Chapter 12, Problem 94E

Interpretation Introduction

Interpretation:

For $55.8\text{ g}$ of water and temperature change from $55°\text{C}$ to $0°\text{C}$, the mass of ice that would have to melt is to be determined.

Concept Introduction:

The heat of fusion is the amount of heat required to melt 1 mole of solid.

It is denoted by $\text{Δ}{H}_{\text{fus}}$.

For $1.0\text{ g}$ of ice, $\text{Δ}{H}_{\text{fus}}$ is equal to $\text{334 J}$ at the freezing point of water.

The heat required for melting of ice is taken from the water and it equals to heat energy released by water and thus, its temperature changes.

Heat released by water is calculated by,

$q=mC\Delta T$ …… (1)

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

The heat capacity of water is $4.186\text{ J}/\text{g}°\text{C}$.

The density of water is assumed to be $1.0\text{ g}/\text{mL}$ at a certain temperature.