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Chemistry: Atoms FirstJulia Burdge & Jason Overby
Chapter 10
Energy Changes in Chemical Reactions
Kent L. McCorkle
Cosumnes River College
Sacramento, CA
ThermochemistryThermochemistry10
10.1 Energy and Energy Changes10.2 Introduction to Thermodynamics
States and State FunctionsThe First Law of ThermodynamicsWork and Heat
10.3 EnthalpyReactions Carried Out at Constant Volume or at Constant PressureEnthalpy and Enthalpy ChangesThermochemical Equations
10.4 CalorimetrySpecific Heat and Heat CapacityConstant-Pressure CalorimetryConstant-Volume Calorimetry
10.5 Hess’s Law10.6 Standard Enthalpies of Formation10.7 Bond Enthalpy and the Stability of Covalent Molecules10.8 Lattice Energy and the Stability of Ionic Compounds
The Born-Haber CycleComparison of Ionic and Covalent Compounds
Energy and Energy ChangesEnergy and Energy Changes
The system is a part of the universe that is of specific interest.
The surroundings constitute the rest of the universe outside the system.
The system is usually defined as the substances involved in chemical and physical changes.
System
Surroundings
Universe = System + Surroundings
10.1
Energy and Energy ChangesEnergy and Energy Changes
Thermochemistry is the study of heat (the transfer of thermal energy) in chemical reactions.
Heat is the transfer of thermal energy.
Heat is either absorbed or released during a process.
Surroundings
heat
Energy and Energy ChangesEnergy and Energy Changes
An exothermic process occurs when heat is transferred from the system to the surroundings.
“Feels hot!”
Surroundings
Universe = System + Surroundings
heat
System
2H2(g) + O2(g) 2H2O(l) + energy
Energy and Energy ChangesEnergy and Energy Changes
An endothermic process occurs when heat is transferred from the surroundings to the system.
“Feels cold”
energy + 2HgO(s) 2Hg(l) + O2(g)
Surroundings
Universe = System + Surroundings
heat
System
Introduction to ThermodynamicsIntroduction to Thermodynamics
Thermodynamics is the study of the interconversion of heat and other kinds of energy.
In thermodynamics, there are three types of systems:
An open system can exchange mass and energy with the surroundings.
A closed system allows the transferof energy but not mass.
An isolated system does not exchangeeither mass or energy with its surroundings.
10.2
Introduction to ThermodynamicsIntroduction to Thermodynamics
State functions are properties that are determined by the state of the system, regardless of how that condition was achieved.
The magnitude of change depends only on the initial and final states of the system.
Energy
Pressure
Volume
Temperature
The First Law of ThermodynamicsThe First Law of Thermodynamics
The first law of thermodynamics states that energy can be converted from one form to another, but cannot be created or destroyed.
ΔU is the change in the internal energy.
“sys” and “surr” denote system and surroundings, respectively.
ΔU = Uf – Ui; the difference in the energies of the initial and final states.
ΔUsys + ΔUsurr = 0
ΔUsys = –ΔUsurr
Work and HeatWork and Heat
The overall change in the system’s internal energy is given by:
q is heatq is positive for an endothermic process (heat absorbed by the system)
q is negative for an exothermic process (heat released by the system)
w is workw is positive for work done on the system
w is negative for work done by the system
ΔU = q + w
Work and HeatWork and Heat
ΔU = q + w
Worked Example 10.1
Strategy Combine the two contributions to internal energy using ΔU = q + w and the sign conventions for q and w.
Calculate the overall change in internal energy, ΔU, (in joules) for a system that absorbs 188 J of heat and does 141 J of work on its surroundings.
Solution The system absorbs heat, so q is positive. The system does work on the surroundings, so w is negative.
ΔU = q + w = 188 J + (-141 J) = 47 J
Think About It Consult Table 10.1 to make sure you have used the proper sign conventions for q and w.
EnthalpyEnthalpy
Sodium azide detonates to give a large quantity of nitrogen gas.
Under constant volume conditions, pressure increases:
2NaN3(s) 2Na(s) + 3N2(g)
10.3
EnthalpyEnthalpy
Sodium azide detonates to give a large quantity of nitrogen gas.
Under constant volume conditions, pressure increases:
2NaN3(s) 2Na(s) + 3N2(g)
EnthalpyEnthalpy
Pressure-volume, or PV work, is done when there is a volume change under constant pressure.
w = −PΔV
P is the external opposing pressure.
ΔV is the change in the volume of the container.
Worked Example 10.2
Strategy Determine change in volume (ΔV), identify the external pressure (P), and use w = −PΔV to calculate w. The result will be in L∙atm; use the equality 1 L∙atm = 101.3 J to convert to joules.
Determine the work done (in joules) when a sample of gas extends from 552 mL to 891 mL at constant temperature (a) against a constant pressure of 1.25 atm, (b) against a constant pressure of 1.00 atm, and (c) against a vacuum (1 L∙atm = 101.3 J).
Solution ΔV = (891 – 552)mL = 339 mL. (a) P = 1.25 atm, (b) P = 1.00 atm, (c) P = 0 atm.
(a) w = -(1.25 atm)(339 mL)
(b) w = -(1.00 atm)(339 mL)
1 L1000 mL
101.3 J1 L∙atm
= -42.9 J
1 L1000 mL
101.3 J1 L∙atm
= -34.3 J
Worked Example 10.2 (cont.)
Solution(c) w = -(0 atm)(339 mL) 1 L
1000 mL101.3 J1 L∙atm
= 0 J
Think About It Remember that the negative sign in the answers to part (a) and (b) indicate that the system does work on the surroundings. When an expansion happens against a vacuum, no work is done. This example illustrates that work is not a state function. For an equivalent change in volume, the work varies depending on external pressure against which the expansion must occur.
EnthalpyEnthalpy
Pressure-volume, or PV work, is done when there is a volume change under constant pressure.
w = −PΔV
When a change occurs at constant volume, ΔV = 0 and no work is done.
ΔU = q + w
qV = ΔU
ΔU = q − PΔV
substitute
EnthalpyEnthalpy
Under conditions of constant pressure:
ΔU = q + w
qP = ΔU + PΔV
ΔU = q − PΔV
EnthalpyEnthalpy
The thermodynamic function of a system called enthalpy (H) is defined by the equation:
H = U + PV
A note about SI units:
Pressure: pascal; 1Pa = 1 kg/(m . s2)
Volume: cubic meters; m3
PV: 1kg/(m . s2) x m3 = 1(kg . m2)/s2 = 1 J
Enthalpy: joulesU, P, V, and H are all state functions.
Enthalpy and Enthalpy ChangesEnthalpy and Enthalpy Changes
For any process, the change in enthalpy is:
ΔH = ΔU + Δ(PV) (1)
ΔH = ΔU + PΔV
If pressure is constant:
(2)
ΔU = ΔH + PΔV
Rearrange to solve for ΔU:
(3)
qp = ΔU + ΔV
Remember, qp:
(4)
qp = (ΔH − PΔV) + PΔV
Substitute equation (3) into equation (4) and solve:
(5)
qp = ΔH for a constant-pressure process
Enthalpy and Enthalpy ChangesEnthalpy and Enthalpy Changes
The enthalpy of reaction (ΔH) is the difference between the enthalpies of the products and the enthalpies of the reactants:
Assumes reactions in the lab occur at constant pressure
ΔH > 0 (positive) endothermic process
ΔH < 0 (negative) exothermic process
ΔH = H(products) – H(reactants)
Thermochemical EquationsThermochemical Equations
Concepts to consider:Is this a constant pressure process?
What is the system?
What are the surroundings?
ΔH > 0 endothermic
H2O(s) H2O(l) ΔH = +6.01 kJ/mol
Thermochemical EquationsThermochemical Equations
Concepts to consider:Is this a constant pressure process?
What is the system?
What are the surroundings?
ΔH < 0 exothermic
CH4(g) + 2O2(g) CO2(g) + 2H2O(l) ΔH = −890.4 kJ/mol
Thermochemical EquationsThermochemical Equations
Enthalpy is an extensive property.
Extensive properties are dependent on the amount of matter involved.
H2O(l) → H2O(g) ΔH = +44 kJ/mol
2H2O(l) → 2H2O(g) ΔH = +88 kJ/mol
Units refer to mole of reaction as written
Double the amount of matter Double the enthalpy
Thermochemical EquationsThermochemical Equations
The following guidelines are useful when considering thermochemical equations:
1) Always specify the physical states of reactants and products because they help determine the actual enthapy changes.
CH4(g) + 2O2(g) ΔH = −802.4 kJ/molCO2(g) + 2H2O(g)
CH4(g) + 2O2(g) ΔH = +890.4 kJ/molCO2(g) + 2H2O(l)
different states different enthalpies
Thermochemical EquationsThermochemical Equations
The following guidelines are useful when considering thermochemical equations:
2) When multiplying an equation by a factor (n), multiply the ΔH value by same factor.
CH4(g) + 2O2(g) ΔH = − 802.4 kJ/molCO2(g) + 2H2O(g)
2CH4(g) + 4O2(g) ΔH = − 1604.8 kJ/mol2CO2(g) + 4H2O(g)
3) Reversing an equation changes the sign but not the magnitude of ΔH.
CH4(g) + 2O2(g) ΔH = − 802.4 kJ/molCO2(g) + 2H2O(g)
CO2(g) + 2H2O(g) ΔH = +802.4 kJ/molCH4(g) + 2O2(g)
Worked Example 10.3
Strategy The thermochemical equation shows that for every mole of C6H12O6 produced, 2803 kJ is absorbed. We need to find out how much energy is absorbed for the production of 75.0 g of C6H12O6. We must first find out how many moles there are in 75.0 g of C6H12O6.
The molar mass of C6H12O6 is 180.2 g/mol, so 75.0 g of C6H12O6 is
75.0 g C6H12O6 ×
We will multiply the thermochemical equation, including the enthalpy change, by 0.416, in order to write the equation in terms of the appropriate amount of C6H12O6.
Given the thermochemical equation for photosynthesis,
6H2O(l) + 6CO2(g) → C6H12O6(s) + 6O2(g) ΔH = +2803 kJ/mol
calculate the solar energy required to produce 75.0 g of C6H12O6.
1 mol C6H12O6
180.2 g C6H12O6
= 0.416 mol C6H12O6
Worked Example 10.3 (cont.)
Solution (0.416 mol)[6H2O(l) + 6CO2(g) → C6H12O6(s) + 6O2(g)]
and (0.416 mol)(ΔH) = (0.416 mol)(2803 kJ/mol) gives
2.50H2O(l) + 2.50CO2(g) → 0.416C6H12O6(s) + 2.50O2(g) ΔH = +1.17×103 kJ
Therefore, 1.17×103 kJ of energy in the form of sunlight is consumed in the production of 75.0 g of C6H12O6. Note that the “per mole” units in ΔH are canceled when we multiply the thermochemical equation by the number of moles of C6H12O6.
Think About It The specified amount of C6H12O6 is less than half a mole. Therefore, we should expect the associated enthalpy change to be less than half that specified in the thermochemical equation for the production of 1 mole of C6H12O6.
CalorimetryCalorimetry
Calorimetry is the measurement of heat changes.
Heat changes are measured in a device called a calorimeter.
The specific heat (s) of a substance is the amount of heat required to raise the temperature of 1 g of the substance by 1°C.
10.4
Specific Heat and Heat CapacitySpecific Heat and Heat Capacity
The heat capacity (C) is the amount of heat required to raise the temperature of an object by 1°C.
The “object” may be a given quantity of a particular substance.
Specific heat capacity has units of J/(g • °C)
Heat capacity has units of J/°C
4.184 Jheat capacity of 1 kg of water = 1000 g = 4184 J/ C
1 g C
Specific heat capacity of water heat capacity of1 kg water
Specific Heat and Heat CapacitySpecific Heat and Heat Capacity
The heat associated with a temperature change may be calculated:
m is the mass.
s is the specific heat.
ΔT is the change in temperature (ΔT = Tfinal – Tinitial).
C is the heat capacity.
q = msΔT q = CΔT
Worked Example 10.4
Strategy Use q = msΔT to calculate q. s = 4.184 J/g∙°C, m = 255 g, ΔT = 90.5°C – 25.2°C = 65.3°C.
Calculate the amount of heat (in kJ) required to heat 255 g of water from 25.2°C to 90.5°C.
Solution q =
Think About It Look carefully at the cancellation of units and make sure that the number of kilojoules is smaller than the number of joules. It is a common error to multiply by 1000 instead of dividing in conversions of this kind.
4.184 Jg∙°C × 255 g × 65.3°C = 6.97×104 J or 69.7 kJ
CalorimetryCalorimetry
Calculate the amount of heat required to heat 1.01 kg of water from 0.05°C to 35.81°C.
Solution:
Step 1:Use the equation q = msΔT to calculate q.
1000 g 4.184 J1.01 kg [35.81 C 0.05 C] = 151000 J = 151 kJ
1 kg g Cq
CalorimetryCalorimetry
A coffee-cup calorimeter may be used to measure the heat exchange for a variety of reactions at constant pressure:
Heat of neutralization:
HCl(aq) + NaOH(aq) → H2O(l) + NaCl(aq)
Heat of ionization:
H2O(l) → H+(aq) + OH‒(aq)
Heat of fusion:
H2O(s) → H2O(l)
Heat of vaporization:
H2O(l) → H2O(g)
CalorimetryCalorimetry
Concepts to consider for coffee-cup calorimetry:
qP = ΔH
System: reactants and products (the reaction)
Surroundings: water in the calorimeter
For an exothermic reaction:
the system loses heat
the surroundings gain (absorb) heat
qsys = −msΔT
The minus sign is used to keep sign conventions consistent.
qsurr = msΔT qsys = −qsurr
Worked Example 10.5
Strategy Water constitutes the surroundings; the pellet is the system. Use qsurr = msΔT to determine the heat absorbed by the water; then use q = CΔT to determine the heat capacity of the metal pellet.
mwater = 125 g, swater = 4.184 J/g∙°C, and ΔTwater = 31.3°C – 25.1°C = 6.2°C. The heat absorbed by the water must be released by the pellet: qwater = -qpellet, mpellet = 100.0 g, and ΔTpellet = 31.3°C – 88.4°C = -57.1°C.
A metal pellet with a mass of 100.0 g, originally at 88.4°C, is dropped into 125 g of water originally at 25.1°C. The final temperature of both pellet and the water is 31.3°C. Calculate the heat capacity C (in J/°C) of the pellet.
Worked Example 10.5 (cont.)
Solution qwater =
Thus, qpellet = -3242.6 J
From q = CΔT we have
-3242.6 J = Cpellet × (-57.1°C)
Thus,Cpellet = 57 J/°C
4.184 Jg∙°C × 125 g × 6.2°C = 3242.6 J
Think About It The units cancel properly to give appropriate units for heat capacity. Moreover, ΔTpellet is a negative number because the temperature of the pellet decreases.
Constant-Volume CalorimetryConstant-Volume Calorimetry
Constant volume calorimetry is carried out in a device known as a constant-volume bomb.
qcal = −qrxn
A constant-volume calorimeter is an isolated system.
Bomb calorimeters are typically used to determine heats of combustion.
Constant-Volume CalorimetryConstant-Volume Calorimetry
qrxn = −CcalΔT
qcal = CcalΔT
qrxn = −qcal
To calculate qcal, the heat capacity of the calorimeter must be known.
Worked Example 10.6
Strategy Use qrxn = -CcalΔT to calculate the heat released by the combustion of the cookie. Divide the heat released by the mass of the cookie to determine its energy content per gram Ccal = 39.97 kJ/°C and ΔT = 3.90°C.
A Famous Amos bite-sized chocolate chip cookie weighing 7.25 g is burned in a bomb calorimeter to determine its energy content. The heat capacity of the calorimeter is 39.97 kJ/°C. During the combustion, the temperature of the water in the calorimeter increases by 3.90°C. Calculate the energy content (in kJ/g) of the cookie.
Solution qrxn = -CcalΔT = -(39.97 kJ/°C)(3.90°C) = -1.559×102 kJ
Because energy content is a positive quantity, we write
energy content per gram = 1.559×102 kJ
7.25 g = 21.5 kJ/g
Think About It According to the label on the cookie package, a service size is four cookies, or 29 g, and each serving contains 150 Cal. Convert the energy per gram to Calories per serving to verify the result.
21.5 kJg ×
1 Cal4.184 kJ ×
29 gserving = 1.5×102 Cal/serving
Hess’s LawHess’s Law
Hess’s law states that the change in enthalpy for a stepwise process is the sum of the enthalpy changes for each of the steps.
CH4(g) + 2O2(g) ΔH = −890.4 kJ/molCO2(g) + 2H2O(l)
CH4(g) + 2O2(g) ΔH = −802.4 kJ/molCO2(g) + 2H2O(g)
2H2O(l) ΔH = +88.0 kJ/mol2H2O(g)
CH4(g) + 2O2(g)
CO2(g) + 2H2O(l)
ΔH = −890.4 kJ
ΔH = +88.0 kJ
CO2(g) + 2H2O(g)
ΔH = −802.4 kJ
10.5
Hess’s LawHess’s Law
When applying Hess’s Law:1) Manipulate thermochemical equations in a manner that gives the
overall desired equation.
2) Remember the rules for manipulating thermochemical equations:
3) Add the ΔH for each step after proper manipulation.
4) Process is useful for calculating enthalpies that cannot be found directly.
Always specify the physical states of reactants and products because they help determine the actual enthalpy changes.
When multiplying an equation by a factor (n), multiply the ΔH value by same factor.
Reversing an equation changes the sign but not the magnitude of ΔH.
Worked Example 10.7
Strategy Arrange the given thermochemical equations so that they sum to the desired equation. Make the corresponding changes to the enthalpy changes, and add them to get the desired enthalpy change.
Given the following thermochemical equations,
determine the enthalpy change for the reaction
NO(g) + O(g) → NO2(g)
NO(g) + O3(g) → NO2(g) + O2(g) ΔH = –198.9 kJ/mol
O3(g) → O2(g) ΔH = –142.3 kJ/mol
O2(g) → 2O(g) ΔH = +495 kJ/mol
32
Worked Example 10.7 (cont.)
Solution The first equation has NO as a reactant with the correct coefficients, so we will use it as is.
The second equation must be reversed so that the O3 introduced by the first
equation will cancel (O3 is not part of the overall chemical equation). We also
must change the sign on the corresponding ΔH value.
These two steps sum to give:
NO(g) + O3(g) → NO2(g) + O2(g) ΔH = –198.9 kJ/mol
O2(g) → O3(g) ΔH = +142.3 kJ/mol32
NO(g) + O3(g) → NO2(g) + O2(g)
O2(g) → O3(g)32
ΔH = –198.9 kJ/mol
ΔH = +142.3 kJ/mol
NO(g) + O2(g) → NO2(g) ΔH = –56.6 kJ/mol12
+ O2(g) 12
Worked Example 10.7 (cont.)
Solution We then replace O2 on the left with O by incorporating the last
equation. To do so, we divide the third equation by 2 and reverse its direction. As a result, we must also divide ΔH value by 2 and change its sign.
Finally, we sum all the steps and add their enthalpy changes.
NO(g) + O3(g) → NO2(g) + O2(g) ΔH = –198.9 kJ/mol
O2(g) → O3(g) ΔH = +142.3 kJ/mol32
+
O(g) → O2(g) ΔH = –247.5 kJ/mol12
O(g) → O2(g) ΔH = –247.5 kJ/mol12
NO(g) + O(g) → NO2(g) ΔH = –304 kJ/mol
Think About It Double-check the cancellation of identical items–especially where fractions are involved.
12
Standard Enthalpies of FormationStandard Enthalpies of Formation
The standard enthalpy of formation (ΔH f°) is defined as the heat change that results when 1 mole of a compound is formed from its constituent elements in their standard states.
Elements in standard states
C(graphite) + O2(g) CO2(g) ΔH f° = −393.5 kJ/mol
1 mole of product
10.6
Standard Enthalpies of FormationStandard Enthalpies of Formation
The standard enthalpy of formation (ΔH f°) is defined as the heat change that results when 1 mole of a compound is formed from its constituent elements in their standard states.
The superscripted degree sign denotes standard conditions.1 atm pressure for gases1 M concentration for solutions
“f” stands for formation.
ΔH f° for an element in its most stable form is zero.
ΔH f° for many substances are tabulated in Appendix 2 of the textbook.
Standard Enthalpies of FormationStandard Enthalpies of Formation
The standard enthalpy of reaction (ΔH °rxn) is defined as the enthalpy of a reaction carried out under standard conditions.
aA + bB → cC + dD
n and m are the stoichiometric coefficients for the reactants and products.
ΔH °rxn = ΣnΔH f°(products) – ΣmΔH f°(reactants)
ΔH °rxn = [cΔH f°(C) + dΔH f°(D) ] – [aΔH f°(A) + bΔH f°(B)]
Worked Example 10.8
Strategy Use ΔH °rxn = ΣnΔH f°(products) – ΣmΔH f°(reactants) and ΔH f° values from Appendix 2 to calculate ΔH °rxn. The ΔH f° values for Ag+(aq), Cl-(aq), and AgCl(s) are +105.9, –167.2, and –127.0 kJ/mol, respectively.
Using data from Appendix 2, calculate ΔH °rxn for Ag+(aq) + Cl-(aq) → AgCl(s).
Solution ΔH °rxn = ΔH f°(AgCl) – [ΔH f°(Ag+) + ΔH f°(Cl-)]
= –127.0 kJ/mol – [(+105.9 kJ/mol) + (–167.2 kJ/mol)]
= –127.0 kJ/mol – (–61.3 kJ/mol) = –65.7 kJ/mol
Think About It Watch out for misplaced or missing minus signs. This is an easy place to lose track of them.
Worked Example 10.9
Strategy Arrange the equations that are provided so that they will sum to the desired equation. This may require reversing or multiplying one or more of the equations. For any such change, the corresponding change must also be made to the ΔH °rxn value. The desired equation, corresponding to the standard enthalpy of formation of acetylene, is
2C(graphite) + H2(g) → C2H2(g)
Given the following information, calculate the standard enthalpy of formation of
acetylene (C2H2) from its constituent elements:
C(graphite) + O2(g) → CO2(g) ΔH °rxn = –393.5 kJ/mol
H2(g) + O2(g) → H2O(l) ΔH °rxn = –285.5 kJ/mol
2C2H2(g) + 5O2(g) → 4CO2(g) + 2H2O(l) ΔH °rxn = –2598.8 kJ/mol
12
(1)
(2)
(3)
Worked Example 10.9 (cont.)
Solution We multiply Equation (1) and its ΔH °rxn value by 2:
We include Equation (2) and its ΔH °rxn value as is:
We reverse Equation (3) and divide it by 2 (i.e., multiply through by 1/2):
Summing the resulting equations and the corresponding ΔH °rxn values:
2C(graphite) + 2O2(g) → 2CO2(g) ΔH °rxn = –787.0 kJ/mol
H2(g) + O2(g) → H2O(l) ΔH °rxn = –285.5 kJ/mol
2CO2(g) + H2O(l) → C2H2(g) + O2(g) ΔH °rxn = +1299.4 kJ/mol
12
52
2C(graphite) + 2O2(g) → 2CO2(g) ΔH °rxn = –787.0 kJ/mol
H2(g) + O2(g) → H2O(l) ΔH °rxn = –285.5 kJ/mol
2CO2(g) + H2O(l) → C2H2(g) + O2(g) ΔH °rxn = +1299.4 kJ/mol
12
52
2C(graphite) + H2(g) → C2H2(g) ΔH °f = +226.6 kJ/mol
Think About It Remember that a ΔH °rxn is only a ΔH °f when there is just one product, just one mole produced, and all the reactants are elements in their standard states.
Bond Enthalpy and the Stability of Covalent Bond Enthalpy and the Stability of Covalent MoleculesMolecules
The bond enthalpy is the enthalpy change associated with breaking a bond in 1 mole of gaseous molecule.
The enthalpy for a gas phase reaction is given by:
H2(g) → H(g) + H(g) ΔH° = 436.4 kJ/mol
ΔH° = total energy input – total energy released
bonds broken bonds formed
10.7
ΔH° = ΣBE(reactants) – ΣBE(products)
Bond Enthalpy and the Stability of Covalent MoleculesBond Enthalpy and the Stability of Covalent Molecules
Bond enthalpy change in an exothermic reaction.:
Bond Enthalpy and the Stability of Covalent MoleculesBond Enthalpy and the Stability of Covalent Molecules
Bond enthalpy change in an endothermic reaction:
Worked Example 10.10
Strategy Draw Lewis structures to determine what bonds are to be broken and what bonds are to be formed.
Bonds to break: 4 C–H and 2 O=OBonds to form: 2 C=O and 4 H–OBond enthalpies from Table 10.4: 414 kJ/mol (C–H), 498.7 kJ/mol (O=O), 799 kJ/mol (C=O in CO2), and 460 kJ/mol (H–O).
Use bond enthalpies from Table 10.4 to estimate the enthalpy of reaction for the combustion of methane:
CH4(g) + 2O2(g) → CO2(g) + 2H2O(l)
Solution [4(414 kJ/mol) + 2(498.7 kJ/mol)] – [2(799 kJ/mol) + 4(460 kJ/mol)] = –785 kJ/mol
H C H
H
H
O O
O C O
H O H
H O HO O
+ +
Think About It Use equation ΔH °rxn = ΣnΔH f°(products) – ΣmΔH
f°(reactants) and data from Appendix 2 to calculate this enthalpy of reaction again; then compare your results using the two approaches. The difference in this case is due to two things: most tabulated bond enthalpies are averages and, by convention, we show the product of combustion as liquid water–but average bond enthalpies apply to species in the gas phase, where there is little or no influence exerted by neighboring molecules.
Lattice Energy and the Stability of Ionic CompoundsLattice Energy and the Stability of Ionic Compounds
A Born-Haber cycle is a cycle that relates the lattice energy of an ionic compound to quantities that can be measured.
Na(s) + Cl2(g) → Na+(g) + Cl-(g)
10.8
12
Lattice Energy and the Stability of Ionic CompoundsLattice Energy and the Stability of Ionic Compounds
A Born-Haber cycle is a cycle that relates the lattice energy of an ionic compound to quantities that can be measured.
Na(s) + Cl2(g) → Na+(g) + Cl-(g)12
Lattice Energy and the Stability of Ionic CompoundsLattice Energy and the Stability of Ionic Compounds
Worked Example 10.11
Strategy Using the Born-Haber Cycle Figure as a guide, combine pertinent thermodynamic data and Hess’s law to calculate the lattice energy.
From Figure 4.8, IE1(Cs) = 376 kJ/mol. From Figure 4.10, EA1(Cl) = 349.0 kJ/mol. From Appendix 2, ΔH °f [Cs(g)] = 76.50 kJ/mol, ΔH °f [Cl(g)] = 121.7 kJ/mol, ΔH °f [CsCl(s)] = – 422.8 kJ/mol. Because we are interested in magnitudes only, we can use the absolute values of the thermodynamic data. And, because only the standard heat of formation of CsCl(s) is a negative number, it is only one for which the sign changes.
Using data from Figure 4.8 and 4.10 and Appendix 2, calculate the lattice energy of cesium chloride (CsCl).
Solution {ΔH °f [Cs(g)] + ΔH °f [Cl(g)] + IE1(Cs) + ΔH °f [CsCl(s)]} – EA1(Cl) = lattice energy
= (76.50 kJ/mol + 121.7 kJ/mol + 376 kJ/mol + 422.8 kJ/mol) – 349.0 kJ/mol= 648 kJ/mol
Think About It Compare this value to that for NaCl in Figure 10.14 (787 kJ/mol). Both compounds contain the same anion (Cl-) and both have cations with the same charge (+1), so the relative sizes of the cations will determine the relative strengths of their lattic energies. Because Cs+ is larger than Na+, the lattice energy of CsCl is smaller than the lattice energy of NaCl.
Chapter Summary: Key PointsChapter Summary: Key Points10
Energy and Energy ChangesForms of EnergyEnergy Changes in Chemical ReactionsUnits of EnergyIntroduction to ThermodynamicsStates and State FunctionsThe First Law of ThermodynamicsWork and HeatEnthalpyReactions Carried Out at Constant Volume or at Constant PressureEnthalpy and Enthalpy ChangesThermochemical EquationsCalorimetry
Specific Heat and Heat CapacityConstant-Pressure CalorimetryConstant-Volume CalorimetryHess’s LawStandard Enthalpies of Formation
System
Surroundings
Universe = System + Surroundings
• A hot piece of copper (at 98.7oC, specific heat = 0.385 J/g•oC) weighs 34.6486 g. When placed in room temperature water, it is calculated that 915.1 J of heat are released by the metal.
• What gains heat? • What loses heat? • What is the final temperature of the metal?• Watch signs!!!!
Group Quiz #21
• Given the following equations:• 2CO2 (g) O2 (g) + 2CO (g) H = 566.0 kJ• ½ N2 (g) + ½ O2 (g) NO (g) H = 90.3 kJ
• Calculate the enthalpy change for:• 2CO (g) + 2NO (g) 2CO2 (g) + N2 (g) H = ?
Group Quiz #22
6363
• Use Standard Heat of Formation values to calculate the enthalpy of reaction for:
• C6H12O6(s) C2H5OH(l) + CO2(g)• Hint: Is the equation balanced?
• Hof (C6H12O6(s)) = -1260.0 kJ/mol
• Hof (C2H5OH(l)) = -277.7 kJ/mol
• Hof (CO2(g)) = -393.5 kJ/mol
Group Quiz #23