Article

Cite This: J. Chem. Educ. 2019, 96, 1407−1411 pubs.acs.org/jchemeduc

Enthalpy and the Second Law of Thermodynamics

David Keifer*
Department of Chemistry, Salisbury University, Salisbury, Maryland 21801, United States
*
S Supporting Information

ABSTRACT: The change in enthalpy of a chemical reaction

conducted at constant pressure is equal to the heat of the reaction
plus the nonexpansion work of the reaction, ΔH = qP + wadditional. After
deriving that relationship, most general and physical chemistry
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textbooks set wadditional = 0 to arrive at the claim that ΔH = qP, and

nearly all further discussion of enthalpy assumes that ΔH = qP. Setting
wadditional = 0 is viable for spontaneous reactions, but for non-
spontaneous reactions, wadditional ≠ 0 as a consequence of the second
law of thermodynamics. Therefore, ΔH ≠ qP for nonspontaneous
reactions. Moreover, nonexpansion work is important for many
interesting and important spontaneous reactions in biology (e.g.,
muscular movement, nerve signal transmission) and in modern society
(e.g., batteries); incorporating wadditional into ΔH allows for a more accurate discussion of the energy flow in these reactions. In
this paper, I show that ΔH ≠ qP for nonspontaneous reactions, and I discuss how ΔH must be partitioned between qP and
wadditional for several kinds of reactions according to the second law of thermodynamics. Finally, I suggest how the discussion of
enthalpy could be corrected in general and physical chemistry textbooks.
KEYWORDS: First-Year Undergraduate/General, Upper-Division Undergraduate, Physical Chemistry,
Misconceptions/Discrepant Events, Textbooks/Reference Books, Thermodynamics, Calorimetry/Thermochemistry

Therefore, ΔH ≠ qP for nonspontaneous reactions, making

W hen chemical reactions are conducted in a laboratory
setting, such as in beakers and flasks, they are most
often spontaneous reactions (i.e., reactions for which ΔG < 0)
“heat of formation”, or “heat of reaction” more generally, a
misnomer for any nonspontaneous reactions. Textbooks are
occurring under constant-pressure conditions. (Note that the technically correct in their claim that ΔH = qP whenever
familiar claim that the sign of ΔG indicates spontaneity is not wadditional = 0, but they neglect to mention that this condition is
quite correct.1,2 Even so, this claim will be used here to avoid impossible for nonspontaneous reactions. I suggest that this
confusion.) When these reactions occur, energy may flow into practice be changed in textbooks and in courses.

■
or out of the system via heat and/or expansion work (i.e., P V
work), both of which change the internal energy of the system, TRADITIONAL TEXTBOOK APPROACH TO
U. The heat flow is usually a much larger quantity than the ENTHALPY
expansion work. Enthalpy, H, is defined to cancel the usually
small amount of expansion work so that the change in enthalpy General and physical chemistry textbooks typically introduce
for these reactions is the heat under constant pressure, ΔH = enthalpy by its definition: H = U + PV, where H is enthalpy, U
qP. Therefore, the change in enthalpy conveniently quantifies is internal energy, P is pressure, and V is volume. Under
the heat flow of reactions carried out in typical laboratory constant-pressure conditions, the change in enthalpy is given
settings. However, enthalpy is not defined to cancel by eq 1.
nonexpansion work, so when nonexpansion work is done,
such as in electrical work, muscular activity, nerve signal ΔH = ΔU + P ΔV (1)
transmission, or mechanical work like pulling a string, the
change in enthalpy is given by ΔH = qP + wadditional, where The change in internal energy is equal to the sum of work
wadditional is nonexpansion work. and heat. Work can be divided into expansion work, which is
In common practice in general and physical chemistry equal to −PΔV,7 and nonexpansion work such as electrical
textbooks, it is often stated that ΔH = qP for any reaction for work or muscular activity. The following equation incorporates
which wadditional = 0. For example, ΔH is typically described as these terms into eq 1, where w is total work, wadditional is
heat under constant pressure for all enthalpy of formation nonexpansion work, and qP is heat under constant pressure:
reactions. In fact, enthalpy of formation is often colloquially
referred to as “heat of formation”.3−6 The problem is that Received: April 3, 2019
wadditional ≠ 0 for nonspontaneous reactions as a consequence of Revised: May 16, 2019
the second law of thermodynamics, as I will show below. Published: June 4, 2019
© 2019 American Chemical Society and
Division of Chemical Education, Inc. 1407 DOI: 10.1021/acs.jchemed.9b00326
J. Chem. Educ. 2019, 96, 1407−1411
Journal of Chemical Education Article

Figure 1. Line at the top of each figure represents the size of ΔH, while the boxes below represent the sizes of ΔG and TΔS. The bold vertical line
shows that the values of ΔG and TΔS are fixed. The white part of each box represents the portion of the change in enthalpy that is composed of
nonexpansion work, and the shaded part of each box represents the portion of the change in enthalpy that is composed of heat. The two panels
represent (A) the water-splitting reaction shown in eq 4 and (B) the reverse of that reaction.

ΔH = w + qP + P ΔV in enthalpy can be composed of heat and how much must be

composed of nonexpansion work.
= wadditional − P ΔV + qP + P ΔV = wadditional + qP For example, consider the water-splitting reaction in eq 4.
ΔH = wadditional + qP (2) 2H 2O(l) → 2H 2(g) + O2 (g) (4)

At this point in most general and physical chemistry For this reaction at room temperature under standard
textbooks, wadditional is set to 0 so that ΔH = qP.8−17 Many conditions, ΔH > 0, ΔG > 0, and ΔS > 0. Figure 1A visualizes
general chemistry textbooks neglect to discuss wadditional entirely the relationship between all of the terms in eq 3 for the forward
in this derivation to get straight to ΔH = qP, implying that reaction. The change in enthalpy is represented by the length
expansion work is the only type of work available.3,4,18−22 of the line at the top. It is equal to the sum of ΔG and TΔS,
Setting wadditional = 0 is consistent with the first law of represented by the rectangles beneath the ΔH line. The bold
thermodynamics for any chemical reaction because wadditional vertical line shows that the sizes of the ΔG and TΔS boxes are
and qP are path functions, so their values can change as long as constants, regardless of the degree of irreversibility. As eq 3
ΔH stays constant. However, I will show below that wadditional shows, when the reaction occurs the change in enthalpy can be
cannot be set to 0 for nonspontaneous reactions as a composed of a combination of heat and nonexpansion work.
consequence of the second law of thermodynamics. This fact The white portion of each rectangle is the amount of
is widely overlooked in discussions of enthalpy by general nonexpansion work that is done on the system; the shaded
chemistry textbooks,3,4,8−14,18−22 physical chemistry text- portion is the amount of heat added to the system. Under
books,15−17 and chemical engineering textbooks.5,6 reversible conditions, q = TΔS and wadditional = ΔG as described

■ ΔH CANNOT EQUAL HEAT FOR

NONSPONTANEOUS REACTIONS
above, so the entire TΔS rectangle is shaded, and the entire
ΔG rectangle is white. If the reaction is conducted under
irreversible conditions so that q < TΔS, the heat portion must
In reference to eq 2, the first law of thermodynamics would shrink, meaning that a larger portion of the change in enthalpy
suggest that ΔH for any reaction may equal qP, or wadditional, or must be composed of nonexpansion work. In the extreme case
a combination, depending on how the reaction is carried out. of complete irreversibility (i.e., the reaction occurs so rapidly
However, the second law of thermodynamics places limits on that heat has no time to flow into the system from the
what portion of ΔH can be composed of heat and what portion surroundings), all of the change in enthalpy must be composed
must be composed of nonexpansion work. To better of nonexpansion work. Thus, for this reaction (and any
understand the partitioning of this energy between non- reaction for which ΔG > 0), nonexpansion work must be
expansion work and heat, the common ΔG = ΔH − TΔS supplied for the reaction to proceed because wadditional ≥ ΔG.
equation can first be rearranged into eq 3. Equation 2 is also The reaction cannot proceed at room temperature if heat is the
incorporated. only energy source. (The reaction could theoretically proceed
by heat alone if the temperature were increased so that T ΔS >
ΔH = ΔG + T ΔS = wadditional + qP (3) ΔH, making ΔG < 0.) The necessity of nonexpansion work is
acknowledged by scientists working on water splitting.24,25 In
ΔH, ΔG, and ΔS are all state functions, so their values are fact, general and physical chemistry textbooks often correctly
constant regardless of how the reaction is carried out as long as describe ΔG as the minimum nonexpansion work that must be
the reaction occurs at constant temperature and pressure. supplied to drive a nonspontaneous reaction, implying that
However, wadditional and qP are path functions and can vary heat alone is insufficient. Yet, these textbooks simultaneously
depending on the degree of irreversibility of the reaction. neglect nonexpansion work to arrive at the claim that ΔH =
According to the second law of thermodynamics (in the form qP.9−12,14−17,20−22 A quick example provides an intuitive
of the Clausius inequality), q ≤ TΔS. Under reversible justification for why nonexpansion work is necessary for
conditions (i.e., theoretical conditions for which the reaction nonspontaneous reactions to proceed: Can you recharge a
occurs at a rate of 023), q = TΔS, and under irreversible battery by heating it up on a stove? Obviously not. Electricity
conditions, q < TΔS. The consequence of this according to eq (one form of nonexpansion work) must flow through the
3 is that wadditional ≥ ΔG. Under reversible conditions, wadditional battery to recharge it.
= ΔG. Under irreversible conditions, wadditional > ΔG. These Figure 1B represents the reverse of the water-splitting
relationships put a limit on how much of the required change reaction, for which ΔH < 0, ΔG < 0, and ΔS < 0. It is still true
1408 DOI: 10.1021/acs.jchemed.9b00326
J. Chem. Educ. 2019, 96, 1407−1411
Journal of Chemical Education Article

that q ≤ TΔS and wadditional ≥ ΔG, which in this case means discuss the relationship among ΔH, nonexpansion work, and
that, for irreversible conditions, q must be more negative than heat for nonspontaneous reactions, as described above.

■
TΔS, and wadditional must be less negative than ΔG. Thus, as
Figure 1B shows for completely irreversible conditions, it is MOTIVATION FOR CHANGING THE TEXTBOOK
possible for enthalpy to change exclusively by releasing heat APPROACH TO ENTHALPY
during the reverse reaction, even though it is impossible for the
enthalpy to change exclusively by absorbing heat during the The most important reason to change how general and
forward reaction. This is all a consequence of the second law of physical chemistry textbooks approach enthalpy is that the
thermodynamics in the form q ≤ TΔS. In other words, the current approach (setting wadditional = 0 to arrive at the
required change in enthalpy can occur via heat alone only for conclusion that ΔH = qP) is valid for spontaneous reactions,
spontaneous reactions (ΔG < 0). In practice, if no apparatus is but it is inaccurate for all nonspontaneous reactions, as shown
present to harness the energy released by these reactions and in the previous section. This is because wadditional ≠ 0 for
put it to work, then all of the ΔH is released as heat. This is the nonspontaneous reactions, so ΔH ≠ qP by eq 2. One might
basis of using calorimetry to determine ΔH for spontaneous suspect that wadditional is usually very small compared to qP so
reactions. that setting wadditional = 0 is simply an approximation. This is a
Similar arguments can be made for reactions for which not poor approximation for many important reactions. For
all of ΔH, ΔG, and TΔS have the same sign. For example, a example, over 80% of the total enthalpy required to split
particular reaction might have ΔH < 0, ΔG > 0, and TΔS < 0. water at room temperature would have to be supplied as
Figure 2A represents possible values of those quantities. Recall wadditional, as suggested by the size of the bars in Figure 1.
(Several other numerical examples and their detailed
calculations are given in the Supporting Information.) One
might also argue that instructors and textbook authors already
know that ΔH ≠ qP for nonspontaneous reactions but that
they choose to focus on the simpler case of spontaneous
reactions for the students’ sakes. There are two problems with
that suggestion. One problem is that textbooks and instructors
do not focus exclusively on spontaneous reactions. For
example, many enthalpy of formation equations that students
may need to use are for nonspontaneous reactions. The second
problem is that I suspect many instructors do not have a
complete grasp of the relationship between enthalpy and the
second law of thermodynamics. These instructors cannot be
blamed: I have yet to find a chemistry or chemical engineering
book that addresses this connection. Even physical chemistry
Figure 2. Diagrams showing visually how ΔG and TΔS sum to give textbooks make claims like, “The enthalpy of reaction, ΔHR... is
ΔH. Part A represents a reaction for which ΔH < 0, ΔG > 0, and ΔS
defined as the heat withdrawn from the surroundings as the
< 0, in which case |qP| > |ΔH|. Part B represents a reaction for which
ΔH > 0, ΔG > 0, and ΔS < 0, in which case qP and ΔH have opposite reactants are transformed into products.”17 As this paper
signs. intends to make clear, that statement cannot be true for
nonspontaneous reactions.
A second reason to change how general and physical
chemistry textbooks approach enthalpy is that wadditional is an
that q ≤ TΔS and wadditional ≥ ΔG, where the equalities hold
important part of many spontaneous reactions, such as those
under reversible conditions. Those relationships are repre-
involved in muscle activity and batteries. Setting wadditional = 0
sented by the arrows alongside the bars for ΔG and TΔS; the
so that ΔH = qP is valid for spontaneous reactions occurring on
wadditional arrow must be at least the size of the ΔG bar for
the benchtop in beakers, flasks, and calorimeters, where
reactions with ΔG > 0, and the qP arrow must be at least the
size of the TΔS bar for reactions with TΔS < 0. Figure 2A nonexpansion work is not done. Those reactions occur very
shows that when this reaction occurs, the heat released must be frequently in chemistry laboratories, so it is understandable
greater in magnitude than ΔH. Figure 2B represents a reaction that ΔH and heat are so often conflated. However, those are
for which ΔH > 0, ΔG > 0, and ΔS < 0. In this case, heat must only a subset of spontaneous reactions. I recommend that
actually be negative for the reaction to proceed, showing that textbooks and instructors use ΔH = qP + wadditional as the
ΔH and qP do not even necessarily have the same sign. default view of change in enthalpy and only set wadditional = 0 in
(Therefore, a reaction cannot be classified as “exothermic” or the specific cases for which it is appropriate to do so.
“endothermic” solely on the basis of the sign of ΔH.) Similar Finally, undergraduate students at both general and physical
figures can be made for any type of reaction. These figures chemistry levels hold a wide variety of misconceptions about
show that ΔH does not typically equal qP. In fact, ΔH = qP enthalpy as it is currently addressed in textbooks and
only under very specific conditions, namely, when pressure and courses.28−30 Updating the discussion of enthalpy in textbooks
temperature are constant, ΔG < 0, and no nonexpansion work and courses in the way that this paper proposes might
is involved. eliminate some of those misconceptions, but it might also lead
It should be noted that several articles have described the to different misconceptions. Thus, the main purpose of this
partitioning of ΔH into qP and wadditional much more thoroughly paper is to improve the accuracy of what we are teaching
than most textbooks do.23,26,27 These articles have focused on students, not necessarily to improve student understanding of
harnessing wadditional from spontaneous reactions but do not what they are being taught.
1409 DOI: 10.1021/acs.jchemed.9b00326
J. Chem. Educ. 2019, 96, 1407−1411
Journal of Chemical Education

■
Article

RECOMMENDATIONS FOR TEXTBOOKS AND THE above. Preferably, the relationship between enthalpy and the
CLASSROOM second law of thermodynamics, shown in the ΔH Cannot
Equal Heat for Nonspontaneous Reactions section above,
Enthalpy in General Chemistry would be discussed in detail in chemical thermodynamics
Enthalpy is an important topic in both general and physical courses and textbooks. After that theoretical background has
chemistry, so the partitioning of ΔH into qP and wadditional is been established, several numerical examples could be given
relevant in general and physical chemistry courses. However, (or thermodynamic data could be given to students so they
instructors and textbook authors might think that the full could do the calculations themselves) that illustrate how
discussion of the relationship between enthalpy and the second important wadditional can be for both spontaneous and
law of thermodynamics shown above is too complicated for the nonspontaneous reactions. Several examples are given in the
general chemistry audience. Even so, the most important following paragraphs. Unique insights that can be drawn from
conclusions of the above discussion can still be addressed in each example are included. Detailed calculations and
undergraduate general chemistry. thermodynamic data are provided in the Supporting
In general chemistry, enthalpy is introduced in the Information.
thermochemistry unit. This is often many chapters before ATP hydrolysis is a spontaneous reaction. This reaction is
Gibbs free energy and entropy, so spontaneity would not have the most important source of the wadditional needed for muscle
been discussed yet. To avoid having to rearrange the order of contraction.
topics in general chemistry, only a small change needs to be ATP(aq) + H 2O(l) → ADP(aq) + P(aq)
i
made to how enthalpy is discussed in thermochemistry. Rather
than teaching students that ΔH is equal to the heat involved in For this reaction, ΔH° = −24.10 kJ/mol, and ΔG° = −38.17
a constant-pressure reaction, instructors and authors can say kJ/mol. Typically about 40% of ΔG is used as work to move
that ΔH is the sum of heat and nonexpansion work of the the muscle,31 leading to wadditional = −15.27 kJ/mol. Therefore,
reaction (eq 2). In this way, ΔH can be compared to the about 63% of the loss of enthalpy is used to do useful work.
change in internal energy equation ΔU = q + w, with which Water splitting is a nonspontaneous reaction. Driving this
many students would already be familiar. So internal energy reaction is an area of research relevant to green energy because
can change by heat and/or any kind of work, whereas enthalpy it produces hydrogen fuel, which does not give off significant
can change by heat at constant pressure and/or nonexpansion amounts of greenhouse gases.
work. We can tell students that the utility of using ΔH rather
2H 2O(l) → 2H 2(g) + O2 (g)
than ΔU is that, in many cases, heat at constant pressure and
nonexpansion work have more important consequences than For this reaction, ΔH° = +571.6 kJ/mol, and ΔG° = +474.2
expansion work. For example, when a battery powers a kJ/mol. Therefore, ΔG°/ΔH° × 100% = 82.96%, meaning that
smartphone, the nonexpansion work is used to run the apps on over 80% of the total enthalpy required to split water would
the phone, and the heat at constant pressure that is generated have to be supplied as wadditional (because wadditional ≥ ΔG).
is why the phone feels warm. Any expansion work is Recharging an alkaline battery is nonspontaneous. For a zinc
inconsequential. For the rest of thermochemistry, students battery, the reaction is
could simply conceptualize ΔH as the net amount of heat at
constant pressure and nonexpansion work (rather than just the ZnO(s) + Mn2O3(s) → Zn(s) + 2MnO2 (s)
amount of heat at constant pressure) released or absorbed by
For this reaction, ΔH° = +272 kJ/mol, and ΔG° = +274.9
the reaction.
kJ/mol. Therefore, ΔG°/ΔH° × 100% = 101%. This example
In the thermodynamics chapter, when ΔG, ΔS, and
shows that in some cases the wadditional required for non-
spontaneity are introduced, instructors and authors could say
spontaneous reactions is actually larger than the ΔH needed.
that nonspontaneous reactions require nonexpansion work to
This is because ΔS° is negative for the reaction (see the
proceed, so ΔH ≠ qP. As mentioned above, the example of
Supporting Information), necessitating that heat leaves the
trying to recharge a battery by heating it up on a stove could be
reaction according to q ≤ TΔS, so the wadditional must make up
used to try to convince students that nonspontaneous reactions
for that loss.
require nonexpansion work. Then, instructors and authors
Finally, several enthalpy of formation reactions are non-
could say that spontaneous reactions are able to proceed
spontaneous, such as that of dinitrogen tetroxide, which is
without any nonexpansion work, so it is possible for ΔH = qP.
often used as a component for rocket fuel.
Any mention of ΔH as heat should be eliminated unless the
instructor or author is explicitly referencing a spontaneous N2(g) + 2O2 (g) → N2O4 (l)
reaction conducted under constant pressure in which no
nonexpansion work is done. In other words, the default view of For this reaction, ΔH° = −19.5 kJ/mol, and ΔG° = +97.5
ΔH should be the sum of heat and nonexpansion work, rather kJ/mol. This is the only numerical example provided here for
than just heat. which ΔH and ΔG have opposite signs. Recall that wadditional ≥
In general chemistry textbooks and courses, there is ΔG and ΔH = wadditional + qP. Therefore, for this reaction to
probably no need to rigorously justify these conclusions occur, at least 97.5 kJ of wadditional would have to be supplied,
using the detailed argument given above. That justification can but for the enthalpy to decrease as needed, at least 117.0 kJ of
be incorporated into textbooks or into advanced or honors heat would have to be released to the surroundings.
general chemistry courses if desired. I chose those four examples for several reasons. First, they all
show that wadditional can be a sizable portion of ΔH, so it really
Enthalpy in Physical Chemistry should not be ignored. Second, students hopefully find the
At a minimum, physical chemistry textbooks and courses could reactions relevant and interesting, making thermodynamics less
be corrected in the way that I describe for general chemistry dry for them. Third, they represent a variety of combinations
1410 DOI: 10.1021/acs.jchemed.9b00326
J. Chem. Educ. 2019, 96, 1407−1411
Journal of Chemical Education Article

of signs of ΔH, ΔG, and ΔS, so students could get practice wexpansion = −PΔV, leading to the cancellation of PΔV and −PΔV in
explaining or thinking about the role of qP and wadditional in the ΔH equation.
many kinds of reactions. (8) Zumdahl, S. S.; Zumdahl, S. A. Chemistry; Houghton Mifflin:

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Boston, MA, 2003.
SUMMARY (9) Brady, J. E.; Senese, F. Chemistry: Matter and Its Changes; Wiley:
Hoboken, NJ, 2004.
The main suggestion in this paper is that the default view of (10) Zumdahl, S. S. Chemical Principles; Houghton Mifflin: Boston,
ΔH as presented in general and physical chemistry textbooks MA, 2005.
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qP. Textbooks and instructors typically adopt the latter view Chemical Reactivity; Brooks/Cole: Belmont, CA, 2012.
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that wadditional ≠ 0 for nonspontaneous reactions or for a variety Cole: Belmont, CA, 2013.
of important spontaneous reactions. A justification of the fact (13) Flowers, P.; Theopold, K.; Langley, R.; Robinson, W. R.
Chemistry; Rice University (OpenStax), 2015. https://cnx.org/
that wadditional ≠ 0 for nonspontaneous reactions has been contents/havxkyvS@12.1:uXg0kUa-@5/Introduction (accessed Dec
presented, as well as a discussion of how that connects to 17, 2018).
enthalpy. The paper also suggests how textbooks and courses (14) Atkins, P.; Jones, L.; Laverman, L. Chemical Principles: The
could be adapted to address this and includes several numerical Quest for Insight; Freeman: New York, NY, 2016.
examples that illustrate the main concepts.

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(15) McQuarrie, D. A.; Simon, J. D. Physical Chemistry: A Molecular
Approach; University Science Books: Sausalito, CA, 1997.
ASSOCIATED CONTENT (16) Atkins, P.; De Paula, J. Physical Chemistry; W. H. Freeman:
* Supporting Information
S New York, NY, 2010.
(17) Engel, T.; Reid, P. Physical Chemistry; Pearson: Upper Saddle
The Supporting Information is available on the ACS River, NJ, 2010.
Publications website at DOI: 10.1021/acs.jchemed.9b00326. (18) Olmsted, J.; Williams, G. M. Chemistry; Wiley: Hoboken, NJ,
Mathematical details for muscle activity, water splitting, 2006.
alkaline batteries, and dinitrogen tetraoxide enthalpy of (19) Chang, R. Chemistry; McGraw Hill: New York, NY, 2007.
(20) Averill, B.; Eldredge, P. Chemistry: Principles, Patterns, and
formation (PDF, DOCX)

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Applications; Pearson: San Francisco, CA, 2007.
(21) Moore, J. W.; Stanitski, C. L.; Jurs, P. C. Chemistry; Thomson
AUTHOR INFORMATION Higher Education: Belmont, CA, 2008.
Corresponding Author (22) Gilbert, T. R.; Kirss, R. V.; Foster, N.; Bretz, S. L.; Davies, G.
Chemistry; W. W. Norton: New York, NY, 2018.
*E-mail: dzkeifer@salisbury.edu. (23) Noll, R. J.; Hughes, J. M. Heat Evolution and Electrical Work of
ORCID Batteries as a Function of Discharge Rate: Spontaneous and
Reversible Processes and Maximum Work. J. Chem. Educ. 2018, 95,
David Keifer: 0000-0003-0770-0213 852−857.
Notes (24) O’Brien, J. C. Thermodynamic Considerations for Thermal
The author declares no competing financial interest. Water Splitting Processes and High Temperature Electrolysis.

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Proceedings of the 2008 International Mechanical Engineering Congress
ACKNOWLEDGMENTS and Exposition; 2008.
(25) Kanoglu, M.; Bolatturk, A.; Yilmaz, C. Thermodynamic analysis
I thank my colleague Dr. Anthony Rojas for providing of models used in hydrogen production by geothermal energy. Int. J.
insightful comments on how to strengthen this paper. I also Hydrogen Energy 2010, 35, 8783−8791.
thank the members of Salisbury University’s chemistry (26) Smith, M. J.; Vincent, C. A. Electrochemistry of the zinc-silver
department for letting me raid their offices and borrow a oxide system. Part 2. Practical measurements of energy conversion
selection of textbooks. using commercial miniature cells. J. Chem. Educ. 1989, 66, 683−687.

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(27) Morikawa, T.; Williamson, B. E. A Chemically Relevant Model
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(7) One detail that many general and physical chemistry books
neglect in this derivation is that “constant pressure” means not only
that the system and surrounding pressures are constant, but also that
they are equal. This is because, for constant-pressure surroundings,
wexpansion = −Psurr ΔV, where Psurr is the pressure of the surroundings.
It is only if the system pressure, P, is equal to Psurr that we can say

1411 DOI: 10.1021/acs.jchemed.9b00326

J. Chem. Educ. 2019, 96, 1407−1411