Download Document

Representing Enthalpy Changes
5.3
How do scientists communicate to each other the size of enthalpy changes
and determine whether they are endothermic or exothermic? Combustion
reactions are often spectacular and are obviously exothermic. However,
it is usually not obvious whether a chemical change will absorb or release
energy, so, when we are discussing thermochemical reactions, we must
indicate this information clearly. The equations we use to do this are
called themochemical equations.
You have already seen that the value of an enthalpy change, ∆H, depends
on the quantity of a substance that undergoes a change. For example,
one mole of hydrogen as it burns has an enthalpy change of –285.8 kJ, and
the enthalpy change for two moles of hydrogen is twice that: –571.6 kJ.
You have also learned that a sign convention identifies reactions as
endothermic or exothermic:
• endothermic enthalpy changes are reported as positive values; and
• exothermic enthalpy changes are reported as negative values.
When water decomposes, the system gains energy from the surroundings
and so the molar enthalpy is reported as a positive quantity to indicate an
endothermic change:
1
H2O(l) → H2(g) O2(g)
2
Hdecomp 285.8 kJ/mol H2O
The law of conservation of energy implies that the reverse process (combustion of
hydrogen) has an equal and opposite energy change.
1
H2(g) O2(g) → H2O(l)
2
Hcomb –285.8 kJ/mol H2
Figure 1
Hydrocarbons such as acetone burn
with a readily visible flame. The
flame produced by combusting
methanol (right) is difficult to see,
and so more dangerous.
The sign convention represents the change from the perspective of the chemical system
itself, not from that of the surroundings. An increase in the temperature of the surroundings implies a decrease in the enthalpy of the chemical system, because the change
was exothermic.
Most information about energy changes, for example, the enthalpy change that accompanies the burning of methanol (Figure 1), comes from the experimental technique of
calorimetry. We can communicate the energy changes, obtained from these empirical
studies, in four different ways. Three use thermochemical equations and one uses a diagram:
• by including an energy value as a term in the thermochemical equation
Potential Energy Diagram for
an Exothermic Reaction
CH3OH( l ) + O2(g)
Ep
∆H
3
e.g., CH3OH(l) + O2(g) → CO2(g) + 2 H2O(g) + 726 kJ
2
• by writing a chemical equation and stating its enthalpy change
3
e.g., CH3OH(l) + O2(g) → CO2(g) + 2 H2O(g)
2
CO2(g) + H2O( l )
H –726 kJ
• by stating the molar enthalpy of a specific reaction
e.g., Hcombustion or Hc –726 kJ/mol CH3OH
Reaction Progress
Figure 2
• by drawing a chemical potential energy diagram (Figure 2)
All four of these methods of expressing energy changes are equivalent and are described
in more detail as follows.
NEL
Thermochemistry 313
LEARNING
TIP
Fractions are convenient in many
thermochemical equations. Note
that these apply to fractions of
3
moles of substances (e.g., mol
2
represents 1.5 mol) rather than
fractions of actual molecules.
LEARNING
TIP
Oxygen is often the reactant given
a fractional coefficient in combustion equations because it occurs
as a diatomic molecule and the
total numbers of oxygen atoms in
the products are often odd
numbers.
Method 1:
Thermochemical Equations with Energy Terms
You are already familiar, from your grade 11 Chemistry course, with the first way to
describe the enthalpy change in a chemical reaction: include it as a term in a thermochemical equation. If a reaction is endothermic, it requires a certain quantity of energy
to be supplied to the reactants. This energy (like the reactants) is “consumed” as the
reaction progresses and is listed along with the reactants.
For example, in the electrolysis of water, energy is absorbed. For our purposes, SATP
conditions are usually assumed for all equations.
1
H2O(l) + 285.8 kJ → H2(g) + O2(g)
2
If a reaction is exothermic, energy is released as the reaction proceeds (Figure 3) and
is listed along with the products. For example, magnesium burns in oxygen as follows:
1
Mg(s) + O2(g) → MgO(s) + 601.6 kJ
2
Figure 3
Combustion reactions are the most
familiar exothermic reactions. The
searing heat produced by a burning
building is a formidable obstacle
facing firefighters.
SAMPLE problem
Writing Thermochemical Equations with Energy Terms
Write a thermochemical equation to represent the exothermic reaction that
occurs when two moles of butane burn in excess oxygen gas. The molar enthalpy
of combustion of butane is –2871 kJ/mol.
First, write the equation for the combustion of butane:
2 C4H10(g) 13 O2(g) → 8 CO2(g) 10 H2O(l)
Then obtain the amount of butane, n , from the balanced equation. In this case, n 2 mol.
From the problem, Hc –2871 kJ/mol,
H nHc
2871 kJ
2
mol 1m
ol
H –5742 kJ
The reaction is exothermic, so the energy term must be a product. Report the enthalpy
change for the reaction by writing it as a product in the thermochemical equation, as follows:
2 C4H10(g) 13 O2(g) → 8 CO2(g) 10 H2O(l) 5742 kJ
314 Chapter 5
NEL
Section 5.3
Example
Write a thermochemical equation to represent the dissolving of one mole of silver
nitrate in water. The molar enthalpy of solution is + 22.6 kJ/mol.
Solution
AgNO3(s) 22.6 kJ → Ag
(aq) NO3 (aq)
Method 2: Thermochemical Equations
with H Values
A second way to describe the enthalpy change in a reaction is to write a balanced chemical equation and then the ∆H value beside it, making sure that H is given the correct
sign. Thus, the production of methanol from carbon monoxide and hydrogen could be
written as:
CO(g) + 2 H2(g) → CH3OH(l)
H –128.6 kJ
Note that the units for the enthalpy change are kilojoules (not kJ/mol), because the
enthalpy change applies to the reactants and products as written, with the numbers of
moles of reactants and products given in the equation. The same equation could be
written as:
1
1
CO(g) + H2(g) → CH3OH(l)
2
2
H –64.3 kJ
Writing Thermochemical Equations with H Values
SAMPLE problem
Sulfur dioxide and oxygen react to form sulfur trioxide (Figure 4). The molar
enthalpy for the combustion of sulfur dioxide, Hcomb , in this reaction is
98.9 kJ/mol SO2. What is the enthalpy change for this reaction?
First, write the balanced chemical equation:
2 SO2(g) O2(g) → 2 SO3(g)
Then obtain the amount of sulfur dioxide, n, from the balanced equation and use
H nHc
n 2 mol and Hc 98.9 kJ/mol, so
98.9 kJ
H 2 mol 1
mol
–197.8 kJ
The enthalpy change and the reaction are
2 SO2(g) O2(g) → 2 SO3(g)
H 197.8 kJ
Figure 4
Most sulfuric acid is produced in
plants like this by the contact
process, which includes two
exothermic combustion reactions.
Sulfur reacts with oxygen, forming
sulfur dioxide; sulfur dioxide, in
contact with a catalyst, reacts with
oxygen, forming sulfur trioxide.
Example
Write a thermochemical equation, including a H value, to represent the exothermic reaction between xenon gas and fluorine gas to produce solid xenon tetrafluoride, given that
the reaction produces 251 kJ per mol of Xe reacted.
NEL
Thermochemistry 315
Solution
Xe(g) 2 F2(g) → XeF4(s)
H 251 kJ
As previously described, the enthalpy change ∆H depends on the chemical equation
as written. Therefore, if the balanced equation for the reaction is written differently, the
enthalpy change should be reported differently. For example,
1
SO2(g) + O2(g) → SO3(g)
2
H –98.9 kJ
Both this thermochemical equation and the one in the sample problem above
agree with the empirically determined molar enthalpy for sulfur dioxide in this reaction.
19 7.8 kJ
Hc 2 mol
–98.9 kJ
1 mol
–98.9 kJ/mol SO2
The enthalpy changes for most reactions must be accompanied by a balanced chemical equation that includes the state of matter of each substance.
Method 3: Molar Enthalpies of Reaction
molar enthalpy of reaction, Hx
the energy change associated with
the reaction of one mole of a substance (also called molar enthalpy
change)
standard molar enthalpy of
reaction, H °x the energy change
associated with the reaction of one
mole of a substance at 100 kPa
and a specified temperature
(usually 25°C)
As you have seen in the previous section, molar enthalpies are convenient ways of
describing the energy changes involved in a variety of physical and chemical changes. In
each case, one mole of a particular reactant or product is specified. For example, the
enthalpy change involved in the dissolving of one mole of solute is called the molar
enthalpy of solution and can be symbolized by ∆Hsol. In Table 1, the substance under consideration in each reaction is highlighted in red.
A molar enthalpy that is determined when the initial and final conditions of the chemical system are at SATP is called a standard molar enthalpy of reaction. The symbol ∆H x°
distinguishes standard molar enthalpies from molar enthalpies, ∆Hx, which are measured
at other conditions of temperature and pressure. Standard molar enthalpies allow chemists
to create tables to compare enthalpy values, as you will see in the next two sections.
Table 1 Some Molar Enthalpies of Reaction
Type of molar enthalpy
solution (Hsol)
LEARNING
TIP
For the purposes of this textbook, tabulated values will be
standard values at 25°C, so that
molar enthalpies will be
assumed to be standard molar
enthalpies. For example, the
values for Hc and H °c will be
equivalent.
316 Chapter 5
Example of change
NaBr(s) → Na+(aq) Br–(aq)
combustion (Hcomb)
CH4(g) + 2 O2(g) → CO2(g) H2O(l)
vaporization (Hvap )
CH3OH(l) → CH3OH(g)
freezing (Hfr)
H2O(l) → H2O(s)
neutralization (Hneut)*
2 NaOH(aq) H2SO4(aq) → 2 Na2SO4(aq) + 2 H2O(l)
neutralization (Hneut)*
NaOH(aq) 1/2 H2SO4(aq) → 1/2 Na2SO4(aq) H2O(l)
formation (Hf)**
*
C(s) + 2 H2(g) + 1/2 O2(g) → CH3OH(l)
Enthalpy of neutralization can be expressed per mole of either base or acid consumed.
** Molar enthalpy of formation will be discussed in more detail in Section 5.5.
NEL
Section 5.3
For an exothermic reaction, the standard molar enthalpy is measured by taking into
account all the energy required to change the reaction system from SATP, in order to initiate the reaction, and all the energy released following the reaction, as the products are
cooled to SATP. For example, the standard molar enthalpy of combustion of methanol
(Figure 5) is
H c° 726 kJ/mol CH3OH
This quantity takes into account the energy input to initiate the reaction, the burning
of 1 mol of methanol in oxygen to produce 1 mol CO2(g) and 2 mol H2O(g), then the
energy released as the products are cooled to SATP.
Molar enthalpies can be used to describe reactions other than combustion, as long
as the reaction is clearly described. For example, methanol is produced industrially by
the high-pressure reaction of carbon monoxide and hydrogen gases.
CO(g) 2 H2(g)
→ CH3OH(l)
Chemists have determined the standard molar enthalpy of reaction for methanol in
this reaction, ∆H r°, to be –128.6 kJ/mol CH3OH. To describe the reaction fully, we would
write the thermochemical equation
CO(g) 2 H2(g)
→ CH3OH(l)
H °r –128.6 kJ/mol CH3OH
The symbol for the molar enthalpy of reaction uses the subscript “r” to refer to the reaction under consideration, with the stated number of moles of reactants and products.
Since two moles of hydrogen are consumed as 128.6 kJ of heat are produced, the standard molar enthalpy of reaction in terms of hydrogen could be described as half the
above value, or 64.3 kJ/mol H2.
Describing Molar Enthalpies of Reaction
Figure 5
Methanol burns more completely
than gasoline, producing lower
levels of some pollutants. The technology of methanol-burning vehicles
was originally developed for racing
cars because methanol burns faster
than gasoline. However, its energy
content is lower so it takes twice as
much methanol as gasoline to drive
a given distance.
LEARNING
TIP
The combustion of fuels is always
exothermic: heat is released to the
surroundings. Enthalpies of combustion are often called heats of
combustion and given as absolute
values. For example,
Hcomb(methanol) 726 kJ/mol.
SAMPLE problem
Write an equation whose energy change is the molar enthalpy of combustion of
propanol (C3H7OH).
Hydrocarbons such as propanol undergo combustion in air by reacting with oxygen gas to
produce carbon dioxide gas and water. Since SATP is assumed unless further information
is provided, water is produced in liquid form.
Since it is a molar enthalpy, we must write the equation for 1 mol of C3H7OH, which
requires a fractional coefficient in front of oxygen gas.
The equation is
C3H7OH(g) 9
2
O2(g) → 3 CO2(g) + 4 H2O(l)
Example
Write an equation whose enthalpy change is the molar enthalpy of reaction of calcium
with hydrochloric acid to produce hydrogen gas and calcium chloride solution.
Solution
Ca(s) 2 HCl(aq) → H2(g) CaCl2(aq)
NEL
Thermochemistry 317
Method 4: Potential Energy Diagrams
potential energy diagram a
graphical representation of the
energy transferred during a physical
or chemical change
INVESTIGATION 5.3.1
Combustion of Alcohols (p. 349)
Do different alcohols produce different quantities of heat when they
combust? How do their molar
enthalpies compare?
Figure 6
(a) During an exothermic reaction,
the enthalpy of the system
decreases and heat flows into
the surroundings. We observe a
temperature increase in the
surroundings.
(b) During an endothermic reaction, heat flows from the surroundings into the chemical
system. We observe a temperature decrease in the surroundings. This corresponds to an
increase in the enthalpy of the
chemical system.
Figure 7
(a) The reaction in which one mole
of magnesium oxide is formed
from its elements is exothermic,
so the reactants must have a
higher potential energy than
the product.
(b) The reaction in which water
decomposes to form hydrogen
and oxygen gases is
endothermic, so the reactant
(water) must have a lower
potential energy than the products (hydrogen and oxygen).
Chemists sometimes explain observed energy changes in chemical reactions in terms
of chemical potential energy. This stored energy is related to the relative positions of
particles and the strengths of the bonds between them. Potential energy is stored or
released as the positions of the particles change, just as it is when a spring is stretched and
then released. As bonds break and re-form and the positions of atoms are altered, changes
occur in potential energy. As you have seen before, the potential energy change in the
system is equivalent to the heat transferred to or from the surroundings.
We can visually communicate this energy transferred by using a potential energy
diagram. In this theoretical description, the energy transferred during a change is represented as changes in the chemical potential energy of the particles as bonds are broken
or formed.
The vertical axis on the diagram represents the potential energy of the system. Since
the reactants are written on the left and the products on the right, the horizontal axis is
sometimes called a reaction coordinate or reaction progress. In an exothermic change
(Figure 6(a)), the products have less potential energy than the reactants: energy is released
to the surroundings as the products form. In an endothermic change (Figure 6(b)), the
products have more potential energy than the reactants: energy is absorbed from the
surroundings. Neither of the axes is numbered; only the numerical change in potential
energy (enthalpy change, ∆H) of the system is shown in the diagrams.
Potential energy diagrams can be used to describe a wide variety of chemical changes
as shown in Figure 7.
Exothermic Reaction
reactants
Ep
products
Ep
∆H
products
(a)
reactants
Reaction Progress
Reaction Progress
Endothermic Chemical Change
Exothermic Chemical Change
Mg(s) +
Ep
(kJ)
∆H
(b)
1
2
O2(g)
H2(g) +
∆H f˚ = –601.6 kJ
Ep
(kJ)
MgO(s)
(a)
1
2
O2(g)
∆H ˚decomp = +285.8 kJ
H2O( l )
(b)
Reaction Progress
318 Chapter 5
Endothermic Reaction
Reaction Progress
NEL
Section 5.3
SUMMARY
Communicating Enthalpy Changes
Figure 8 uses the chemical reactions for photosynthesis and respiration to summarize
the four methods of communicating the molar enthalpy or change in enthalpy of a
chemical reaction. Each method has advantages and disadvantages. To best communicate energy changes in chemical reactions, you should learn all four methods.
1 C6H12O6(s) + 6 O2(g)
6 CO2(g) + 6 H2O( l ) + 2802.7 kJ
1 6 CO2(g) + 6 H2O( l ) + 2802.7 kJ
2 C6H12O6(s) + 6 O2(g)
6 CO2(g) + 6 H20( l ) ∆H = –2802.7 kJ
2 6 CO2(g) + 6 H2O( l )
C6H12O6(s) + 6 O2(g)
C6H12O6(s) + 6 O2(g)
∆H = +2802.7 kJ
3 Molar enthalpy for cellular respiration:
∆Hrespiration = –2802.7 kJ/mol glucose
3 Molar enthalpy for photosynthesis:
∆Hphotosynthesis = +2802.7 kJ/mol glucose
4 Potential energy diagram for cellular respiration:
4 Potential energy diagram for photosynthesis:
Cellular Respiration of Glucose
Photosynthesis
C6H12O6(s) + 6 O2(g)
Ep
(kJ)
C6H12O6(s) + 6O2(g)
Ep
(kJ)
∆H = –2802.7 kJ
6 CO2(g) + 6 H2O( l )
∆H = +2802.7 kJ
6CO2(g) + 6H2O( l )
Reaction Progress
Reaction Progress
Practice
Understanding Concepts
1. Communicate the enthalpy change by using the four methods described in this sec-
tion for each of the following chemical reactions. Assume standard conditions (SATP)
for the measurements of initial and final states.
(a) The formation of acetylene (ethyne, C2H2) fuel from solid carbon and gaseous
hydrogen (H ° +228 kJ/mol acetylene)
(b) The simple decomposition of aluminum oxide powder (H° +1676 kJ/mol
aluminum oxide)
(c) The complete combustion of pure carbon fuel (H° 393.5 kJ/mol CO2)
2. For each of the following balanced chemical equations and enthalpy changes, write
Figure 8
Energy is transformed in cellular
respiration and in photosynthesis.
Cellular respiration, a series of
exothermic reactions, is the
breakdown of foodstuffs, such as
glucose, that takes place within
cells. Photosynthesis, a series of
endothermic reactions, is the
process by which green plants
use light energy to make glucose
from carbon dioxide and water.
the symbol and calculate the molar enthalpy of combustion for the substance that
reacts with oxygen.
(a) 2 H2(g) O2(g) → 2 H2O(g)
H° 483.6 kJ
(b) 4 NH3(g) 7 O2(g) → 4 NO2(g) 6 H2O(g) 1134.4 kJ
(c) 2 N2(g) O2(g) 163.2 kJ → 2 N2O(g)
(d) 3 Fe(s) 2 O2(g) → Fe3O4(s)
H° 1118.4 kJ
3. The neutralization of a strong acid and a strong base is an exothermic process.
H2SO4(aq) 2 NaOH(aq) → Na2SO4(aq) 2 H2O(l) 114 kJ
(a)
(b)
(c)
(d)
NEL
What is the enthalpy change for this reaction?
Write this thermochemical equation, using the H°x to produce H2O(g) notation.
Calculate the molar enthalpy of neutralization in kJ/mol sulfuric acid.
Calculate the molar enthalpy of neutralization in kJ/mol sodium hydroxide.
Answers
2. (a) 241.8 kJ/mol H2
(b) 283.6 kJ/mol NH3
(c) 81.6 kJ/mol N2
(d) 372.8 kJ/mol Fe
3. (c) 114 kJ/mol H2SO4
(d) 57 kJ/mol NaOH
Thermochemistry 319
4. The standard molar enthalpy of combustion for hydrogen to produce H20(g) is –241.8 kJ/mol.
The standard molar enthalpy of decomposition for water vapour is 241.8 kJ/mol.
(a) Write both chemical equations as thermochemical equations with a H° value.
(b) How does the enthalpy change for the combustion of hydrogen compare with the
enthalpy change for the simple decomposition of water vapour? Suggest a generalization to include all pairs of chemical equations that are the reverse of one
another.
5. Classify the reactions in Figure 9 as endothermic or exothermic. Explain your classifi-
cation.
Ep
∆H
Ep
(b)
(a)
Figure 9
∆H
Reaction Progress
Reaction Progress
Section 5.3 Questions
Understanding Concepts
1. Draw a potential energy diagram with appropriately labelled
axes to represent
(a) the exothermic combustion of octane (H° –5.47 MJ)
(b) the endothermic formation of diborane (B2H6) from its
elements (H ° +36 kJ)
2. Translate each of the molar enthalpies given below into a
balanced thermochemical equation, including the enthalpy
change, H.
(a) The enthalpy change for the reaction in which solid
magnesium hydroxide is formed from its elements at
SATP is 925 kJ/mol.
(b) The standard molar enthalpy of combustion for pentane, C5H12, is 2018 kJ/mol.
(c) The standard molar enthalpy of simple decomposition,
H °decomp, for nickel(II) oxide to its elements is 240
kJ/mol.
3. For each of the following reactions, write a thermochemical
equation including the energy as a term in the equation.
(a) Butane obtained from
natural gas is used as a fuel in lighters (Figure 10). The
standard molar enthalpy of combustion for butane is
2.86 MJ/mol.
(b) Carbon exists in two different forms, graphite and diamond, which have very different crystal forms. The molar
enthalpy of transition of graphite to diamond is 2 kJ.
(c) Ethanol, obtained from the fermentation of corn and
other plant products, can be added to gasoline to act
as a cheaper alternative. The standard molar enthalpy
of combustion for ethanol is 1.28 MJ/mol.
320 Chapter 5
Figure 10
Butane is the fuel used in lighters.
Applying Inquiry Skills
4. A calorimeter is used to determine the enthalpy change
involved in the combustion of eicosane (C20H42), a solid
hydrocarbon found in candle wax. Complete the Analysis
and Evaluation sections of the investigation report.
Experimental Design
A candle is placed under a copper can containing water,
and a sample of candle wax (eicosane) is burned such that
the heat from the burning is transferred to the calorimeter.
NEL
Section 5.3
Evidence
Table 2 Observations When Burning Candle Wax
Quantity
Measurement
mass of water, m
200.0 g
specific heat capacity of
copper, ccopper
0.385 J/(g•°C)
mass of copper can, mcopper
50.0 g
initial temperature of calorimeter, T1 21.0°C
NEL
final temperature of calorimeter, T2
76.0°C
initial mass of candle wax, mwax,1
8.567 g
final mass of candle wax, mwax,2
7.357 g
Analysis
(a) Calculate the molar enthalpy of combustion of
eicosane.
(b) Was the reaction exothermic or endothermic? Explain.
(c) Write two thermochemical equations to represent the
combustion of eicosane: using an energy term in the
equation, and using a H value.
Evaluation
(d) If the accepted value for the molar enthalpy of combustion of eicosane is 13.3 MJ, calculate the percentage
error of this procedure.
Thermochemistry 321