Chapter 13, Problem 98A

Interpretation Introduction

(a)

Interpretation:

The volume of air is to be calculated when pressure and temperature of the gas are given at two conditions.

Concept introduction:

Ideal gas equation helps to calculate volume of a gas at given temperature and pressure. According to this law,

$\mathrm{PV}=nRT$

Where

$\mathrm{P}$ is pressure of the gas

$\mathrm{V}$ is volume of the gas

$\mathrm{n}$ is the number of moles of the gas

$\mathrm{R}$ is the ideal gas constant

$\mathrm{T}$ is the temperature of the gas

Answer to Problem 98A

The volume of one breath is $1.17L$

Explanation of Solution

Ideal gas equation helps to calculate volume of a gas at given temperature and pressure. According to this law,

$\mathrm{PV}=nRT$

Or

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

Given data is:

$\begin{array}{l}{P}_1=760mmHg\\ P_2=253mmHg\\ V_1=0.50L\\ T_1=273K\\ T_2=-60°C\\ T_2(K)=T_2(°C)+273\\ =-60+273\\ =213K\end{array}$

Now substituting the values into formula,

$\begin{array}{c}{V}_2=\frac{P_1{V}_1{T}_2}{P_2{T}_1}\\ =\frac{760\times 0.50\times 213}{253\times 273}\\ =1.17L\end{array}$

Therefore volume of air is $1.17L$

(b)

Interpretation Introduction

Interpretation:

If percentage of oxygen is 14 % then what volume of air need to breathe by human?

Concept introduction:

Percentage calculations will help to solve the problem. More volume of air is to breathe at height to supply the body with same amount of oxygen.

Answer to Problem 98A

0.75L air is required to breathe by human to supply the body with same oxygen amount.

Explanation of Solution

$\begin{array}{c}Amountofair=\frac{21\%}{14\%}\times 0.50L\\ =0.75L\end{array}$