Chapter 6 Page 1

CHAPTER SIX: THERMOCHEMISTRY

1. Thermochemistry is a branch of chemistry concerned with energy changes accompanying chemical and physical processes.

2. Examples:

a. heat liberated in a chemical reaction. b. work done in motion of a piston. c. heat required to change physical state. d. conditions required to attain equilibrium. (not in this chapter) e. forces driving processes that occur spontaneously. (not in this chapter)

A. Energy and its Units. (Section 6.1)

Energy = capacity to do work or transfer heat. 1. Kinetic Energy - energy of motion (mechanical)

€

Ek =mv 2

2

m=mass v = speed 2. Potential Energy - energy possessed by virtue of position or composition.

(gravitational, electrical, chemical, nuclear, etc.)

Ep = mgh g = acceleration of gravity = 9.81 m/s2 h= height

Chapter 6 Page 2

3. The SI Unit of Energy is the Joule (J). 1 Joule = 1 kg m2/s2 4. Problem: suppose a 50 kg object is traveling at 30 m/s. What is its kinetic energy?

€

Ek =mv2

2=50kg∗ 30 m s( )2

2= 22500kgm2 s2 = 22500J ≈ 22kJ

5. Problem: what is the potential energy of a 50 kg object suspended 30 m above ground

level? Ep = mgh = 50 kg * 9.81 m/s2 * 30 m = 14711 J ≈ 15 kJ 6. More common everyday unit of energy is the calorie (cal)

1 cal = energy required to raise the temperature of 1 gram of liquid water by 1 degree Celsius.

1 cal = 4.184 J 7. Nutritionists “Calorie” is really 1000 cal: 1 “Calorie” = 1000 cal = 1 kcal 8. Problem: About 1 joule of energy is required for the heart to beat once. Heart rate

averages 1 beat/second. How much energy is required for entire day of heart function in calories?

1 Joule/beat x 1 beat/sec x 60 sec/min x 60 min/hr x 24 hr/1 day x 1 cal/4.184 = 2.065 x 104 cal. How many nutritional Calories? 2.065 x 104 cal x 1 “Cal”/1000 cal = 20.65 “Cal” 9. Internal energy: consider the 50 kg object again. We calculated its kinetic energy by

considering its motion as a whole. However, even when the object is at rest, since it consists of atoms and molecules that are in constant rapid ‘thermal’ motion, it still has energy. This is its Internal Energy U.

Etot = Ek + Ep + U When we consider a lab sample, we consider its thermodynamic internal energy U.

Chapter 6 Page 3

10. Law of Conservation of Energy:

Energy is neither created or destroyed but may be converted between various forms.

This is the essence of First Law of Thermodynamics.

B. Heat of Reaction. (Section 6.2)

1. We are interested in the heat liberated or absorbed in a chemical reaction or physical

change. 2. Necessary terminology needed: System = that sample of matter we are concerned with. Surroundings = environment around the system. Universe = system and surroundings. Thermodynamic state = set of conditions that specify the properties of a system. State variables = P, V, T, U, H, etc. (all capital lettered functions) Change in a state variable X = ΔX.

example ΔU = Ufinal - Uinitial

Exothermic processes are those releasing energy to the surroundings in the form of heat.

Endothermic processes require absorption of energy from the surroundings to occur. 3. Heat = a form of energy called thermal energy, a manifestation of the random, chaotic

molecular motion in a sample (extensive property). 4. Temperature = a measure of the intensity of heat, the “hotness” or “coldness” of a

body, which relates to heat energy per amount of material (an intensive property). 5. Heat always flows spontaneously from a hotter body to a colder body, high T to low

T.

Chapter 6 Page 4

6. Can’t measure heat energy directly, but we can measure temperature change.

q = Heat flow across the system boundary is (+) if heat flowed in is (-) if heat flowed out

Heat of reaction = q necessary to restore a system’s temperature after a reaction has taken place in the system.

7. Example: 20 mL of aqueous 1 M NaOH is poured into 20 mL of 1 M aqueous HCl.

Both samples were initially at 25°C. The temperature rises several degrees, and as a result, heat flows out of the system into the surroundings until the solutions are eventually restored to 25 °C.

Heat of reaction = q Is q positive or negative?

C. Statement of First Law.

1. U ≡ total internal energy possessed by a system. 2. q = heat absorbed by system during a process. 3. w = work done on system during a process. 4.

ΔU = q + w 5. Scenario:

w = work involved expanding against its surroundings = -PΔV

Chapter 6 Page 5

6. If system is heated but not allowed to respond in any way, then:

ΔU = q

7. So all heat absorbed in a process in which system is not allowed to expand against its

surroundings (constant volume) goes into increasing its internal energy. All energy input remains in the system.

D. Enthalpy Changes. (Section 6.3) 1. Most processes we care about occur at constant Pressure, not constant Volume. 2. Example: Heating an open beaker of water. 3. Heat absorbed by system heated at constant pressure.

↑↑ expands slightly against surroundings Tiny amount of energy input q does not end up increasing U q > ΔU

4. Enthalpy H = “heat content” of a system. enthalpy change = ΔH = q occurring under constant P 5. ΔH slightly > ΔU. 6. Later, when the system is asked to give back its energy as heat, it can give back more

than ΔU; it can give back ΔH.

q

Chapter 6 Page 6

7. Enthalpy and Energy are nearly synonymous, but ΔH is more directly measurable for heat transfers under constant P conditions.

H = U + PV ΔH = ΔU + Δ (PV) But if reaction happening at constant P last term becomes: ΔH = ΔU + PΔV

PΔV = the work done = the energy expended by the system to expand against its surroundings in order to keep the pressure constant.

This term is typically small compared to ΔH or ΔU. E. Thermochemical Equations. (Section 6.4)

1. The ΔH of reaction always refers to enthalpy change of a reaction as it is written,

interpreting coefficients as moles:

2H2(g) + O2(g) → 2H2O(l) ΔH = -571.6 kJ Says: “571.6 kJ are liberated when 2 moles H2 gas react with 1 mole O2 gas to form 2

moles liquid H2O.” 2. What is ΔH of this reaction as written?

H2(g) + 12 O2(g) → H2O(l) ΔH = -285.8 kJ (half of -571.6)

3. What is ΔH of this reaction?

H2O(l) → H2(g) + 12 O2(g) ΔH = +285.8 kJ

4. Physical states (s), (l), (g), (aq) of reactants and products are important and must be specified.

Problem: How much energy (in kJ) is required to produce 10.0 grams of molecular oxygen in the electrolytic decomposition of water above?

€

10.0gO2 ∗1mol O2

32.0 gO2

∗285.8kJ

0.50 mol O2

=179kJ

Chapter 6 Page 7

F. Heat Transfer and Measurement of Heat. (Section 6.6)

1. Heat Capacity of a sample = amount of heat required to raise the temperature of the

whole sample by 1 ° Celsius (or Kelvin). Units = energy/°C q = CΔT where C = heat capacity heat capacity thus relates heat to temperature. An intensive or extensive property of a substance? Which? extensive OK, let’s factor out the extensive part, the size-dependent part: C = n Cm n = moles Cm = molar heat capacity (intensive)

So now q = nCmΔT

Chapter 6 Page 8

Another way to factor out system size: C = m Cs m= mass in grams Cs = specific heat capacity (heat capacity per gram of material) Such that q = mCsΔT 2. The Specific Heat of a substance = the amount of heat required to raise the

temperature of 1 gram of that substance by 1 degree Celsius. Units = energy/gram-°C. An intensive or extensive property of a substance? Which? intensive specific heat = Cs = (amount of heat required) (mass in g)(temp rise in °C)

Thus for liquid water, the specific heat = 1 cal/g-°C or = 4.184 J/g-°C G. Measurement of Heat of Reaction – Calorimetry.

1. Calorimetry measures heat liberated or absorbed in reactions, called the “heat of

reaction,” ΔH. 2. Usually performed at constant P, so ΔH measured, not ΔU. 3. Directly measures ΔT of reaction system. 4. Must relate this ΔT to energy absorbed or released by chemical reaction. 5. In general: q = CΔT where we define q = rxn heat flowing from reacting system into calorimeter and its contents

C = heat capacity of calorimeter and its contents ΔT = T change of calorimeter and its contents due to rxn

Chapter 6 Page 9

6. C = heat capacity of calorimeter + contents, is found by adding known amount of heat energy (qcalibrate) to setup and observing ΔTcalibrate.

qcalibrate = C * ΔTcalibrate

Thus we can obtain C of the calorimeter. 7. Finally, reaction is performed with exactly the same setup, and ΔTrxn is measured:

qrxn = C * ΔTrxn Solve for qrxn:

Answer: ΔHrxn = -qrx = heat of rxn for given amount of reactant materials

Report: ΔHrxn negative if rxn is exothermic ΔHrxn positive if rxn is endothermic 8. Problem: When 3.40 kJ of heat is added to a calorimeter containing 50.0 g water, T

rises from 24.0 to 36.5°C. In a second experiment in the same calorimeter, when 25.0 mL of 1.0 M H2SO4 is added to 25.0 mL of 2.0 M NaOH (still ~50.0 g water), T rises from 24.0 to 31.2°C. What is ΔHrxn of the reaction:

H2SO4 + 2 NaOH ---> 2 H2O + Na2SO4(aq) ΔH = ? kJ

First get calorimeter heat capacity: qcalibrate = C ΔTcalibrate 3.40 kJ = C * 12.5° C = 3.40 kJ/12.5° = 0.272 kJ/°C Now look at the reaction itself: qrxn = C * ΔTrxn = 0.272 kJ/°C * 7.2°C qrxn = +1.96 kJ So ΔHrxn = -1.96 kJ for the amount of materials reacted here. But what about when 1 mol H2SO4 reacts with 2 moles NaOH, as the problem asks? The reaction that actually ran involved only 1.0 M H2SO4 * 0.025 L = 0.025 moles

acid. Final answer = -1.96 kJ / 0.025 mol = -78 kJ/mol

Chapter 6 Page 10

H. Hess’ Law of Heat Summation. (Section 15-8) 1. ΔH of a reaction is the same whether it occurs in one step or by any series of steps. 2. Elevation illustration. 3. Example: Use Hess’ Law to find ΔHrxn° of:

(Rxn A) CO(g) + 12 O2(g) → CO2(g) Given:

(Rxn B) C(s) + O2(g) → CO2(g) ΔH = -393.5 kJ

(Rxn C) C(s) + 12 O2(g) → CO(g) ΔH = -110.5 kJ

Is there some way to combine (Rxn B) and (Rxn C) to produce (Rxn A)?

(Rxn B) C(s) + O2(g) → CO2(g) -393.5 kJ -(RxnC) -[C(s) + 12 O2(g) → CO(g)] -(-110.5 kJ) (Rxn A) CO(g) + 12 O2(g) → CO2(g) -393.5-(-110.5)

= -283 kJ 4. Pictorially:

Chapter 6 Page 11

I. Standard States and Standard ΔH’s. (Section 6.8) 1. Useful to tabulate ΔH of known rxns because they can be algebraically combined (by

Hess’ Law) to calculate ΔH of unmeasured rxns. 2. Define a thermochemical standard state:

a. pressure = 1 atm b. all pure substances (elements and compounds) in their pure unmixed states. c. solutes are at 1 molar concentration. d. T is not part of S.S. def., must be specified separately.

3. Symbolism ΔH° (superscript denotes standard state conditions) 4. Most important types of tabulated quantities:

a. ΔHf° = “heats of formation” b. ΔHc° = “heats of combustion”

J. Standard Molar Heat of Formation, ΔHf°.

1. Refers to enthalpy change in forming 1 mole of a substance from its elements in their

reference states. 2. Reference state of an element:

• pure • most stable allotropic form (solid, liquid, gas) • for Carbon, Carbon-graphite, not diamond • for Bromine, Br2(l) • for Hydrogen, Oxygen, Nitrogen, Chlorine, and Fluorine it is

diatomic gases: H2, O2, etc. • for Sulfur, S8(s) • for Phosphorus, P4(s) • metals are all solids - M(s)

3. ΔHf° of an element in its reference state is defined to be zero.

Chapter 6 Page 12

4. See Table 6.2. ΔHf° of CH4(g) = -74.81 kJ refers to this reaction as written:

C(s) + 2H2(g) → CH4(g) liberates 74.81 kJ

5. Easily remembered formula: (a consequence of Hess’ Law)

€

ΔHrxn° = n

products∑ ΔHf

° − nreac tan ts∑ ΔHf

°

6. Example use of formula:

CH4(g) + 2O2(g) → CO2(g) + 2H2O(g) ΔHrxn° = ? ΔHrxn° = [ΔHf°(CO2(g)) + 2 ΔHf°(H2O(g))] - [ΔHf°(CH4(g)) + 2 ΔHf°(O2(g))]

= [-393.5 + 2(-241.8)] - [-74.8 + 2(0)]

= -802.3 kJ 7. Can be used to find ΔH° of any rxn for which ΔHf° data is available for all species

present. K. Bond Energies. (Optional Section)

1. Energy liberated or absorbed in chemical reactions is due to energy of breaking and

forming bonds.

2. Bond Energy (B.E.) = energy needed to break one mole of particular type of bond.

3. The stronger the bond, the larger the B.E.

4. Simple case:

Reaction H2(g) → 2H(g); ΔHrxn° = +436 kJ Therefore B.E. of H-H = +436 kJ

5. More complicated case:

CH4(g) + 2O2(g) → CO2(g) + 2H2O(g)

ΔHrxn° = -800 kJ (experimental)

ΔHrxn° = 4 BE(C-H) + 2 BE(O=O) – 2 BE – 4BE(O-H)

Chapter 6 Page 13

6. In general:

ΔHrxn° = ∑ B.E. (reactants) - ∑ B.E. (products)

7. Difficulty: C-H bond in one hydrocarbon slightly different than C-H bond in another. True of all other bond types as well.

8. So B.E. is an average and is useful for estimating ΔHrxn°.

L. Applications of Thermochemistry:

1. Nutrition: Given that the human body typically requires 2400 Calories (nutritionist) per day to operate, how many grams of glucose must be metabolized daily to meet this demand, given:

C6H12O6(s) + 6 O2(g) 6 CO2(g) + 6 H2O(l) ΔH=-2803 kJ

€

2400kcal ∗ 4.184kJ1kcal

∗1mol glucose2803kJ

∗180g glucose1mol glucose

= 645g glucose

2. By the same token, how many fat grams are burned off in a day of fasting, if 2400

Calories are expended by exercise, given that fat can be represented adequately as glyceryl trimyristate:

C45H86O6(s) + 127/2 O2(g) 45 CO2 + 43 H2O(l) ΔH=-27820kJ

€

2400kcal ∗ 4.184kJ1kcal

∗1mol "fat"27820kJ

∗723.1g "fat"1mol "fat"

= 260.9g "fat"

3. Given that 1 watt = is 1 J/s, what is the wattage of consumption of energy by the

human body given 2400 Calories are expended per day? (Most of this is used by your brain.)

€

2400Calday

∗1kcal1Cal

∗4.184kJ1kcal

∗103 JkJ

∗1day24hr

∗1hr60min

∗1min60 sec

=116 J s

Chapter 6 Page 14

4. If your automobile ran on pure ethanol, how many liters per day would you need to operate it, given that you travel 1000 miles/month in a car getting 20 miles per gallon. Ethanol density = 0.80 g/mL.

€

1000mimonth

∗1month30days

∗1gal20mi

∗4qt1gal

∗1L

1.06qt= 6.29 L

day

5. How much heat is released into the surroundings by combustion of that much ethanol?

€

6.29L ∗103mLL

∗0.80gmL

= 5.0 ×103g ethanol C2H5OH + 3 O2

€

ΔH → 2 CO2 + 3 H2O(l) ΔH = 2 ΔHf (CO2) + 3 ΔHf (H2O(l)) – ΔHf (C2H5OH) = 2 * (-393.5 kJ) + 3 * (-285.8 kJ) – (-277.7 kJ) = -1367 kJ