Chapter 8, Problem 8.108CP

Interpretation Introduction

Interpretation:

The volume of space occupied by $\text{1}\text{mol}$ of hydrogen atoms and the density of hydrogen gas in atom per litre should be determined if the gas pressure outside the space shuttle is ${\text{1×10}}^{\text{-14}}\text{mm}\text{Hg}$ at $\text{1}\text{K}$.

Concept Introduction:

Ideal gas Equation:

Any gas is described by using four terms namely pressure, volume, temperature and the amount of gas. Thus combining three laws namely Boyle’s, Charles’s Law and Avogadro’s Hypothesis the following equation could be obtained. It is referred as ideal gas equation.

$\begin{array}{l}\text{V }\propto \frac{\text{nT}}{\text{P}}\\ \text{V = R}\frac{\text{nT}}{\text{P}}\\ \text{PV = nRT}\end{array}$

Where,

$\begin{array}{l}\text{n = moles}\text{of}\text{gas}\\ \text{P = pressure}\\ \text{T = temperature}\\ \text{R = gas }\text{constant}\end{array}$

Avogadro’s hypothesis:

• To relate the amount of gas and the volume.
• $\begin{array}{l}\text{V}\propto \text{n}\\ \text{n}\text{is}\text{the}\text{number}\text{of}\text{molecules}\text{at}\text{constant}\text{T}\text{and}\text{P}\end{array}$
• $\begin{array}{l}\frac{{\text{V}}_{\text{1}}}{{\text{n}}_{\text{1}}}\text{=}\frac{{\text{V}}_{\text{2}}}{{\text{n}}_{\text{2}}}\\ {\text{V}}_{\text{2}}\text{=}{\text{V}}_{\text{1}}\frac{{\text{n}}_{\text{2}}}{{\text{n}}_{\text{1}}}\end{array}$