Chapter U3.18, Problem 5E

Interpretation Introduction

Interpretation: The vapor density at $100\%$ humidity for $35°\text{C}$ is 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 5E

Water vapor density at $\text{1}00\%$ relative humidity for $\text{35}°\text{C}$ is about $\text{2}.\text{2 mol}$ per $\text{1}000\text{ L}$ .

Explanation of Solution

The percent of maximum humidity for a specified temperature is called relative humidity. When the air holds the maximum concentration of water vapor for the temperature of the air, it is at $\text{1}00\%$ relative humidity.

The maximum vapor density at $\text{3}0°\text{C}$ is $\text{1}.\text{7}$ mol per $\text{1}000\text{ L}$ . So, in a region, if this value is $0.\text{85}$ , at $\text{3}0°\text{C}$ , then, relative humidity is,

  $\begin{array}{c}\left(\frac{0.\text{85}}{\text{1}.\text{7}}\right)\times \text{ 1}00\%=0.5\times 100\%\\ =50\%\end{array}$

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 $\text{1}00\%$ relative humidity and maximum vapor density are the same. So, the maximum vapor density value on the graph will be the value for vapor density at maximum relative humidity.

The value of y, for $\text{x }=\text{ 35}$ , is $\text{2}.\text{2}$ mol per $\text{1}000\text{ L}$ .