Chapter 20, Problem 1PS

In the discussion on the composition of air, mention is made of the fact that water vapor may have a concentration as high as 40,000 ppm. Calculate the partial pressure exerted by water vapor at this concentration. Assume that this represents a situation with 100% humidity. What temperature would be needed to achieve this value? (See Appendix G.)

Interpretation Introduction

Interpretation:

The partial pressure exerted by water vapor at $40,000ppm$ concentration and the temperature which is needed to achieve the calculated partial pressure should be determined.

Concept introduction:

Parts per million (ppm) concentrations: It is the ratio of the number of grams of solute for every one million grams of solution.

  $Partspermillion(ppm)=\frac{Massofsolute}{Massofsolution}\times {10}^6$

For gases, ppm refers to numbers of particles and hence to mole fraction. And the gas pressure exerted is directly proportional to the mole fraction.

Answer to Problem 1PS

The partial pressure exerted by water vapor at $40,000ppm$ concentration is $30.4mmHg$.

Explanation of Solution

For gases, ppm refers to numbers of particles and hence to mole fraction. And the gas pressure exerted is directly proportional to the mole fraction.

The pressure exerted by water vapor at $40,000ppm$ concentration is,

    $\begin{array}{c}\frac{40000}{1000000}ofoneatmosphere\cong 0.04\times 760mmHg\\ =30.4mmHg\end{array}$

This pressure partial pressure can be achieved if the temperature value reaches above $29{}^{0}C$.

Conclusion

The partial pressure exerted by water vapor at $40,000ppm$ concentration and the temperature which is needed to achieve the calculated partial pressure was determined