Real Gases Do Not Behave Ideally

CH4

H2

N2

CO2

Idealgas

2.0

1.0

00 200 400 600 800 1000

P (atm)

PVnRT

Equation of State of an Ideal Gas

• Robert Boyle (1662) found that at fixed temperature– Pressure and volume of a gas is inversely proportional

PV = constant Boyle’s Law

• J. Charles and Gay-Lussac (circa 1800) found that

at fixed pressure– Volume of gas is proportional to change in temperature

Volume

Temp-273.15 oC

All gases extrapolate to zero volume at a temperature corresponding to –273.15 oC (absolute zero).

He CH4

H2O

H2

Copyright © 2007 Pearson Benjamin Cummings. All rights reserved.

T1 T2

V1 V2=

(Pressure is held constant)

T1 T2

P1 P2=

(Volume is held constant)

CharlesCharles Gay-LussacGay-Lussac

Kelvin Temperature Scale

• Kelvin temperature (K) is given by

K = oC + 273.15 where K is the temperature in Kelvin, oC is temperature in Celcius

• Using the ABSOLUTE scale, it is now possible to write Charles’ Law as

V / T = constant Charles’ Law• Gay-Lussac also showed that at fixed volume

P / T = constant • Combining Boyle’s law, Charles’ law, and Gay-Lussac’s law,

we have

P V / T = constant

Gay-Lussac

Charles