Thermodynamics

1. Thermodynamics Thermodynamics is the study of systems involving energy in the form of heat and work.

2. First Law of Thermodynamics • The change in internal energy of a system (DU) must be related to the energy exchange of heat (q) and work (w). DU = q + w DU, q and w are measured in joules (J) the metric unit for energy

3. First Law of Thermodynamics • q is positive if heat is added to the system, and negative if heat is removed • w is positive if work is done on the system, and negative if work is done by the system.

4. What does it mean for the system to do work? • Work is simply a force multiplied by the distance moved in the direction of the force. • A good example of a thermodynamic system that can do work is the gas confined by a piston in a cylinder.

5. If the gas is heated, it will expand and push the piston up, doing work on the piston. If the piston is pushed down, the piston does work on the gas and the gas does negative work on the piston. An example of how work is done by a thermodynamic system

6. Pressure-Volume Work • Work = Force x distance • Pressure = Force/Area and, PDV = Force x distance So , Work (w) = -PDV *Vf -Vi must be positive and when work is done on the system (w) must be negative. DU = q – DVP

7. Sign Conventions • Positive sign – energy is absorbed from the surroundings, and work is done on the system • Negative sign - energy is released to the surroundings and work is done by the system.

8. Calorimetry • Heat capacity- the quantity of heat needed to change the temperature of the system 1K • Cp = q/ DT (units are J/k or J/oc) • Specific Heat capacity – the quantity of heat need to raise the temperature of 1 gram of a substance 1 oC • q = C m DT

9. Specific Heat • The quantity of heat required to raise 1 gram of water 1oC. • The higher the specific heat the harder it is to change the temperature of the substance. C (J/goC) • Al .092 • Cu. .385 • Ethanol 2.46 • Water 4.182

10. Calorimetry • Measures the amount of heat generated from a chemical reaction by letting the heat generated flow into a mass of cooler water. q= m DT C q = heat DT = Tf – Ti m = mass C = specific heat (J/g oC)

11. Coffee Cup Calorimeter • A coffee cup calorimeter is essentially a polystyrene (Styrofoam) cup with a lid. • The cup is partially filled with a known volume of water and a thermometer is inserted through the lid of the cup so that its bulb is below the water surface. • When a chemical reaction occurs in the coffee cup calorimeter, the heat of the reaction if absorbed by the water. • The change in the water temperature is used to calculate the amount of heat that has been absorbed or evolved in the reaction.

12. For example, a chemical reaction which occurs in 200 grams of water with an initial temperature of 25.0°C. The reaction is allowed to proceed in the coffee cup calorimeter. As a result of the reaction, the temperature of the water changes to 31.0°C. The heat flow is calculated: • qwater = 4.18 J/(g·°C) x 200 g x (31.0°C - 25.0°C) • qwater = +5.0 x 103 J • ΔHreaction = -(qwater)

13. Bomb Calorimeter • A coffee cup calorimeter is great for measuring heat flow in a solution, but it can't be used for reactions which involve gases, since they would escape from the cup. • The coffee cup calorimeter can't be used for high temperature reactions, either, since these would melt the cup. • A bomb calorimeter is used to measure heat flows for gases and high temperature reactions. • In a coffee cup calorimeter, the reaction takes place in the water. In a bomb calorimeter, the reaction takes place in a sealed metal container, which is placed in the water in an insulated container.

14. Bomb calorimetry is used to determine the enthalpy of combustion, DH, for hydrocarbons:

15. Bomb Calorimeter • In a coffee cup calorimeter, the reaction takes place in the water. • In a bomb calorimeter, the reaction takes place in a sealed metal container, which is placed in the water in an insulated container. • Heat flow from the reaction crosses the walls of the sealed container to the water. • The temperature difference of the water is measured, just as it was for a coffee cup calorimeter.

16. Bomb Calorimeter • Analysis of the heat flow is more complex than for the coffee cup calorimeter because the heat flow into the metal parts of the calorimeter must be accounted for (heat capacity, Cp): • qreaction = - (qwater + qbomb) • where qwater = 4.18 J/(g·°C) x mwater x Δt • qbomb = Cp x Δt

17. Calorimetry • A 1.5886 g sample of glucose (C6H12O6) was ignited in a bomb calorimeter. The temperature increased by 3.682oc. The heat capacity of the calorimeter was 3.56 kJ/oc, and the calorimeter contained 1.00 kg of water. Find the molar heat in kJ/molrxn C6H12O6 + 6 O2 6 CO2 + 6 H2O

18. Calorimetry qbomb = 3.562 kJ/oc (3.682oc) = 13.12 kJ qwater = 1000g (4.184 J/goc) (3.682oc) = 15400 J Qtotal = qbomb + qwater qtotal = - 28.52 kJ (exothermic) per molrxn 1.5886 g / 180.16g/mol = .0088177 mol -28.52 kJ/ .0088177 mol = -3234 kJ/molrxn

19. Enthalpy • Enthalpy is a measure of the total emery of a thermodynamic system. • Most chemistry reactions take place at constant pressure, open to the atmosphere. So, Enthalpy (H) is used to describes these types of reactions. H = U + PV

20. Enthalpy (H) – The Heat of the Reaction • The change in enthalpy (DH) is equal to the difference in the heat of the reaction. DH = DHfinal – DHinitial = DHproducts – DHreactants • Heat of formation (DHof) - the change in enthalpy when a compound forms from its pure elements. (table in back of text book) • DHof of a pure element = 0

21. Enthalpy and Internal Energy DH = DU + DVP • DVP = DngasRT @ const. T and P DH = DU + DngasRT • DU and DH are very close to the same value and are the same when no gas is generated by the reaction.

22. Hess’s Law • The heat of a reaction is equal to the sum of the individual DH values for each step. Example: What is the DH for C + ½ O2 CO? CO + ½ O2  CO2DH = -283.0 kJ C + O2  CO2DH = -393.5 kJ

23. What is the DH for C + ½ O2 CO? CO2  CO + ½ O2DH = +283.0 kJ C + O2  CO2DH = -393.5 kJ C + ½ O2  CO DH = -110.5 kJ