Chapter 5

Class Notes

1. Energy: the capacity to do work
1. The first law of thermodynamics - the conservation of energy: energy can neither be created nor destroyed in chemical reactions, although it can be transferred (heat, light) or transformed (from heat to light, etc.)
2. Potential energy: the energy a body has based on its position (gravitational potential energy)
1. Chemical potential energy: energy stored in chemical bonds

3. Kinetic energy: energy associated with motion - translational, rotational, vibrational, spin
4. Internal energy: total energy, sum of potential and kinetic energies
5. Measured in calories and Joules (4.184 J = 1 cal)

2. Thermodynamics 101 - four important thermodynamic values
1. During the course of a chemical reaction the internal energy changes
1. ΔU = U_final - U_initial
2. ΔU = q + w = q - PΔV
3. Definitions
1. System: the part of the world in which we have an interest
2. Surroundings: everything else
1. Open system: a system that can exchange matter and energy with the surroundings
2. Closed system: a system that can exchange energy but not matter with the surroundings
3. Isolated system: a system that cannot exchange either matter or energy with the surroundings

3. Work: a transfer of energy that can be used to the change the height of a weight somewhere in the surroundings
1. In chemical reactions most work is PV work (expansion work), work done by an expanding gas

4. Heat: a transfer of energy as a result of a temperature difference between the system and the surroundings
5. Given ΔU = q + w = q - PΔV work and heat are equivalent ways of the changing the internal energy of the system
6. Sign conventions
1. From system to surroundings: (-)
2. From surroundings to system: (+)

2. Enthalpy: in a system at constant pressure the heat associated changes in internal energy is called enthalpy
1. H = U + PV
1. H_i = U_i + PV_i
2. H_f = U_f + PV_f
3. ΔH = H_f - H_i = (U_f - U_i) + P(V_f - V_i) = ΔU + PΔV
4. Since ΔU = q - PΔV in a system that does only PV work on its surroundings, then
5. ΔH = q + PΔV - PΔV = q
6. Sign conventions
1. Exothermic (-) - heat flows from system to surroundings
2. Endothermic (+) - heat flows from surroundings to system

7. Types of enthalpy (different processes that, at constant pressure, lead to changes in internal energy with consequent releases or absorbing of energy)
1. Enthalpy of reaction
2. Enthalpy of formation
3. Enthalpy of physical change (phase change)
4. Enthalpy of ionization and enthalpy of electron gain

3. Gibbs Free Energy - the energy available to do useful work changes during the course of chemical reactions - depends on enthalpy, entropy, and temperature

1. ΔG = ΔH - TΔS
2. -ΔG = spontaneous reaction; +ΔG = nonspontaneous reaction
1. S = entropy - a measure of disorder, usually increases during reactions (+) and is usually about 1% or less the size of ΔH
2. Usually: if -ΔH then -ΔG; if +ΔH, then +ΔG

3. Enthalpy of reaction (heat of reaction or ΔH_rxn )
1. General
1. Since ΔH_rxn = H_final - H_initial, then ΔH_rxn = H_products - H_reactants
2. Thermochemical equations: the coefficients of the balanced equation represent the number of moles of reactants and products producing the associated enthalpy change
1. 2 H_{2 (g)} + O_{2 (g)} => 2 H₂O_(g); ΔH_rxn = -483.6 kJ

2. The enthalpy of substances varies with their state of matter, it is essential that the state of each reactant and product be specified
3. Enthalpy is a extensive property - depends on the masses (the extent of the samples) involved in the reaction (as compared to intensive properties such as boiling point and melting point, which are independent of mass)
1. 2 H_{2 (g)} + O_{2 (g)} => 2 H₂O_(g); ΔH_rxn = -483.6 kJ
2. H_{2 (g)} + ½O_{2 (g)} => H₂O_(g); ΔH_rxn = -241.8 kJ
3. 20 H_{2 (g)} + 10 O_{2 (g)} => 20 H₂O_(g); ΔH_rxn = -4836 kJ
4. "Molar" enthalpy values and fractional coefficients

4. Enthalpy is an state function, i.e., the enthalpy change for a phase change or for a chemical reaction does not depend on the path taken from initial conditions to the final conditions
1. A path function depends on the way in which the final conditions are reached from the initial conditions
2. The road to the top of Pike's Peak: elevation vs. the length of the road to the top

5. ΔH_rxn is equal in magnitude but opposite in sign for the reverse reaction
1. CH_{4 (g)} + 2 O_{2 (g)} => CO_{2 (g)} + 2 H₂O_(l); ΔH_rxn = -890 kJ
2. CO_{2 (g)} + 2 H₂O_(l) => CH_{4 (g)} + 2 O_{2 (g)}; ΔH_rxn = +890 kJ

6. Stoichiometry
1. Nitroglycerin (NG) is a powerful explosive that creates four different gaseous products when detonated:
   
   4 C₃H₅(NO₃)_{3 (l)} => 6 N_{2 (g)} + O_{2 (g)} + 12 CO_{2 (g)} + 10 H₂O_(g); ΔH_rxn = -5684 kJ
   
   Calculate the enthalpy of reaction when 10.0 g of NG is detonated:
   
   (10.0 g NG) x (1 mol NG / 227.1 g NG) x (-5684 kJ / 4 mol NG) = -62.6 kJ
2. Calculate the enthalpy of reaction for the combustion of 100.0 g of methane gas:
   
   (100.0 g CH₄) x ( 1 mole CH₄ / 16.04 g CH₄) x (-890 kJ / mole CH₄) = -5549 kJ

4. Measuring enthalpy
1. Specific heat and heat capacity
1. Specific heat: the amount of heat required to raise the temperature of 1.00 g of a substance by 1 K
2. The greater the specific heat the more energy required to raise the temperature of a substance
1. The specific heats of solid aluminum, solid iron, and liquid water are 0.90 J/g·K, 0.45 J/g·K, and 4.18 J/g·K respectively. A 1.00 g sample of each substance is placed in identical glass test tube. The test tubes are immersed for 5 minutes in boiling water. At the end of the 5 minutes, the temperature of the three substances is measured. Which of the three will be the warmest? Which will be the coolest?

3. Heat capacity: the amount of heat required to raise the temperature of a substance by 1 K
4. Molar heat capacity: the amount of heat required to raise the temperature of 1 mole of a substance by 1 K

2. Calculating heat flow: q = (SH) x (m) x (ΔT)
1. How much heat is required to raise the temperature of 250.0 g of liquid water from 22°C to a temperature of 100°C?
   
   q = (4.18 J/g·K) x (250.0 g) x (100°C - 22°C / 1 K / 1°C) = 81588 J = 81.5 kJ
2. An aluminum pan weighing 750.0 g is filled with boiling water. The pan is emptied and placed in a freezer until it reaches the ambient temperature of 0°C. How much heat does the pan emit?
   
   q = (0.90 J/g·K) x (750.0 g) x (-100 K) = -67500 J = -67.5 kJ; since the heat is emitted the correct value is -67.5 kJ

3. Calorimetry (qualitative)

5. Hess's Law: if a reaction can be written as the sum of a series of two or more reactions, the overall enthalpy of reaction is equal to the sum of the enthalpies of reactions for each member of the series
1. A + B => C + D; ΔH_rxn = X kJ
   C + D => E + F; ΔH_rxn = Y kJ
   E + F=> G + H; ΔH_rxn = Z kJ
   
   overall: A + B => G + H; ΔH_rxn = X + Y + Z kJ
2. CH_{4 (g)} + 2 O_{2 (g)} => CO_{2 (g)} + 2 H₂O_(g); ΔH_rxn = -802 kJ
   2 H₂O_(g) =>2 H₂O_(l); ΔH_rxn = -88 kJ
   CH_{4 (g)} + 2 O_{2 (g)} => CO_{2 (g)} + 2 H₂O_(l); ΔH_rxn = -890 kJ
3. The molar enthalpy of combustion of solid carbon to carbon dioxide gas is -393.5 kJ / mole of carbon and the molar enthalpy of combustion of carbon monoxide gas to carbon dioxide gas -283.0 kJ / mole of carbon monoxide. Using these data calculate the enthalpy change for the combustion of solid carbon to carbon monoxide.
   
   C_(s) + O_{2 (g)} => CO_{2 (g)}; ΔH = -393.5 kJ
   CO_(g) + ½ O_{2 (g)} => CO_{2 (g)}; ΔH = -283.0 kJ
   
   C_(s) + O_{2 (g)} => CO_{2 (g)}; ΔH = -393.5 kJ
   CO_{2 (g)} => CO_(g) + ½ O_{2 (g)} ; ΔH = +283.0 kJ
   
   C_(s) + ½ O_{2 (g)} => CO_(g) ; ΔH = -393.5 kJ + 283.0 kJ = -110.5 kJ
4. Calculate ΔH for the reaction
   
   2 C_(s) + H_{2 (g)} => C₂H_{2 (g)}
   
   given the following reactions and their respective enthalpy changes:
   C₂H_{2 (g)} + 5/2 O_{2 (g)} => 2 CO_{2 (g)} + H₂O_(l); ΔH_rxn = -1299.6 kJ
   C_(s) + O_{2 (g)} => CO_{2 (g)}; ΔH_rxn = -393.5 kJ
   H_{2 (g)} + ½O_{2 (g)} => H₂O_(l); ΔH_rxn = -285.8 kJ
   
   2 CO_{2 (g)} + H₂O_(l) => C₂H_{2 (g)} + 5/2 O_{2 (g)} ; ΔH_rxn = +1299.6 kJ
   2 C_(s) + 2 O_{2 (g)} => 2 CO_{2 (g)}; ΔH_rxn = -787 kJ
   H_{2 (g)} + ½O_{2 (g)} => H₂O_(l); ΔH_rxn = -285.8 kJ
   
   2 C_(s) + H_{2 (g)} => C₂H_{2 (g)} ; ΔH = +1299.6 kJ - 787 kJ - 285.8 kJ = +226.8 kJ

6. Enthalpy of formation
1. ΔH°_f for a compound is the enthalpy change for the reaction that forms one mole of the compound from its elements with all elements in their standard states
1. "°" indicates that calculations were made with the substances in their standard states
2. Usually 298 K and 1 atm
3. If an element exists in two or more forms under standard conditions the most stable form is used in the calculation of ΔH°_f
4. The stoichiometry is always for the formation of one mole of compound (product)
5. ΔH°_f are always in units of kJ/mol of substance formed
6. ΔH°_f of the most stable form of an element in the standard state is 0 kJ/mol; no formation reaction is needed if the element already exists in the standard state

2. Using Hess's Law if we know ΔH°_f for the participants in a reaction (all of the reactants and all of the products) we can calculate ΔH_rxn
1. ΔH°_rxn = E (n)(ΔH°_{f prod}) - E (n)(ΔH°_{f rxt})

3. Examples
1. C₃H_{8 (g)} + 5 O_{2 (g)} => 3 CO_{2 (g)} + 4 H₂O_(l); ΔH_rxn = ?
   
   3 C_(s) + 4 H_{2 (g)} => C₃H_{8 (g)}; ΔH°_f = -103.85 kJ/mol
   3 x (C_(s) + O_{2 (g)} => CO_{2 (g)}); ΔH°_f = -393.5 kJ/mol
   4 x ( H_{2 (g)} + ½O_{2 (g)} => H₂O_(l)); ΔH°_f = -285.8 kJ/mol
   
   ΔH°_rxn = [(3 moles) x (-393.5 kJ/mol) + (4 moles) x (-285.8 kJ/mol)] - [(1 mole) x (-103.85 kJ/mol)] = -2219.85 kJ
   
2. Calculate the standard enthalpy change for the combustion of 1 mole of liquid benzene to carbon dioxide gas and liquid water.
   C₆H_{6 (l)} + 15/2 O_{2 (g)} => 6 CO_{2 (g)} + 3 H₂O_(l);
   ΔH°_rxn = [(6 moles) x (ΔH°_f CO_{2 (g)}) + (3 moles) x (ΔH°_f H₂O_(l))] - [(1 mole) x (ΔH°_f C₆H_{6 (l)}) + (15/2 moles) x (ΔH°_f O_{2 (g)})]
   ΔH°_rxn = [(6 moles) x (-393.5 kJ/mol) + (3 moles) x (-285.8 kJ/mol)] - [(1 mole) x (+49.0 kJ/mol) + (15/2 moles) x (0 kJ/mol)] = -3267 kJ
3. The standard enthalpy change for the reaction
   
   CaCO_{3 (s)} => CaO_(s) + CO_{2 (g)}; ΔH°_rxn = +178.1 kJ
   
   If the ΔH°_f for solid calcium oxide is -635.5 kJ/mol and for carbon dioxide gas is -393.5 kJ/mol, what is the standard enthalpy of formation of solid calcium carbonate?
   
   ΔH°_rxn = [(1 mole) x (ΔH°_f CaO_(s)) + (1 mole) x (ΔH°_f CO_{2 (g)})] - [(1 mole) x (ΔH°_f CaCO_{3 (s)} )]
   
   [(1 mole) x (ΔH°_f CaCO_{3 (s)} )] = [(1 mole) x (ΔH°_f CaO_(s)) + (1 mole) x (ΔH°_f CO_{2 (g)})] - [(1 mole) x (ΔH°_f CaCO_{3 (s)} )] - ΔH°_rxn
   
   ΔH°_f CaCO_{3 (s)} = [(1 mole) x (-635.5 kJ/mol ) + (1 mole) x (-393.5kJ/mol)] - [ +178.1 kJ] = -1207.1 kJ