   # What mass of water vapor is present in a dormitory room when the relative humidity is 55% and the temperature is 23 °C? The dimensions of the room are 4.5 m 2 floor area and 3.5 m ceiling height. (See Study Question 93 for a definition of relative humidity and Appendix G for the vapor pressure of water.) ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 10, Problem 94GQ
Textbook Problem
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## What mass of water vapor is present in a dormitory room when the relative humidity is 55% and the temperature is 23 °C? The dimensions of the room are 4.5 m2 floor area and 3.5 m ceiling height. (See Study Question 93 for a definition of relative humidity and Appendix G for the vapor pressure of water.)

Interpretation Introduction

Interpretation:

The mass of water vapor present in the under given conditions should be determined.

Concept introduction:

Arrhenius equation:

• Arrhenius equation is a formula that represents the temperature dependence of reaction rates
• The Arrhenius equation has to be represented as follows

k=AeEa/RTlnk=lnAeEa/RTlnk=(EaR)(1T)+lnA

• Ea represents the activation energy and it’s unit is kJ/mol
• R represents the universal gas constant and it has the value of 8.314 J/K.mol
• T represents the absolute temperature
• A represents the frequency factor or collision frequency
• e represents the base of natural logarithm
•  Arrhenius equation equation was proposed by Svante Arrhenius in 1889.

### Explanation of Solution

Given:

percentage of humidity = 55%Temperature = 23C = 273.15+23= 296.15KDimensions = 4.5m2×3.5m =15.75m3

Using the ideal gas equation the mass present in the given amount of humidity is determined as follows,

It is given in appendix that the vapor pressure of water at given 23 is 21.1mmHg

Partial pressure = vapor pressure × relative humidity=2799

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