All of what we discuss in this section has been presented to you in your chemistry class. Boyle's law states that if the temperature of a gas is kept constant, then the product of the pressure and the volume is constant. Thus

Topic 3.2 ExtendedA – The gas laws

pV = constant

p1V1 = p2V2

If T = constant then Boyle's law

BOYLE'S LAW

0

10 20

30

Consider the following demonstration:A graduated syringe which is partially filled with air is placed in an ice bath and allowed to reach the temperature of the water.

Topic 3.2 ExtendedA – The gas laws

BOYLE'S LAW

p1 = 15 V1 = 10

p2 = 30 V2 = 5Why is the graduated syringe placed in the ice water?

p1V1 = 150

p2V2 = 150

Why doesn't it matter what the units are for pressure and volume?

T1 = 0°C

T2 = 0°C

Does it matter what the units are for temperature?

Charles' law states that if the pressure of a gas is kept constant, then the quotient of the volume and the temperature is constant. Thus

Topic 3.2 ExtendedA – The gas laws

V T

= constant

If P = constant then Charles' law

CHARLES' LAW

V1

T1

= V2

T2

where T is ABSOLUTE TEMPERATURE

We will define absolute temperature shortly.

We can put Boyle's and Charles' laws together into one law that we call the ideal gas law:

Topic 3.2 ExtendedA – The gas laws

THE IDEAL GAS LAW

pV T

= constant

p1V1

T1

=p2V2

T2

The Ideal Gas Law

If you memorize the IGL it reduces to Boyle's law if T is constant, and Charles' law if p is constant. No need to memorize all three.By the way, the great Wallahs of chemistry even figured out a value for the constant: NkB, where N is the number of molecules in the sample, and

kB = 1.3810-23 J/K Boltzmann's constant

Thus we can write

pV = NKBT

where T is ABSOLUTE TEMPERATURE

The Ideal Gas Law

Now we are ready to talk about the Kelvin temperature scale.

Topic 3.2 ExtendedA – The gas laws

ABSOLUTE ZERO AND THE KELVIN SCALE

Suppose we have a fixed volume filled with an ideal gas of some kind, and suppose we attach a pressure gauge to it, and a thermometer:Now we apply a heat source, and plot pressure vs. temperature:

0

10 20

30p

T (°C)-300 -200 -100 0 100 200 300

FYI: We can extrapolate our points to find the temperature at which we expect the pressure of the gas to become 0:

FYI: Different gases will have different slopes. But all will extrapolate to the same value of T when their pressure reaches 0:

FYI: That temperature is -273.15 °C.

-273.15 °C

FYI: Since there is no pressure less than zero, there is no temperature less than -273.15 °C. We take this temperature to be ABSOLUTE ZERO.

An alternate, and perhaps more useful form, of the ideal gas law looks like this:

Topic 3.2 ExtendedA – The gas laws

THE IDEAL GAS LAW (ANOTHER FORM)

where R is the universal gas constant and n (lower case) in the number of moles (mol) of the gas.

R = 8.31 J/mol·K Universal Gas Constant

pV = nRT The Ideal Gas Law

R = 0.0821 L·atm/mol·K

The second form is probably the one you used in chemistry, where volumes are in liters and pressures are in atmospheres.Don't forget, a mole of a substance is the quantity of it that contains Avagadro's number NA of molecules:

NA = 6.021023 molecules/mole Avagadro's Number