Question

What is the total pressure of the dry gas collected if the vapor pressure due to water at ${25^o}C$ is $24\;mm\;Hg$?
A. $24\;mm\;Hg$
B. $240\;mm\;Hg$
C. $736mm\;Hg$
D. $760mm\;Hg$

Answer 1

In many cases, we are interested in knowing the amount of gas evolved by a reaction. But since gases have small densities it is always difficult to find the mass of the gas. And also practically it is not possible to collect gas and find its mass. But for gases that are not particularly soluble in water, it is possible to collect the evolved gas by finding the displacement of water from a container. This process is known as the collection of gas over water.

Complete step by step answer:
During the collection of gas, the level of the water in the container will adjust such that the pressure inside will be equal to the outside of the container. Therefore we can say that the total pressure inside the container is equal to the atmospheric pressure.
The formula for finding the total pressure is given by Dalton’s law of pressure. It says that the total pressure in the container will always be equal to the sum of the individual pressure of the gas that we collected and the water vapor.
${P_T} = {P_{gas}} + {P_{{H_2}O}}$
Rearranging the above equation in order to find the pressure of the dry gas,
${P_{gas}} = {P_T} - {P_{{H_2}O}}$ …… (1)
Given that the vapor pressure due to water is equal to $24\;mm\;Hg$. Also, we said that the total pressure of the container will be equal to the atmospheric pressure which will be equal to $760{\text{ }}mm{\text{ }}Hg$. Therefore substituting this in the above equation we get,
${P_{gas}} = 760 - 24$
${P_{gas}} = 736\;mm{\text{ }}Hg$
Therefore the pressure of the dry is given as $736\;mm{\text{ }}Hg$
Therefore the correct option is C.

Note: Vapor pressure is said to be the pressure that is applied by the vapor of the liquid on its surface. Whenever we evaporate a liquid the gaseous molecules that are formed will escape into the air. But if we evaporate the liquid inside a closed container it cannot escape into the air. It will remain above the liquid. These evaporated particles will create a pressure above the liquid and this pressure is known as the vapor pressure.