# Lecture09222

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Published on July 29, 2008

Source: slideshare.net

## Description

a supplemental resource for students

Gas State: Boyle’s, Charles’s and Avogadro’s Laws Lecture 9

The physical behavior of gas can be described completely by four variables: pressure (P), volume (V), temperature (T), and amount of substance (n).

Pressure, volume, temperature, and amount of gas are interdependent. Any one of them can be determined by measuring the other three.

Ideal gas exhibits simple linear relationships among pressure, volume, temperature, and amount. The higher the temperature and the smaller amount, the closer this real gas to the ideal.

Robert Boyle (1627-1691), British scientist

Robert Boyle (1627-1691), British scientist

Boyle’s book

Boyle’s law: at constant temperature, the volume occupied by a fixed amount of gas is inversely proportional to the applied (external) pressure.

Boyle’s law

Boyle’s law

Boyle’s law

Boyle’s law

Key mathematical points: The product of corresponding P and V values is a constant: PV = constant or P 1 V 1 =P 2 V 2 V is inversely proportional to P V is directly proportional to 1/P: V~1/P

The product of corresponding P and V values is a constant: PV = constant or P 1 V 1 =P 2 V 2

V is inversely proportional to P

V is directly proportional to 1/P: V~1/P

A sample problem on volume-pressure relationship.

Joseph Louis Gay-Lussac (1778-1850), French scientist

Joseph Louis Gay-Lussac (1778-1850), French scientist

Jacques Alexandre César Charles (1746–1823), French scientist

Jacques Alexandre César Charles (1746–1823), French scientist

Charles/Gay-Lussac’s law: at constant pressure, the volume occupied by a fixed amount of gas is directly proportional to its absolute temperature:

Charles’s law

Charles’s law

Important relationships: Amonton’s law. At constant volume, the pressure exerted by a fixed amount of gas is directly proportional to the absolute temperature: P~T or P/T=constant or P 1 /T 1 =P 2 /T 2 or P=constant x T The combined gas law : V~(T/P) or PV/T=constant or P 1 V 1 /T 1 =P 2 V 2 /T 2

Amonton’s law. At constant volume, the pressure exerted by a fixed amount of gas is directly proportional to the absolute temperature: P~T or P/T=constant or P 1 /T 1 =P 2 /T 2 or P=constant x T

The combined gas law : V~(T/P) or PV/T=constant or P 1 V 1 /T 1 =P 2 V 2 /T 2

A sample problem on volume-temperature relationship.

Given: A 58 L sample of dry air is cooled from 127°C to -23°C while the pressure is maintained at 2.85 atm. What is the final volume? Plan: As the pressure is constant, apply Charles’s law: V 1 /T 1 =V 2 /T 2 . Do not forget to convert temperatures into kelvins. Solution: V 2 =V 1 T 2 /T 1 V 2 =58L*250K/400K=36L - Looks realistic.

Given: A 58 L sample of dry air is cooled from 127°C to -23°C while the pressure is maintained at 2.85 atm. What is the final volume?

Plan: As the pressure is constant, apply Charles’s law: V 1 /T 1 =V 2 /T 2 . Do not forget to convert temperatures into kelvins.

Solution: V 2 =V 1 T 2 /T 1 V 2 =58L*250K/400K=36L - Looks realistic.

A sample problem on temperature-pressure relationship.

Lorenzo Romano Amedeo Carlo Avogadro (1776-1856), Italian scientist

Lorenzo Romano Amedeo Carlo Avogadro (1776-1856), Italian scientist

Avogadro’s law: at fixed temperature and pressure, equal volumes of any ideal gas contain equal number of particles (or moles). V~n or V/n=constant or V=constant x n

A sample problem on applying the volume-amount relationship.

THE END