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.

 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