount of NaOH}}{\text{Molar mass of NaOH}}\\ \text{moles of NaOH}=\frac{25.0g}{40.0\text{g/mol}}=0.625\text{mol}\end{array}$

For $\text{1 mol}$ of $\text{NaOH}$ dissolved, heat released is = $\text{44}\text{.51 kJ}$

Thus, for $0.625\text{mol}$ of $\text{NaOH}$ dissolved, heat released is = $\frac{44.51\text{ kJ}}{1\text{ mol}}\times 0.625\text{ mol}=27.81\text{ kJ}$