THERMOCHEMISTRY
5
• The Nature of Chemical
Energy
• The First Law of
Thermodynamic
• Enthalpy
• Enthalpies of Reaction
• Calorimetry
• Hess’s Law
• Enthalpies of Formation
THERMITE REACTION. The reaction between aluminum metal
and iron oxide produces aluminum oxide and iron metal. It
also generates enough heat to melt the iron metal formed in
the reaction. The thermite reaction is a dramatic illustration of
how potential energy stored in chemical bonds can be
converted to heat.
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• Bond Enthalpies
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• Foods and Fuels
Energy and thermodynamics
• Energy is the ability to do work or transfer heat.
• Thermodynamics is the study of energy and its
transformations.
• Specifically, thermochemistry is the study of chemical
reactions and the energy changes that involve heat.
• If we are to properly understand chemistry, we must understand
the energy changes that accompany chemical reactions.
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Figure 5.1 Chemical reactions and energy.
Chemical energy
• With the exception of the energy from the Sun, most of the
energy used in our daily lives comes from chemical reactions.
• The combustion of gasoline,
• the production of electricity from coal,
• the heating of homes by natural gas,
• the use of batteries to power electronic devices.
• Chemical reactions provide the energy that sustains living
systems.
• Plants use solar energy to carry out photosynthesis, allowing
them to grow. In the process, they store a portion of the Sun’s
energy in the chemical bonds of the molecules that are
produced during photosynthesis.
• When animals eat and digest plants, they derive the energy
needed to move, maintain body temperature, and carry out all
other bodily functions from that same chemical energy.
⻄元1776年 英國⼈瓦特的蒸汽機
James Watt (1736-1819)
Finally, in 1776, the first engines were installed and working in commercial enterprises.
⻄元1814年 英國⼈史蒂⽂⽣（George Stephenson）
The steam locomotive operates by converting thermal energy into mechanical
energy. The diesel locomotive converts chemical energy into electrical energy, then
electrical energy into mechanical energy to generate motion. All these energy
conversion processes are governed by thermodynamics.
The global contribution to world's GDP by major economies from 1 AD to 2008 AD according to Angus
Maddison's estimates.
Chemical Energy is Mainly Potential Energy
• The most important form of
potential energy in
molecules is electrostatic
potential energy, Eel:
• Reminder: the unit of energy
commonly used is the Joule:
Figure 5.2 Electrostatic potential energy.
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Attraction between Ions
• Electrostatic attraction is seen between oppositely
charged ions.
• Energy is released when chemical bonds are formed;
energy is consumed when chemical bonds are broken.
Figure 5.3 Electrostatic potential
energy and ionic bonding.
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First Law of Thermodynamics
Energy can be converted from one form to another,
but it is neither created nor destroyed.
• To heat your home, chemical energy needs to be
converted to heat.
• Sunlight is converted to chemical energy in green plants.
• There are MANY more examples of conversion of energy.
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Definitions: System and Surroundings
• The portion of the universe that
we single out to study is called
the system (here, the hydrogen
and oxygen molecules).
• The surroundings are
everything else (here, the
cylinder, piston and everything
beyond).
Figure 5.4 A closed system.
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Types of Systems
1) Open System: a region of the
universe being studied that can
exchange heat AND mass with its
surroundings.
2) Closed System: a region of the
universe being studied that can
ONLY exchange
heat with its surroundings (NOT
mass)
3) Isolated System: a region of the
universe that can NOT exchange
heat or mass with its surroundings
Figure 5.4 A closed system.
Note that this is a
CLOSED system.
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Internal Energy
• The internal energy of a system is the sum of all kinetic
and potential energies of all components of the system;
we use E to represent it.
• We generally don’t know E, only how it CHANGES (ΔE).
• By definition, the change in internal energy, ΔE, is the
final energy of the system minus the initial energy of the
system:
ΔE = Efinal − Einitial
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Changes in Internal Energy
IF: ΔE > 0, Efinal > Einitial
the system absorbed energy from the surroundings.
Figure 5.5 Changes in internal energy.
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Changes in Internal Energy
IF: ΔE < 0, Efinal < Einitial
the system released energy to the surroundings.
Figure 5.5 Changes in internal energy.
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Thermodynamic Quantities
Have Three Parts
1. A number
2. A unit
3. A sign
Note about the sign:
– A positive ΔE results when the system gains energy
from the surroundings.
– A negative ΔE results when the system loses energy
to the surroundings.
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Energy Diagram
• The energy diagram shows that the internal energy of the
mixture of H2 and O2 is greater than that of the H2O
produced in the reaction.
Figure 5.6 Energy diagram for the
reaction 2 H2(g) ☞ O2(g) → 2 H2O(I).
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Changes in Internal Energy
• When energy is exchanged between the system and
the surroundings, it is exchanged as either heat (q) or
work (w).
• That is, ΔE = q + w.
Figure 5.7 Sign conventions for
heat and work.
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ΔE, q, w, and Their Signs
– Notice that any energy entering the system as either
heat or work carries a positive sign.
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Exchange of Heat between System and
Surroundings
• When heat is absorbed by the system from the
surroundings, the process is endothermic.
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Figure 5.8 (a) Endothermic reaction
Exchange of Heat between System and
Surroundings
• When heat is released by the system into the
surroundings, the process is exothermic.
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Figure 5.8 (b) Exothermic reaction
State Functions
• Usually we have no way of knowing the internal energy
of a system; finding that value is simply too complex a
problem.
• However, we do know that the internal energy of a
system is independent of the path by which the system
achieved that state.
– In the system below, the water could have reached room
temperature from either direction.
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Figure 5.9 Internal energy, E, a state function.
State Functions
• Therefore, internal energy is a state function.
• It depends only on the present state of the system, not
on the path by which the system arrived at that state.
• And so, ΔE depends only on Einitial and Efinal.
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State Functions
• However, q and w are not
state functions.
• Whether the battery is
shorted out or is
discharged by running the
fan, its ΔE is the same,
but q and w are different
in the two cases.
Figure 5.10 Internal energy is a state
function, but heat and work are not.
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Work
• Usually the only work done by chemical or physical
change is the mechanical work associated with a
change in volume of gas.
Figure 5.13 Pressure–volume work.
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Work
• We can measure the work done by the gas if the
reaction is done in a vessel that has been fitted with a
piston: w = −PΔV
• The work is NEGATIVE because it is done BY the
system.
Figure 5.11 A system that does
work on its surroundings.
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Enthalpy
• If a process takes place at constant pressure (and we
usually work at atmospheric pressure) and the only
work done is this pressure–volume work, we can
account for heat flow during the process by measuring
the enthalpy (H) of the system.
• Enthalpy is the internal energy plus the product of
pressure and volume:
H = E + PV
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Enthalpy
• When the system changes at constant pressure, the
change in enthalpy, ΔH, is
ΔH = Δ (E + PV)
• This can be written
ΔH = ΔE + PΔV
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Enthalpy
• Since ΔE = q + w and w = −PΔV, we can substitute
these into the enthalpy expression:
ΔH = ΔE + PΔV
ΔH = (q + w) − w
ΔH = q
• So, at constant pressure, the change in enthalpy is the
heat gained or lost.
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Endothermic and Exothermic
• A process is endothermic
when ΔrH is positive.
• A process is exothermic
when ΔrH is negative.
Figure 5.12 Endothermic and
exothermic processes.
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Enthalpy of Reaction
• The change in enthalpy, ΔrH, is the enthalpy of the
products minus the enthalpy of the reactants:
ΔrH = ΔHrxn = Hproducts − Hreactants
• This quantity, ΔrH, is called the enthalpy of reaction,
or the heat of reaction.
Figure 5.14 Exothermic reaction of
hydrogen with oxygen.
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Enthalpy of Reaction
• The exothermic nature of this reaction is also shown in
the enthalpy diagram in the Figure 5.14.
Figure 5.14 Exothermic reaction of hydrogen with oxygen.
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The Truth about Enthalpy
1. Enthalpy is an extensive property.
2. The enthalpy change for a reaction is equal in
magnitude, but opposite in sign, to ΔrH for the reverse
reaction.
3. The enthalpy change for a reaction depends on the
states of the reactants and the products.
Figure 5.15 ΔH for a reverse reaction.
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Using Enthalpy as a Guide
• Chemical reactions that are highly exothermic (ΔH much
less than 0) usually occur spontaneously.
• But often need some energy to get the process started.
Figure 5.16 Exothermic
reactions and spontaneity.
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Calorimetry
• Since we cannot know the
exact enthalpy of the
reactants and products, we
measure ΔrH through
calorimetry, the
measurement of heat flow.
• The instrument used to
measure heat flow is called
a calorimeter.
Figure 5.18 Coffee-cup calorimeter.
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Heat Capacity and Specific Heat
• The amount of energy required to raise the temperature of a
Q
substance by 1 K (1 °C) is its heat capacity, C =
.
ΔT
(extensive)
• If the amount of the substance heated is one gram, it is the
1 Q
specific heat, Cs =
. (intensive)
m ΔT
• If the amount is one mole, it is the molar heat capacity ,
1 Q
Cm =
. (intensive)
n ΔT
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Constant volume vs constant
pressure heat capacity
• Heat is not a state function.
• Heat absorbed by the system depends on the path.
Q
.
• Heat capacity is a path function! C =
ΔT
• Heat capacity measured at constant volume,
Q
ΔE
CV =
=
( ΔT )
( ΔT )
V
V
QV = ΔE
• Heat capacity measured at constant pressure, QP
Q
ΔH
CP =
=
( ΔT )
( ΔT )
P
P
• In general, CP
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≠ CV
= ΔH
Constant volume vs constant
pressure heat capacity
• Consider infinitesimal temperature change, ΔT
∂E
Constant volume heat capacity CV =
•
( ∂T )
V
→0
∂H
Constant pressure heat capacity CP =
•
( ∂T )
P
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Thermodynamic properties (variables)
• A thermodynamic property is any macroscopic property that is
measurable, whose value describes a state of a physical
system.
• Any variable that can be used to characterize the system is
called a variable of state, a state variable, or a state function.
• Important variables:
• Extensive (
• Intensive (
∝ n): n, V, E, H, CV, CP, …
∝ n 0 = 1): P, T, CV,m, CP,m, …
• System consisting of single component, single phase: only
three are independent: (n, V, T), or (n, p, T), or (n, V, p)…
• The choice of independent variables are predetermined by
researchers.
• The other thermodynamic variables are functions of these
independent variables. E(V, T ), E(P, T ), H(P, T ), …
Heat Capacity and Specific Heat
• For example, 209 J is required to increase the
temperature of 50.0 g of water by 1.00 K.
• Thus, the specific heat of water is
Figure 5.17 Specific heat of water.
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Heat Capacity and Specific Heat
• Notice that the specific heat of liquid water is higher
than those of the other substances listed.
• The high specific heat of water affects Earth’s climate
because it makes the temperatures of the oceans
relatively resistant to change.
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Constant-Pressure Calorimetry
• By carrying out a reaction in aqueous
solution in a simple calorimeter, the heat
change for the system can be found by
measuring the heat change for the water
in the calorimeter.
• The specific heat for water is
4.184 J/g·K. We use this value for dilute
solutions.
• We can calculate ΔH for the reaction with
this equation:
qsoln = Cs × msoln × ΔT = –qrxn
Figure 5.18 Coffee-cup
calorimeter.
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Bomb Calorimetry
• Reactions can be carried out in a
sealed “bomb” such as this one.
• The heat absorbed (or released)
by the water is a very good
approximation of the enthalpy
change for the reaction.
qrxn = – Ccal × ΔT
Figure 5.19 Bomb calorimeter.
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Bomb Calorimetry
• Because the volume in the
bomb calorimeter is constant,
what is measured is really the
change in internal energy, ΔE,
not ΔH.
• For most reactions, the
difference is very small.
Figure 5.19 Bomb calorimeter.
© 2018 Pearson Education Ltd.
Sample Exercise 5.7 Measuring qrxn Using a Bomb Calorimeter
The combustion of methylhydrazine (CH6N2), a liquid rocket fuel, produces N2(g), CO2(g), and H2O(l):
2 CH6N2(l) + 5 O2(g)
2 N2(g) + 2 CO2(g) + 6 H2O(l)
When 4.00 g of methylhydrazine is combusted in a bomb calorimeter, the temperature of the calorimeter increases from 25.00 to
39.50 °C. In a separate experiment the heat capacity of the calorimeter is measured to be 7.794 kJ/°C. Calculate the heat of
reaction for the combustion of a mole of CH6N2.
Solution
Analyze We are given a temperature change and the total heat capacity of the calorimeter. We are also given the amount of reactant
combusted. Our goal is to calculate the enthalpy change per mole for combustion of the reactant.
Plan We will first calculate the heat evolved for the combustion of the 4.00-g sample. We will then convert this heat to a molar
quantity.
Solve
For combustion of the 4.00-g sample of methylhydrazine, the temperature change of the calorimeter is:
ΔT = (39.50 °C – 25.00 °C) = 14.50 °C
We can use ΔT and the value for Ccal to calculate the heat of reaction (Equation 5.23):
© 2018 Pearson Education Ltd.
Sample Exercise 5.7 Measuring qrxn Using a Bomb Calorimeter
Continued
We can readily convert this value to the heat of reaction for a mole of CH6N2:
Check The units cancel properly, and the sign of the answer is negative as it should be for an exothermic reaction. The magnitude of
the answer seems reasonable.
Practice Exercise 1
The combustion of exactly 1.000 g of benzoic acid in a bomb calorimeter releases 26.38 kJ of heat. If the combustion
of 0.550 g of benzoic acid causes the temperature of the calorimeter to increase from 22.01 to 24.27 °C, calculate the
heat capacity of the calorimeter. (a) 0.660 kJ/°C (b) 6.42 kJ/°C (c) 14.5 kJ/°C (d) 21.2 kJ/g-°C (e) 32.7 kJ/°C
Practice Exercise 2
A 0.5865-g sample of lactic acid (HC3H5O3) reacts with oxygen in a calorimeter whose heat capacity is 4.812 kJ/°C. The
temperature increases from 23.10 to 24.95 °C. Calculate the heat of combustion of lactic acid (a) per gram and
(b) per mole.
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The Regulation of Body Temperature
• The body increases its internal energy content by
ingesting foods.
Δr H = − 2803 kJ/mol
• Heat is removed from the body as the perspiration
evaporates into the surroundings.
Δr H = 44 kJ/mol
Figure 5.20 Perspiration.
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• Macroscopic variables:
Δ vs Δr
• Physical variables: T, V, p, …
• Chemical variables: ni, ξ, …
• Two kind of deltas, Δ vs Δr:
• Physical changes: ΔT
ΔE = E2 − E1…
= T2 − T1, ΔV = V2 − V1,
• Chemical reaction aA + bB
→ cC + dD:
Δr E = cEC + dED − aEA − bEB,
Δr H = cHC + dHD − aHA − bHB
•
More generally, for a chemical reaction, 0
Δr H =
∑
i
νiHi
=
∑
i
νiAi:
Hess’s Law
• ΔrH is well known for many reactions, and it is
inconvenient to measure ΔrH for every reaction in
which we are interested.
• However, we can calculate ΔrH using published ΔrH
values and the properties of enthalpy.
• Hess’s law states that if a reaction is carried out in a
series of steps, ΔrH for the overall reaction equals the
sum of the enthalpy changes for the individual steps.
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Hess’s Law
/mol
/mol
/mol
/mol
Figure 5.21 Enthalpy diagram for
combustion of 1 mol of methane.
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Hess’s Law
• Because H is a state function, for a particular set of
reactants and products, ΔrH is the same whether the
reaction takes place in one step or in a series of steps.
/mol
/mol
Figure 5.22 Enthalpy diagram illustrating Hess’s law.
© 2018 Pearson Education Ltd.
Enthalpies of Formation
• An enthalpy of formation, ΔHf (ΔfH), is defined as the
enthalpy change for the reaction in which a compound
is made from its constituent elements in their elemental
forms.
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Standard Enthalpies of Formation
• Standard enthalpies of formation, ΔHf° (ΔfH°), are
measured under standard conditions (25 °C and 1.00
atm pressure).
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Calculation of ΔrH
• We can write this equation as the sum of three
formation equations:
Δf H ∘[CO2(g)]
• Use values from Table 5.3 to calculate ΔH°rxn
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Using Enthalpies of Formation to Calculate
Enthalpies of Reaction
Calculation of ΔrH
Figure 5.23 Enthalpy diagram for propane combustion.
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Calculation of ΔrH
• We can use Hess’s law in this way:
where n and m are the stoichiometric coefficients.
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Bond Enthalpy
• The enthalpy associated with breaking one mole of a
particular bond in a gaseous substance.
Cl2(g) → 2Cl(g)
ΔrH = 242 kJ/mol
CH4(g) → C(g) + 4H(g)
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ΔrH = 242 kJ/mol
Bond Enthalpy
• The bond enthalpy is always positive because energy
is required to break chemical bonds.
• Energy is always released when a bond forms
between gaseous fragments.
• The greater the bond enthalpy, the stronger the bond.
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Bond Enthalpy
• A molecule with strong chemical bonds is generally
less likely to undergo chemical change than one with
weak bonds.
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Bond Enthalpies and
Enthalpy of Reaction
• ADD bond energy for ALL bonds made (+)
• SUBTRACT bond energy for ALL bonds broken (–)
• The result is an estimate of ΔrH.
ΔrH = Σ (bond enthalpies – Σ (bond enthalpies
of bonds broken)
of bonds formed)
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Bond Enthalpies and
Enthalpy of Reaction
•
So, we can predict
whether a chemical
reaction will be
endothermic or
exothermic using bond
energies.
© 2018 Pearson Education Ltd.
Figure 5.24 Using bond enthalpies to estimate ΔHrxn.
Energy in Foods
• The energy released when one gram of food is
combusted is its fuel value.
© 2018 Pearson Education Ltd.
Energy in Foods
• Most of the energy in foods comes from carbohydrates, fats,
and proteins.
• Carbohydrates (17 kJ/g):
C6H12O6(s) + 6 O2(g)
6 CO2(g) + 6 H2O(l)
ΔrH° = –2803 kJ/mol
• Fats (38 kJ/g):
2 C57H110O6(s) + 163 O2(g)
ΔrH° = –71609 kJ/mol
114 CO2(g) + 110 H2O(l)
71609/163 = 439 kJ/mol
• Proteins produce 17 kJ/g (same as carbohydrates): Their
chemical reaction in the body is NOT the same as in a
calorimeter.
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Energy in Fuels
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Energy in Fuels
•
The vast majority of the energy consumed in
the United States comes from fossil fuels.
•
Nuclear fission produces 8.6% of the U.S.
energy needs.
•
Renewable energy sources, like solar,
wind, geothermal, hydroelectric, and biomass
sources produce 9.9% of the U.S. energy
needs.
Figure 5.26 Energy consumption in
the United States.
Figure 5.27 Sugarcane can be converted to a
sustainable bioethanol product.
© 2018 Pearson Education Ltd.
Why Combustions Are Always Exothermic?
• The double bond in O2 is much weaker than other double bonds or pairs of single
bonds, and therefore the formation of the stronger bonds in CO2 and H2O results in
the release of energy, which is given off as heat or increases thermal motion.
• This explains why fire is hot regardless of fuel composition.
• The bond energies in the fuel play only a minor role; for example, the total bond
energy of CH4 is nearly the same as that of CO2.
• A careful analysis in terms of bond enthalpies, counting double bonds as two
bonds to keep the total number of bonds unchanged, gives the heat of combustion
close to −418 kJ/mol (i.e., −100 kcal/mol) for each mole of O2, in good agreement
(±3.1%) with data for >500 organic compounds; the heat of condensation of H2O,
−44 kJ/mol, is also included in the analysis. For 268 molecules with ≥ 8 carbon
atoms, the standard deviation from the predicted value is even smaller, 2.1%. This
enables an instant estimate of the heat of combustion simply from the elemental
composition of the fuel, even for a complex mixture or unknown molecular
structure, and explains principles of biofuels production.
• The analysis indicates that O2, rather than fuels like octane, H2, ethanol, or
glucose, is the crucial “energy-rich” molecule; we briefly explain why O2 is
abundant in air despite its high enthalpy.
Why Combustions Are Always Exothermic, Yielding About 418 kJ per Mole of O2
Klaus Schmidt-Rohr*
J. Chem. Educ. 2015, 92, 12, 2094–2099
Why Combustions Are Always Exothermic?
Why Combustions Are Always Exothermic, Yielding About 418 kJ per Mole of O2
Klaus Schmidt-Rohr*
J. Chem. Educ. 2015, 92, 12, 2094–2099
• Hydrocarbons combusted in air react with O2 to form
CO2 and H2O.* The number of molecules of O2
required and the number of molecules of CO2 and
H2O formed depend on the composition of the
hydrocarbon, which acts as the fuel in the reaction.
• Many substances, fuels for example, release energy
when they react.
• The chemical energy of a fuel is due to the potential
energy stored in the arrangements of its atoms.
• Chemical energy is released when bonds between atoms
are formed, and consumed when bonds between atoms
are broken. When a fuel burns, some bonds are broken
and others are formed, but the net effect is to convert
chemical potential energy to thermal energy, the energy
associated with temperature. The increase in thermal
energy arises from increased molecular motion and
hence increased kinetic energy at the molecular level.