1. Ideal Gas Equation/Molar & Molecular Mass Thermal Physics Lesson 4

2. Learning Objectives Define a mole Calculate the number of moles in a gas using N=nN A Perform calculations using the ideal gas equation pV=nRT Describe the conditions for which a real gas behaves like an ideal gas

3. Avogadro’s Constant One mole of any gas contains the same number of particles. This number is called Avogadro’s constant and has the symbol N A. The value of N A is 6.02 × 10 23 particles per mole.

4. Calculating the Number of Moles The number of moles, n, of a gas can be can be calculated using:- Where N is the total number of molecules and N A is Avogadro’s constant (=6.02 × 10 23 )

5. Avogadro’s Law The most significant consequence of Avogadro's law is that the ideal gas constant has the same value for all gases. This means that the constant is given by:-

6. Deriving Ideal Gas Equation From Boyle’s Law: From Pressure Law: From Avogadro’s Law: Combining these three: Rewriting using the gas constant R: Therefore:-

7. The Ideal Gas Equation Combining the three gas laws gives the equation:- The constant is equal to nR. Works well for gases at low pressure and fairly high temperatures

8. Equation of State Recall that each phase can exist in a variety of states e.g. the temperature and pressure Thus the Ideal Gas Equation of State pV = nRT summarises the physically possible combinations of p, V and T for n moles of the ideal gas.