Chapter 8, Problem 8.74AP

Interpretation Introduction

Interpretation:

The total mass of ${\text{O}}_{\text{2}}$ in a room at STP should be calculated if the air contains $\text{29\%}{\text{O}}_{\text{2}}\text{and}\text{79\%}{\text{N}}_{\text{2}}$ and the room is $\text{4}\text{cm}\text{long,}\text{5}\text{cm}\text{wide}\text{and}\text{2}\text{.5}\text{cm}\text{high}$

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