Chapter 15, Problem 63A

(a)

Interpretation Introduction

Interpretation: The maximum density of water needs to be determined.

Concept Introduction: Density is defined as the mass of a substance occupied per unit of volume. It changes with temperature.

Explanation of Solution

The given graph shows the density of water over the temperature range $0{}^{\text{o}}\text{C}$ to $20{}^{\text{o}}\text{C}$ .

  

From the graph, it can be seen that the maximum density of water is 1.0000 g/mL. This is the point at the peak of the curve obtained when density and temperature are plotted.

Therefore, the maximum density of water is 1.0000 g/mL.

(b)

Interpretation Introduction

Interpretation: The temperature at which the maximum density of water occurs needs to be determined.

Concept Introduction: Density is defined as the mass of a substance occupied per unit of volume. It changes with temperature.

Explanation of Solution

The given graph shows the density of water over the temperature range $0{}^{\text{o}}\text{C}$ to $20{}^{\text{o}}\text{C}$ .

  

From the graph, it can be seen that the maximum density of water is 1.0000 g/mL. This is the point at the peak of the curve obtained when density and temperature are plotted. Now, the point meets the x-axis (where the temperature is plotted) at $4{}^{\text{o}}\text{C}$ .

Therefore, the temperature at which the maximum density of water occurs is $4{}^{\text{o}}\text{C}$ .

(c)

Interpretation Introduction

Interpretation: Whether it is meaningful to expand the smooth curve if the graph to the left to temperatures below $0{}^{\text{o}}\text{C}$ or not needs to be determined.

Concept Introduction: The state of water also changes with a change in temperature. At $0{}^{\text{o}}\text{C}$ , the state of water changes from liquid to ice and at $100{}^{\text{o}}\text{C}$ , it changes from liquid to water vapor or gas.

Explanation of Solution

The state of water below $0{}^{\text{o}}\text{C}$ is ice. The density of ice is 0.917 g/mL. Thus, it causes a break in the curve at $0{}^{\text{o}}\text{C}$ . Thus, it is not meant to expand the smooth curve.

The main reason is that liquid water changes its state from liquid to solid (ice) at $0{}^{\text{o}}\text{C}$ . Due to changes in state, the smooth curve cannot be expanded.