Chapter 8, Problem 8.84AQAP

Interpretation Introduction

Interpretation:

“The pressure of $N_2$ gas present in the cylinder” 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’ Law and the Avogadro’s Law

► Boyle’s Law: It states that at constant temperature, the pressure is inversely proportional to the volume

$P\alpha \frac{1}{V}$

► Charles’ Law: It states that at constant pressure, the volume of the gas is directly proportional to the temperature

$V\alpha T$

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

Volume of the gas $\alpha$ Number of molecules

$\alpha$ Moles of the gas

$V\alpha n$

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

$\text{Vα}\frac{\text{nT}}{\text{P}}$

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

$\text{PV= nRT}$

where, $\text{R=}$ 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}{$12th$}\right.$ the mass of an atom of $\text{carbon}-12$. It can be calculated by adding the atomic masses of all the atoms present in the molecule.

Given:

Volume of the cylinder, $\text{V}=15\text{L}$

Temperature of the gas, $\text{T}={25}^{0}C$

Mass of $N_2$ gas, $\text{m}=50\text{g}$