Chapter 11.5, Problem 43PP

Interpretation Introduction

Interpretation:

The combined gas law should be rearranged in terms of T₂.

Concept Introduction:

Boyle's Law gives the relationship between Pressure (P) and Volume (V).

According to Boyle's Law, the volume of gas changes inversely with the pressure of the gas if temperature and amount of a gas are constant.

PV = constant

  $\text{Pα}\frac{\text{1}}{\text{V}}$

Boyle’s Law can be written as:

  ${\text{P}}_{\text{1}}{\text{V}}_{\text{1}}{\text{=P}}_{\text{2}}{\text{V}}_{\text{2}}$ (Temperature and amount of a gas remain constant)

Where, P₁ and V₁ are the initial pressure and volume.

P₂ and V₂ are the final pressure and volume.

Charles’s Law gives the relationship between Volume (V) and Temperature (T)

According to Charles’s Law, the volume of gas has direct relationship with temperature of the gas if pressure and amount of a gas are constant.

  $\frac{\text{V}}{\text{T}}$ = constant

  $\text{VαT}$

Charles’s Law can be written as:

  $\frac{{\text{V}}_{\text{1}}}{{\text{T}}_{\text{1}}}\text{=}\frac{{\text{V}}_{\text{2}}}{{\text{T}}_{\text{2}}}$ (Pressure and amount of a gas remain constant)

Where, T₁ and V₁ are the initial temperature and volume.

T₂ and V₂ are the final temperature and volume.

Gay Lussac’s Law gives the relationship between Pressure (P) and Temperature (T)

According to Gay Lussac’s Law, the pressure of gas has direct relationship with temperature in Kelvin of the gas if volume and amount of a gas are constant.

  $\frac{\text{P}}{\text{T}}$ = constant

  $\text{PαT}$

Gay Lussac’s Law can be written as:

  $\frac{{\text{P}}_{\text{1}}}{{\text{T}}_{\text{1}}}\text{=}\frac{{\text{P}}_{\text{2}}}{{\text{T}}_{\text{2}}}$ (Volume and amount of a gas remain constant)

Where, T₁ and P₁ are the initial temperature and pressure.

T₂ and P₂ are the final temperature and pressure.

On combining above three laws, combined gas law is obtained.

The relationship between Pressure- Volume- Temperature of gases, which is studied in above laws and combined into a single relationship, is known as Combined Gas Law.

The mathematical expression for Combined Gas Law is given by:

  $\frac{{\text{P}}_1{\text{V}}_{\text{1}}}{{\text{T}}_{\text{1}}}\text{=}\frac{{\text{P}}_2{\text{V}}_{\text{2}}}{{\text{T}}_{\text{2}}}$ (Amount of a gas or number of moles remain constant)