Chapter 8, Problem 8.101CQ

Interpretation Introduction

Interpretation:

“The volume of the chamber containing ${\text{O}}_{\text{2}}$” should be calculated

Concept Introduction:

Here we have used the concept of ideal gases and its equation.

► Ideal gases are the gases which obeys the ideal gas equation under all conditions of temperature and pressure. The ideal gas equation can be obtained by combining the Boyle’s Law, Charles’s Law and Avogadro Law.

► Boyle’s Law: It states that at constant temperature, the pressure has an inverse relation with volume

$\text{Pα}\frac{\text{1}}{\text{V}}$

► Charles’s Law: It states that at constant pressure, the volume of the gas has direct relation with temperature

$\text{VαT}$

► Avogadro Law: It states that equal volumes of all gases under same conditions of temperature and pressure contains the same number of molecules

Volume of the gas $\alpha$ Number of molecules

$\alpha$ Moles of the gas

$\text{Vα}\text{n}$

► Combining these three laws, we get the ideal gas equation

$\mathrm{V}\alpha \frac{nT}{P}$

$\text{V = }\frac{\text{nRT}}{\text{P}}$

$\text{PV = nRT}$

where,

$\text{R}$ is universal gas constant

$\text{V}$ is the volume

$\text{n}$ is the number of moles

$\text{P}$ is the pressure

$\text{T}$ is the temperature

► The relation between number of moles and mass of the gas is

$\text{n = }\frac{\text{m}}{\text{M}}$

Where $\text{m}$ is the mass of the gas

$\text{M}$ is molar mass of the gaseous compound

► Molar mass is the number of times a molecule of the substance is heavier than $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$12^{\text{th}}$}\right.$ the mass of an atom of carbon $-12$.

Given:

Mass of ${\text{O}}_{\text{2}}\text{= 2400}\text{g}$

Pressure inside a hyperbaric chamber, $\text{P = 3}\text{.0}\text{atm}$

Temperature of the chamber, $\text{T = 28°C}$