Chapter U5.6, Problem 6E

a.

Interpretation Introduction

Interpretation: The amount of energy required to melt $\text{56 g}$ of ice needs to be calculated.

Concept introduction: The energy absorbed or released during a phase change under constant temperature is said to be latent heat. The heat energy required, $\text{Q}$ for a specific phase change for an object of mass, $\text{m}$ is given by the formula:

  $\text{Q = Lm}$ - (1)

Where $\text{L}$ represents latent heat.

Answer to Problem 6E

The amount of energy required to melt $\text{56 g}$ of ice is $\text{18}\text{.704 kJ}$ .

Explanation of Solution

The amount of energy required to melt $\text{56 g}$ of ice into water at constant temperature is calculated using equation (1) as:

  ${\text{Q = L}}_f\text{m}$

Where $\text{Q }$ represents energy of fusion, ${\text{L}}_f$ represents latent heat of fusion and $\text{m}$ is mass of the ice.

The value of ${\text{L}}_f$ is $334\text{ kJ/kg}$ and the value of $\text{m}$ is $\text{56 g}$ .

Converting mass from g to kg as:

  $\text{56 g}\times \frac{{10}^{-3}\text{ kg}}{1\text{ g}}\text{ = }0.056\text{ kg}$

Substituting the values as:

  $\begin{array}{l}\text{Q = }334\text{ kJ/kg}\times 0.056\text{ kg}\\ \text{Q = 18}\text{.704 kJ}\end{array}$

Hence, the amount of energy required to melt $\text{56 g}$ of ice is $\text{18}\text{.704 kJ}$ .

b.

Interpretation Introduction

Interpretation: The amount of energy required to melt $\text{56 mol}$ of ice needs to be calculated.

Concept introduction: The energy absorbed or released during a phase change under constant temperature is said to be latent heat. The heat energy required, $\text{Q}$ for a specific phase change for an object of mass, $\text{m}$ is given by the formula:

  $\text{Q = Lm}$ - (1)

Where $\text{L}$ represents latent heat.

Answer to Problem 6E

The amount of energy required to melt $\text{56 mol}$ of ice is $\text{336}\text{.7 kJ}$ .

Explanation of Solution

The amount of energy required to melt $\text{56 mol}$ of ice into water at constant temperature is calculated using equation (1) as:

  ${\text{Q = L}}_f\text{m}$

Where $\text{Q }$ represents energy of fusion, ${\text{L}}_f$ represents latent heat of fusion and $\text{m}$ is mass of the ice.

The value of ${\text{L}}_f$ is $334\text{ kJ/kg}$ and the value of $\text{m}$ for $\text{56 mol}$ of ice is determined as follows:

  $\text{number of moles = }\frac{\text{given mass }}{\text{Molar mass}}$

Since, molar mass of ice is 18 g/mol so:

  $\begin{array}{l}\text{56 moles = }\frac{\text{mass }}{\text{18 g/mol}}\\ \text{mass }=\text{ 56 moles}\times \text{18 g/mol}\\ \text{mass }=\text{ 1008 g}\\ \text{mass }=\text{ 1008 g}\times \frac{{10}^{-3}\text{ kg}}{1\text{ g}}\text{ = }1.008\text{ kg}\end{array}$

Substituting the values as:

  $\begin{array}{l}\text{Q = }334\text{ kJ/kg}\times 1.008\text{ kg}\\ \text{Q = 336}\text{.7 kJ}\end{array}$

Hence, the amount of energy required to melt $\text{56 mol}$ of ice is $\text{336}\text{.7 kJ}$ .