3. The gas laws
Summary and ideal gas equation P.16

We now have three gas laws:

For a fixed mass of gas: kept constant
Pressure law: p/T = constant1 volume
Charles law: V/T = constant2 pressure
Boyle’s law p.V = constant3 temperature
We can combine these into a single equation as follows:
p.V = constant4.T

This is for a fixed mass, i.e. a constant number of particles. What if the number of particles changes?

Doubling the number of particles will double the volume of a gas. So:
V = constant5.N at constant T and P
N is the number of particles
If we combine these last two equations, we get:
p.V = N.k.T N is the number of molecules;
k is a special constant called the Boltzman constant. It has the value: 8.31 J K-1

And in moles . .
A mole of gas has 6.0 x 1023 particles (this is the Avogadro number, NA). So, for n moles of a gas, we can say that:
p.V = n.R.T Where n is the number of moles;
R is the molar gas constant. It has the value: 1.38 x 10–23 J K–1 mol-1

This is the ideal gas equation.

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Question 13
The mole is a fixed amount of gas consisting of 6 x 1023 particles. This number is the Avogadro number (NA). Show, using the equations above, that R/k= NA.

Summary                                           Close
  • the ideal gas equation is:
  • p.V = N.k.T