Unit 5: Energetics IB Topics 5 & 15
AP Chapters (Zumdahl): 6.1-6.4; 8.4 & 8.5; 16.1-16.6
EXOTHERMIC & ENDOTHERMIC RXNS

____________________________: a measure of the ability to do work. o ___________________: to move an object against an opposing force. o Energy (J) = Force (N) x Distance (m) o Forms of energy include: heat, light, sound, electricity, and chemical energy (energy released or absorbed during chemical rxns)

Enthalpy (_______): a measure of internal energy stored in a substance. o Absolute value of enthalpy of reactants cannot be known, nor can enthalpy of products in a rxn. o Enthalpy change (

H) in a rxn can be measured (difference between reactants and products). o Standard enthalpy change of a rxn (

H
ϴ
): measured at pressure = ___________; temp = ____________

Exothermic reactions: release energy in the

Endothermic reactions: absorb energy in the form of heat (because bonds in the products are stronger than the bonds in the reactants); decreasing enthalpy has neg. sign (

H < 0) o Diagram: form of heat; increasing enthalpy, positive value
(

H > 0) o Diagram:
TEMPERATURE AND HEAT

Heat: a measure of the total energy in a given amount of a substance (and therefore depends on the amount of substance present).

Temperature: a measure of the “hotness” of a substance. It represents the average kinetic energy of the substance (but is independent of the amount of substance present). o Example: Two beakers of water. Both have same temperature, but a beaker with 100 cm 3 of water contains twice as much heat as a beaker containing 50 cm 3 . o The increase in temp. when an object is heated depends on
 The __________________ of the object
 The __________________ added
 The nature of the substance (different substances have different “specific heat” values)
CALORIMETRY

The enthalpy change for a rxn can be measured experimentally by using a calorimeter. o In a simple “coffee cup” calorimeter, all heat evolved by an exothermic rxn is used to raise temp. of a known mass of H
2
O. o For endothermic rxns, heat transferred from the H
2
O to the rxn can be calculated by measuring the lowering of the temperature of a known mass of water.
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AP Chapters 1-5

Unit 5: Energetics

Compensating for heat loss: o Graph temp. v. time
IB Topics 5 & 15
AP Chapters (Zumdahl): 6.1-6.4; 8.4 & 8.5; 16.1-16.6
AP Chapters 1-5
Figure 5.1: Compensating for heat loss with a temp. v. time graph o By extrapolating the graph, the temp rise that would have taken place had the rxn been instantaneous can be calculated.
CALCULATION OF ENTHALPY CHANGES (

H)

The heat involved in changing the temperature of any substance can be calculated as follows: o Heat energy =

Specific heat capacity of H
2
O = __________________ o Thus, 4.18 kJ of energy are required to raise the temp of 1 kg of water by one Kelvin. o Note that this is effectively the same as the complex unit J/g

°C (from Honors Chem)

Enthalpy changes are normally quoted in kJ mol -1 for either a reactant or product, so it is also necessary to work out the number of moles involved in the reaction which produces the heat change in the water.
Example 1: 50.0 cm 3 of 1.00 mol dm -3 hydrochloric acid solution was added to 50.0 cm 3 of 1.00 mol dm -3 sodium hydroxide solution in a polystyrene beaker. The initial temperature of both solutions was 16.7 °C. After stirring and accounting for heat loss the highest temperature reached was 23.5 °C. Calculate the enthalpy change for this reaction.
Step 1: Write the equation for reaction
Step 2: Calculate molar quantities
Step 3: Calculate heat evolved
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Unit 5: Energetics IB Topics 5 & 15
AP Chapters (Zumdahl): 6.1-6.4; 8.4 & 8.5; 16.1-16.6
Example 2: A student uses a simple calorimeter to determine the enthalpy change for the combustion of ethanol
(C
2
H
5
OH). When 0.690 g of ethanol was burned it produced a temperature rise of 13.2 K in 250 g of water.
(a) Calculate

H for the reaction
(b) The IB Data Book value is -1371 kJ mol -1 . Provide reasons for any discrepancy between this and the calculated value above.
Example 3:The neutralization reaction between solutions of NaOH and H
2
SO
4
was studied by measuring the temperature changes when different volumes of the two solutions were mixed (hint: just like your molar ratio lab). The total volume was kept constant at 120.0 cm 3 and the concentrations of the two solutions were both 1.00 mol dm -3 (Figure 5.2).
AP Chapters 1-5
Figure 5.2: Temperature changes produced when different volumes of NaOH and H
2
SO
4
are mixed. a) Annotate Fig. 5.2 appropriately and determine the volumes of the solutions which produce the largest increase in temperature. b) Calculate the heat produced by the reaction when the maximum temperature was produced. c) Calculate the heat produced for one mole of NaOH.
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Unit 5: Energetics IB Topics 5 & 15
AP Chapters (Zumdahl): 6.1-6.4; 8.4 & 8.5; 16.1-16.6
d) The literature value for the enthalpy of neutralization is -57.5 kJ mol -1 . Calculate the percentage error value and suggest a reason for the discrepancy between the experimental and literature values.
Example 4: 50.0 cm 3 of 0.200 mol dm -3 copper (II) sulfate solution was placed in a polystyrene cup. After two minutes,
1.20 g of powdered zinc was added. The temperature was taken every 30 seconds and the following graph obtained.
Calculate the enthalpy change for the reaction taking place (Figure 5.3).
AP Chapters 1-5
Figure 5.3: Compensating for heat lost in an experiment measuring temperature changes in an exothermic reaction.
Step 1: Write the equation for the reaction.
Step 2: Determine the limiting reagent.
Step 3: Extrapolate the graph to compensate for heat loss and determine

T.
Step 4: Calculate the heat evolved in the experiment for 0.0100 mol of reactants.
Step 5: Express this as the enthalpy change for the reaction (

H).
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Unit 5: Energetics IB Topics 5 & 15
AP Chapters (Zumdahl): 6.1-6.4; 8.4 & 8.5; 16.1-16.6

BOND ENTHALPIES
Enthalpy change (

H) can also be calculated directly from bond enthalpies.
Bond enthalpy for a diatomic molecule is defined as the enthalpy change for the following process:
X-Y(g) ↔ X(g) + Y(g)
Breaking bonds:

H = __________________________________________
Forming bonds:

H = __________________________________________
Calculating

H from bond enthalpies:
Table 5.1: Some average bond enthalpies (all values in kJ mol -1 )
Single Bonds Double Bonds Triple Bonds
H-H 436
C-C 348
C-H 412
O-H 463
N-H 388
N-N 163
C=C 612
O=O 496
Example: Calculate

H for the hydrogenation of ethane
C≡C 837
N≡N 944
Example: Calculate

H for the combustion of hydrazine in oxygen. This reaction has been used to power spacecraft.
Limitations of Using Average Bond Enthalpies

Average bond enthalpies can only be used if all reactants and products are gases. o If the H
2
O product in the above example were a liquid, then even more heat would be evolved since the

H vap
for H
2
O would also need to be included in the calculation.
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AP Chapters 1-5

Unit 5: Energetics IB Topics 5 & 15
AP Chapters (Zumdahl): 6.1-6.4; 8.4 & 8.5; 16.1-16.6

Average bond enthalpies are obtained by considering a number of similar compounds, but in reality the energy of a particular bond will vary slightly in different compounds (it will be affected by neighboring atoms).

Thus,

H values obtained using average bond enthalpies are not necessarily very accurate.
HESS’ LAW:
The value of

H for a reaction is the same whether it occurs in one step or in a series of steps.

H for the overall equation is the sum of the

H’s for the individual equations.

H rxn
=

H
1
+

H
2
+ …
Example: Calculate the enthalpy of reaction,

H rxn
, for the formation of nitrogen monoxide from its elements
N
2
+ O
2

2NO

H rxn
= ?
Using these equations:
4NH
3
+ 3O
2

2N
2
+ 6H
2
O
4NH
3
+ 5O
2

4NO + 6H
2
O


H = -1530 kJ
H = -1170 kJ
Another way of thinking about Hess’ Law is graphically in terms of “energy cycles.” The enthalpy change for a reaction depends only on the difference between the enthalpy of the products and the enthalpy of the reactants. It is independent of the reaction pathway.
The enthalpy change going from A to B is the same whether the reaction proceeds directly to A or whether it goes via an intermediate.
(Remember vector addition?)
This law is simply a statement of the law of conservation of energy. It can be used to determine enthalpy changes which cannot be measured directly. For example, the enthalpy of combustion of both carbon and carbon monoxide to form carbon dioxide can easily be measured directly, but the combustion of carbon to carbon monoxide cannot. This can be represented by an energy cycle.
Example: Calculate the standard enthalpy change when one mole of methane is formed from its elements in their standard states. The standard enthalpies of combustion ( 
H
 c
) of carbon, hydrogen and methane are -393, -286 and -
890 kJ mol -1 respectively.
Step 1: Write the equation for enthalpy change with the unknown 
H

value. Call this value 
H
 x
.
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AP Chapters 1-5

Unit 5: Energetics IB Topics 5 & 15
AP Chapters (Zumdahl): 6.1-6.4; 8.4 & 8.5; 16.1-16.6
Step 2: Construct an energy cycle showing the different routes to the products (in this case the products of combustion).
Step 3: Use Hess’ Law to equate the energy changes for the two different routes.
Step 4: Rearrange the equation and substitute values to solve for the unknown

H value.
STANDARD ENTHALPY CHANGE OF FORMATION, 
H
 f
Definition: the enthalpy change when one mole of the compound is formed from its elements in their standard states at
298 K and 1 atm of pressure.
Note: it follows that the 
H
 f for an element in its standard state will be zero.
STANDARD ENTHALPY CHANGE OF COMBUSION,  H
 c
Definition: the enthalpy change when one mole of a substance is completely combusted in oxygen under standard conditions.
Example: An accurate value for the standard enthalpy change of formation of ethanol can be determined from the cycle below.
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AP Chapters 1-5

Unit 5: Energetics IB Topics 5 & 15
AP Chapters (Zumdahl): 6.1-6.4; 8.4 & 8.5; 16.1-16.6
LATENT HEAT OF FUSION,  H fus
- the enthalpy change (energy absorbed) when one mole of the compound is converted from a solid to a liquid without a change in temperature. “Latent” means hidden; the heat absorbed/released during a phase change does not cause the temperature to change.
Note: 
H fus for water is ______________________________________________
LATENT HEAT OF VAPORIZATION, 
H vap
- the enthalpy change (energy absorbed) when one mole of the compound is converted from a liquid to a gas without a change in temperature.
Note: 
H vap for water is ______________________________________________
Example: How much heat is released by 250.0 g of H
2
O as it cools from 125.0

C to -40.0

C? (Recall that the specific heat of water = 4.18 J/g

C)
Example: What will be the final temperature of 50.0 mL of water, initially at 60

C, after a 3.2 g ice-cube is dropped in and allowed to melt. Assume no heat transfer to/from the surroundings.
ENTHALPY OF ATOMIZATION,  H
 at
- standard enthalpy change when one mole of gaseous atoms is formed from the element in its standard state under standard conditions. For diatomic molecules this is equal to half the bond dissociation enthalpy.
ELECTRON AFFINITY, 
H

EA
- the enthalpy change when an electron is added to an isolated atom in the gaseous state.
Atoms “want” an excess electron, so electron affinity values are negative for the first electron. However, when oxygen forms the O 2 ion, the overall process is endothermic.
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AP Chapters 1-5

Unit 5: Energetics IB Topics 5 & 15
AP Chapters (Zumdahl): 6.1-6.4; 8.4 & 8.5; 16.1-16.6
LATTICE ENTHALPY,  H
 latt
- relates either to the endothermic process of turning a crystalline solid into its gaseous ions or to the exothermic process of turning gaseous ions into a crystalline solid.

The sign of the lattice enthalpy indicates whether the lattice is being formed (-) or broken (+).

The size of the lattice enthalpy depends both on the size of the ions and on the charge carried by the ions.
Anion size ______________________ Cation size ______________________
LiCl NaCl KCl NaCl NaBr NaI
Lattice
Enthalpy
(kJ mol -1 )
Cation charge ____________________
NaCl MgCl
2
Anion charge ____________________
MgCl
2
MgO
Lattice
Enthalpy
(kJ mol -1 )
BORN-HABER CYCLES – energy cycles for the formation of ionic compounds.
Example: The enthalpy change for the formation of sodium chloride can be considered to occur through a series of separate steps.
Use of Born-Haber Cycles: Like any energy cycle, Born-Haber cycles can be used to find the value of an unknown. They can also be used to assess how ionic a substance is. The lattice enthalpy can be calculated theoretically by considering the charge and size of the constituent ions. It can also be obtained indirectly from the Born-Haber cycle. If there is good agreement between the two values then it is reasonable to assume that there is a high degree of ionic character (e.g.
NaCl). However, if there is a big difference between the two values then it is because the compounds possess a considerable degree of covalent character (eg. AgCl).
Table 5.2: Determining degree of ionic character
NaCl AgCl Compound
Theoretical value (kJ mol -1 )
Experimental value (kJ mol -1 )
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AP Chapters 1-5

Unit 5: Energetics IB Topics 5 & 15
AP Chapters (Zumdahl): 6.1-6.4; 8.4 & 8.5; 16.1-16.6
ENTROPY (S): a measure of the degree of disorder in a system; in nature, things tend to increase in entropy, or disorder.
All physical & chemical changes involve a change in entropy, or

S.

The more disordered a system becomes the more positive the

S.
 
S is negative for systems that become more ordered. o Example:
An increase in disorder (entropy) can result from:

_________________________ different types of particles (e.g. the dissolving of sugar in water)

A change in ____________________ where the distance between particles increases (e.g. liquid water

steam)


The increased _____________________________ of particles (e.g. heating a liquid or gas)
Increasing the ____________________________ of particles, e.g. 2H
2
O
2
(l)

2H
2
O(l) + O
2
(g)
Note: The greatest increase in disorder is usually found where the number of particles in the gaseous state increases.
ABSOUTE ENTROPY VALUES

The standard entropy of a substance is the entropy change per mole that results from heating the substance from _______________ to the standard temperature of __________________.

Unlike enthalpy, absolute values of entropy can be measured.

The standard entropy change for a reaction can then be determined by calculating the difference between the entropy of the products and the reactants.
Example: Determine the entropy change for the formation of ammonia from hydrogen and nitrogen.
SPONTANEITY – a reaction is said to be spontaneous if it causes a system to move from a less stable to a more stable state.

Enthalpy and entropy are DRIVING FORCES for spontaneous reactions (rxns that happen at normal conditions)
 it is the interplay of these 2 driving forces that determines whether or not a physical or chemical change will actually happen.
Free Energy Change (

G), a.k.a. Gibbs Energy Change: relates enthalpy and entropy in a way that indicates which predominates; the quantity of energy that is available or stored to do work or cause change.

G: pos value means change is NOT spon.

G: neg value means change IS spon.
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AP Chapters 1-5

Unit 5: Energetics IB Topics 5 & 15
AP Chapters (Zumdahl): 6.1-6.4; 8.4 & 8.5; 16.1-16.6
Note: the fact that a reaction is spontaneous does not necessarily mean that it will proceed without any input of energy.
For example, the combustion of coal is a spontaneous reaction and yet coal is stable in air. It will only burn on its own accord after it has received some initial energy so that some of the molecules have the necessary activation energy for the reaction to occur.
Table 5.2: Relating Enthalpy and Entropy to Spontaneity
Example of reaction 
H

S Spontaneity
H
2
O
(g)
 H
2
O
(l)
H
2
O
(s)
 H
2
O
(l)
Calculating

G values
1) Calculating 
G
 rxn from 
G
 f
Example: Find the standard free energy of combustion of methane given the standard free energies of formation of methane, carbon dioxide, water and oxygen.
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AP Chapters 1-5

Unit 5: Energetics IB Topics 5 & 15
AP Chapters (Zumdahl): 6.1-6.4; 8.4 & 8.5; 16.1-16.6
2) Using

S rxn and

H rxn
values to calculate

G rxn
at all temperatures
Example: Determine whether or not the decomposition of calcium carbonate is spontaneous at all temperatures. If not, provide conditions of temperatures (if any) at which the reaction is spontaneous.
More Practice Problems:
Example: For the decomposition of O
3
(g) to O
2
(g): 2O
3
(g)

3O
2
(g)

H = -285.4 kJ/mol and

S = 137.55 J/mol•K at 25°C. a) Calculate

G for the reaction. b) Is the reaction spontaneous? c) Is

H or

S (or both) favorable for the reaction?
Example: What is the minimum temperature (in °C) necessary for the following reaction to occur spontaneously?
Fe
2
O
3
(s) + 3CO(g)

2Fe(s) + 3CO
2
(g)

H rxn
= +144.5 kJ/mol;

S rxn
= +24.3 J/K•mol
AP Chapters 1-5
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