Chapter 12, Problem 96E

Interpretation Introduction

Interpretation: The amount of evolved heat in kilojoules needed to warm given amount of ice is to be calculated.

Concept Introduction: The amount of heat required to melt 1 mole of a solid is known as heat of fusion. It is denoted by the symbol $\text{Δ}{H}_{\text{fus}}$. For water, $\text{Δ}{H}_{\text{fus}}$ is equal to $6.02\text{ kJ/mol}$.

The amount of heat required to vaporize 1 mole of liquid is termed as heat of vaporization.

It is denoted by the symbol $\text{Δ}{H}_{\text{vap}}$.

For water, $\text{Δ}{H}_{\text{vap}}$ is equal to $\text{40}\text{.7 kJ/mol}$.

Calculate the heat released by water as:

$q=mC\Delta T$

Here, m is the mass of water, C is the heat capacity of water in that state and $\Delta T$ is the temperature change.

For liquid water, heat capacity is $4.186\text{ J}/\text{g }°\text{C}$.

For steam, heat capacity is $\text{1}\text{.84 J}/\text{g}°\text{C}$.

For ice, heat capacity is $\text{2}\text{.09 J}/\text{g }°\text{C}$.

Number of moles $\left(n\right)$ is equals to mass of species divided by its molar mass.

$n=\frac{\text{mass}}{\text{molar mass}}$