Chemistry - A Molecular Science

Chapter 7 States of Matter and Changes in State

The volume of a given amount of gas at

a constant temperature varies with its

pressure, and shortly after the invention of

the barometer, Robert Boyle found the

relationship, which is now called

Boyle’s law

:

The volume of a gas varies inversely with its

pressure; or the pressure-volume product of a

gas is constant as long as the amount

and temperature of the gas are constant.

PV = k(n,T)

Eq. 7.2

k(n,T) is a function of the number of moles (n) and the temperature (T) of the gas. Figure 7.3 shows the volume of one mole of gas as a function of its pressure at 0

oC.

ABSOLUTE TEMPERATURE AND CHARLES’ LAW Experiments with gases in the late 1700’s

and early 1800’s determined the relationship

between the volume of a gas and its temperature. As shown in Figure 7.4, the volume of a given amount of gas at constant pressure increases linearly with its temperature. Although the slope of the straight line varies with the number of moles and pressure of the gas, extrapolation of all lines to the temperature of zero volume yields the same temperature, -273.15

oC (degrees Celcius). At lower temperatures the volume of the gas would be

negative, which is not physically possible, so

we conclude that temperatures can be no

lower than -273.15

oC. The absolute temperature or Kelvin scale was defined based on this

absolute minimum in temperature.

K =

oC + 273.15

Eq. 7.3

Equation 7.3 shows that you add 273.15 to a

temperature in degrees Celsius to convert it

to the absolute scale. For example, water freezes at 0

oC, which is 273 K,* and boils at

100

oC, which is 373 K. Room temperature is usually assumed to be 25

oC, which is 298

K.

The absolute temperature must be used in all equations involving the temperature of a

chemical system.

However, either the Celsius or abso

lute scales can be used in equations

involving a

change

in the temperature of a system be

cause the unit size is the same in both

scales. Once the new temperature scale was defined, the relationship between the volume and temperature of a gas, which is known as

Charles' law

, could be stated as

The volume of a gas is directly proportional

to its temperature expressed in kelvins.

V = k(n,P)T

Eq. 7.4

k(n,P) is a constant that depends upon the numbe

r of moles of gas (n) and its pressure (P).

10080 60 40 20

002

4

6

Pressure (atm)

Volume (L)

PV=k

Figure 7.3 Boyle’s Law The volume of one mole of gas at 0

oC plotted versus its pressure in

atmospheres. k = 22.4 L-atm for 1 mole of gas at 0

oC, but it is a

function of both the number of moles and the temperature.

2 mol 1 mol0.6 mol0.2 mol

T = 0

100

200

300 K

t = -273

-200

-100

0

100 C

o

60 40 20 0

Volume (L)

V=k(t+273)=kT

Figure 7.4 Charles’ Law The volume of the specified number of moles of gas plotted as a function of its temperature. The bo

ttom scale is the temperature (t)

in degrees Celsius, while the bottom scale is the temperature (T) in kelvins.

* Note that the degree symbol (

o) is used for degrees Celsius (0

o C)

but not for kelvins (273 K).

© by

North

Carolina

State

University