1. Chapter 14 The Ideal Gas Law and Kinetic Theory

2. Hydrogen Oxygen Carbon Sodium Every element has an atomic mass (1 u = 1.6605 x 10 -27 kg) Measured in atomic mass units (u) ………

3. Molecules – combinations of atoms Ex: Water 2 Hydrogens 1 Oxygen H2OH2O = 2 (1.00794 u) + 1 (15.9994 u) Molecular mass = 2 (m H ) + 1 (m O ) = 18.0153 u

4. Objects contain billions of particles 1 mole of particles = 6.022 x 10 23 particles = N A Avogadro’s NumberEx: Calculate the mass in grams of 1 mole of hydrogen atoms. (The SI unit for quantity of a substance)

5. One mole of a substance has the same mass in grams (g) that one particle has in atomic mass units (u).

6. The Ideal Gas Law Web Link: Ideal GasIdeal Gas PV=nRT P = Pressure V = Volume n = # of moles R = 8.31 J/mol K T = Temp. (Kelvins) If N = # of particles PV=NkT k = Boltzmann’s Constant = 1.38 x 10 -23 J/K = R/N A

7. Ideal Gas at Constant Temperature Isothermic PV=nRT constant PV=constant P i V i = P f V f or Boyle’s Law Since Pressure and Volume are inversely proportional: P V

9. Ideal Gas at Constant Pressure PV=nRT constant or Charles’ Law

10. Use the ideal gas law to decide which answer best reflects the number of moles of particles in an automobile tire: a).0025 mol b).025 mol c) 2.5 mol d) 2500 mol

11. We haven’t yet calculated the speeds of the molecules in an ideal gas…… Web Link: Gas TemperatureGas Temperature Ideal Gas This molecule has an average speed This one has a different average speed

12. Distribution Curve:

13. What about the Kinetic Energy of a gas molecule? m v KE = ½mv 2 What about the average Kinetic Energy of a group of gas molecules? KE = ½mv rms 2

14. Recall: Higher temperature Greater average molecule speedMore Kinetic Energy KE  Temp Average KE of an ideal gas molecule (k = Boltzmann’s constant = 1.38 x 10 -23 J/K) Kelvin temperature

15. So now we can relate the mass, speed, and temperature of molecules in an ideal gas:  A single molecule has no temperature since temperature is an averaging effect.  Temperature is simply a measure of the average Kinetic Energy of the molecules of a substance. Notes:

16. Web Link: Molecules in MotionMolecules in Motion Two containers of different ideal gases have the same temperature. Do the molecules of both gases have the same v rms ? A. Yes B. No

17. Internal Energy (U) – the sum of all types of energies of the molecules of a substance For a Monatomic Ideal Gas: one-atom U = (# atoms)(½mv rms 2 ) Why isn’t this true for a Diatomic (2-atom)gas? Web Link: Diatomic MoleculeDiatomic Molecule Internal Energy of n moles of a monatomic, ideal gas at temp T (Example:Neon) (U  T for any ideal gas)

18. Diffusion – when molecules move from a region of higher concentration to a region of lower concentration perfume in air Solute – the substance that is diffusing Solvent – what it’s diffusing into Web Link: DiffusionDiffusion Examples: cream in coffee

19. Web Link: Brownian MotionBrownian Motion

20. Remember heat conduction? The equation for diffusion is similar. Just replace the conduction quantities with the diffusion quantities: A L Q mass (m) Fick’s Law of Diffusion T concentration diff. (C) k diffusion constant (D)

21. Chapter 15 Thermodynamics

22. Heat (Q) Chapters 12,13,14 Work (W) Chapter 6 Ex: Rub hands together W Q Car engine Q W Ex:

23. Surroundings System Walls can be either: Diathermal - heat can flow through or Adiabatic – heat can’t flow through In Thermodynamics we talk about the state of the system: Pressure, Volume & Temperature

24. 4 Laws of Thermodynamics(0 th, 1 st, 2 nd, 3 rd ) 0 th Law of Thermodynamics Consider 3 objects and their temperatures: T1T1 T2T2 T3T3 If T 1 = T 2 and T 2 = T 3 then T 1 = T 3 Duuuu

25. Recall: Forces do Work (W) Can change Kinetic Energy (KE) Can change Potential Energy (PE) Heat (Q) Can change Internal Energy (U) also In any of the above cases, Total Energy is conserved which brings us to…………

26. 1 st Law of Thermodynamics U = U f – U i = Q - W U = Change in internal energy of a system Q = Heat added to the system W = Work done by the system- (Work done on the system)

27. Ex: a)If 600 J of heat is added to a system as 200 Joules of work is done on the system, what is the change in its internal energy? b)If 300 J of heat is added to a system as 300 joules of work is done by the system, what is the change in its internal energy?

28. Ex: A monatomic, ideal gas 3 moles If the temperature is raised by 200 K while 5000 Joules of heat is added, find the work done on the gas. A. -2500 J B. +2500 J C. -7500 J D. +7500 J