Chapter 17.3, Problem 23SP

Interpretation Introduction

Interpretation: The amount of heat required to melt $\text{50}\text{.0 g}$ of popsicle at $\text{0°C }$ with the same molar mass and heat of fusion as water.

Concept Introduction: The enthalpy of fusion 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 23SP

The amount of heat required to melt $\text{50}\text{.0 g}$ of popsicle at $\text{0°C }$ with the same molar mass and heat of fusion as water is

Explanation of Solution

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

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

As the molar mass and heat of the fusion of popsicle is the same as that of water, the enthalpy of the fusion of popsicle will be the same.

  $\text{1 g}$ of popsicle at $\text{0°C }$ will require heat to melt = $\text{343 J}$

Thus, $\text{50}\text{.0 g}$ of popsicles at $\text{0°C }$ will require heat to melt $\frac{\text{343 J}}{\text{1}\text{.0 g}}\text{×50}\text{.0 g=17150 J=}\frac{17150}{1000}\text{ kJ=17}\text{.15 kJ}$