Chapter 17.3, Problem 22SP

Interpretation Introduction

Interpretation: The amount of ice at $\text{0}°\text{C}$ that could be melted by the addition of a certain amount of heat.

Concept Introduction: The enthalpy of fusion, ${\text{ΔH}}_{\text{fus}}$ , is the amount of energy that must be added to a solid substance to transform a quantity of that substance into a liquid at constant pressure.

Answer to Problem 22SP

The amount of ice at $\text{0}°\text{C}$ that could be melted by the addition of $\text{0}\text{.400 kJ}$ of heat is $\text{1}\text{.17g}$

Explanation of Solution

The enthalpy of fusion of ice at $\text{0}°\text{C}$ is $\text{343 J/g}$ .

This means to convert $\text{1 g}$ of ice at $\text{0}°\text{C}$ to water at $\text{0}°\text{C}$ , $\text{343 J}$ of heat must be absorbed by ice.

Amount of heat given = $\text{0}\text{.400 kJ=0}\text{.400}\times \text{1000 J=400 J}$

  $\text{343 J}$ of heat is used for conversion of = $\text{1 g}$ of ice at $\text{0}°\text{C}$ to water

Thus, $\text{400 J}$ of heat is used for the conversion of = $\frac{\text{1 g}}{\text{343 J}}\text{×400 J=1}\text{.17 g}$