Chapter U3.66, Problem 4E

Interpretation Introduction

Interpretation: Whether it is possible for the water vapour density in the air to reach $\text{1}0$ moles per $\text{1}000\text{ L}$ at a temperature of $\text{4}0°\text{C}$ or not needs to be explained.

Concept Introduction: Water vapor concentration in air is termed as humidity. There is a limit on the number density of molecules of water which may be in the air for a given temperature. The air saturated at certain point due to which no net evaporation takes place further.

Answer to Problem 4E

It is possible for the water vapour density in the air to reach $\text{1}0$ moles per $\text{1}000\text{ L}$ at a temperature of $\text{4}0°\text{C}$ if the vapor density crosses limit of $\text{2}.\text{8}$ mol per $\text{1}000\text{ L}$ . Thus, vapor density of water cannot reach 10 mol per 1000L at a temperature of $\text{4}0°\text{C}$ .

Explanation of Solution

The water vapor concentration has an upper limit that can be in the air at the given temperature. The upper limit is termed as 100% relative humidity, or maximum vapor density. The graph showing variation in vapor density with temperature represents the maximum number density, that is, for air maximum vapor density is in temperatures range between $-\text{1}°\text{C}$ and $\text{4}0°\text{C}$ . The representation of maximum vapor density is done at Y-axis while representation of the temperature in $°\text{C}$ is done at X-axis.

The value of y, for $\text{x }=\text{ 4}0$ , is $\text{2}.\text{8}$ mol per $\text{1}000\text{ L}$ . Hence, at $\text{4}0°\text{C}$ maximum vapor density of water is about $\text{2}.\text{8}$ mol per $\text{1}000\text{ L}$ .

Hence, it is clear that the vapor density of water cannot reach 10 mol per 1000L at a temperature of $\text{4}0°\text{C}$ .