Chapter 8, Problem 8.68AP

Interpretation Introduction

Interpretation:

The Avogadro’s law should be explained basis on kinetic-molecular theory of gases.

Concept Introduction:

Kinetic-molecular theory of gases:

• Gases are made up of particles like atoms or molecules which randomly moves and there will be no attractive forces between them.
• Comparing the space occupied by the gas particles and the space between particles, the former is much smaller than the latter.
• The average kinetic energy of gas particles and the Kelvin temperature is proportional.
• There is an elastic collision between gas particles or with the wall of their container and thus no energy is lost during collision and total kinetic energy of the particles is constant.

Avogadro’s hypothesis:

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