Chapter U3.18, Problem 7E

Interpretation Introduction

Interpretation: For 25% humidity and temperature 30 ^oC, the water vapor density needs to be determined.

Concept Introduction:

The relative humidity is related to water vapor density as follows:

  $\text{Relative humidity}=\frac{\text{Measured water vapor density}}{\text{Maximum possible water vapor density}}\times 100\%$

Answer to Problem 7E

  $0.425\text{ moles}/1000\text{ L}$

Explanation of Solution

The maximum water vapor density can be seen from the water vapor density vs. temperature graph.

  

It can be seen from the graph that the water vapor density is approximately 1.7 moles/1000L at 30 ^oC. This corresponds to 100% humidity.

The relative humidity is related to water density as follows:

  $\text{Relative humidity}=\frac{\text{Measured water vapor density}}{\text{Maximum possible water vapor density}}\times 100\%$

The given relative humidity is 25% thus,

  $\text{25\%}=\frac{\text{Measured water vapor density}}{\text{1}\text{.7 moles/1000 L}}\times 100\%$

On rearranging,

  $\begin{array}{l}\text{Measured water vapor density}=\frac{\text{25\%}\times \text{1}\text{.7 moles/1000 L}}{100\%}\\ =0.425\text{ moles}/1000\text{ L}\end{array}$

Conclusion

Thus, the water vapor density at 30^oC is $0.425\text{ moles}/1000\text{ L}$ .