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Bis2A 4.1 Thermodynamics
∗
The BIS2A Team
This work is produced by OpenStax-CNX and licensed under the
†
Creative Commons Attribution License 4.0
Abstract
This module will discuss endergonic and exergonic reactions and their relevance in biology.
Section Summary
A series of laws, called the laws of thermodynamics, describe how energy is transferred and dispersed in a
reaction. We consider two of these. The rst law states that the total amount of energy in the universe is
constant. This means that energy can't be created or destroyed in a reaction or process, only transferred.
The second law of thermodynamics states the entropy of the universe is always increasing. We describe the
general relevance of these two laws and their application in biology.
1 Laws of Thermodynamics
Thermodynamics is concerned with describing the changes in systems before and after a change. This usually
involves a discussion about the energy transfers and its dispersion within the system. In nearly all practical
cases, these analyses require that the system and its surroundings be completely described. For instance,
when discussing the heating of a pot of water on the stove, the system may includes the stove, the pot, and
the water and the environment or surroundings may include everything else. Biological organisms are what
are called open systems; energy is transferred between them and their surroundings.
1st Law of Thermodynamics
The rst law of thermodynamics deals with the total amount of energy in the universe. It states that this
total amount of energy is constant. In other words, there has always been, and always will be, exactly
the same amount of energy in the universe. According to the rst law of thermodynamics, energy may be
transferred from place to place (module 4.0), but it cannot be created or destroyed. The transfers of energy
take place around us all the time. Light bulbs transfer energy an electrical power station into heat and
photons to produce light. Gas stoves transfer energy stored in the bonds of chemical compounds into heat
and light. Heat, by the way, is the amount of energy transferred from one system to another because of a
temperature dierence. Plants perform one of the most biologically useful energy transfers on earth: they
transfer energy in the photons of sunlight into the chemical bonds of organic molecules. In every one of these
cases energy is neither made or destroyed and we must try to account for all of the energy when we examine
some of these reactions.
1st Law and the Energy Story
The rst law of thermodynamics is deceptively simple. Students often understand that energy cannot be
created or destroyed. Yet, when describing an energy story of a process they often make the mistake of
saying things such as "energy is produced from the transfer of electrons from atom A to atom B". While
most of us will understand the point the student is trying to make, the wrong words are being used. Energy
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is not made or produced, it is simply transferred. To be consistent with the rst law, when telling an energy
story, make sure that you try to explicitly track all of the places that ALL of the energy in the system at
the start of a process goes by the end of a process.
2nd Law of Thermodynamics
An important concept in physical systems is that of entropy. Entropy is related to the with the ways in
which energy can be distributed or dispersed within the particles of a system. The 2nd Law of Thermodynamics states that entropy is always increasing in a system AND its surroundings (everything outside the
system). This idea helps explain the directionality of natural phenomena. In general the notion is that the
directionality comes from the tendency for energy in a system to move towards a state of maximal dispersion.
The 2nd law, therefore, means that in any transformation we should look for an overall increase in entropy (or
dispersion of energy), somewhere. A idea that is associated with increased dispersion of energy in a system or
its surroundings is that as dispersion increases the ability of the energy to be directed towards work decreases.
There will be many examples of where the entropy of a system decreases. To be consistent with the second
law, however, we must try to nd something else (likely a closely connected system in the surroundings) that
must compensate for the "local" decrease in entropy with an equal or greater increase in entropy.
The entropy of a system can increase when:(a) it gains energy;(b) a change of state occurs from solid
to liquid to gas; (c) mixing of substances occurs;(d) the number of particles increases during a reaction.
note:
Does the second law say that entropy is conserved?
Biological systems, on the surface, see to defy the Second Law of Thermodynamics. They
don't. Why?
note:
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Figure 1:
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An increase in disorder can happen in dierent ways. An ice cube melting on a hot sidewalk
is one example. Here, ice is displayed as a snowake, with organized, structured water molecules forming the snowake. Over time, the snowake will melt into a pool of disorganized, freely moving water
molecules.
Source:
https://www.boundless.com/physics/textbooks/boundless-physics-textbook/thermodynamics-
14/entropy-119/order-to-disorder-417-6459/
If we consider the rst and second laws together (the conservation of energy and the need for entropy to
increase if a process happens) we come to a useful conclusion. In any process where energy is transferred or
redistributed within a system entropy must increase. This increase in entropy is related to how "useful" the
energy is to do work (generally becoming less available as entropy increases). So, we can conclude that in
any transformation we consider that while all of the energy must be conserved the required change increase
in entropy means that some of the energy will become distributed in a way that makes it less useful for work.
In many cases, particularly in biology, some of the increase in entropy can be tracked to a transfer of energy
to heat in the environment.
2 Free Energy
If we want to describe transformations, therefore, it is useful to have a measure of (a) how much energy is
in a system and (b) the dispersal of that energy within the system and of course how these change between
the start and end of a process. The concept of free energy, often referred to as Gibbs free energy or free
enthalpy (abbreviated with the letter G), in some sense does just that. Gibbs free energy can be dened in
several interconvertible ways, but a useful one in the context of biology is the enthalpy (internal energy) of
a system minus the entropy of the system scaled by the temperature. The dierence in free energy when a
process takes place is often reported in terms of the change (delta) of enthalpy (internal energy) denoted H,
minus the temperature scaled change (delta) in entropy, denoted S. See the equation below.
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∆G = ∆H − T∆S
The Gibbs energy is often interpreted as the amount of energy available to do useful work. With a bit
of handwaving we can interpret this by invoking the idea presented above that the dispersion of energy
(required by the Second Law) associated with a positive change in entropy somehow renders some of the
energy that is transferred less useful to do work. One can say that this is reected in part in the T∆S term
of the Gibbs equation.
To provide a basis for fair comparisons of changes in Gibbs free energy amongst dierent biological
transformations or reactions the free energy change of a reaction is measured under a set of common standard
experimental conditions. The resulting standard free energy change of a chemical reaction is expressed as an
amount of energy per mole of the reaction product (either in kilojoules or kilocalories, kJ/mol or kcal/mol;
1 kJ = 0.239 kcal) when measured at a standard pH, temperature, and pressure conditions. Standard
pH, temperature, and pressure conditions are generally calculated at pH 7.0, 25 degrees Celsius, and 100
kilopascals (1 atm pressure), respectively. It is important to note that cellular conditions vary considerably
from these standard conditions, and so actual ∆G inside a cell will dier considerably from those calculated
under standard conditions.
3 Endergonic and Exergonic Reactions
Reactions that have a ∆G < 0 means that the products of the reaction have less free energy than the reactants. Since ∆G is the dierence between the enthalpy and entropy changes in a reaction a net negative ∆G
can arise in dierent ways. The left panel of Figure 2 below shows a common graphical representation an
exergonic reaction. Free energy is plotted on the y-axis and the x-axis in arbitrary units shows model for the
progress of a reaction. This type of graph is called a reaction coordinate diagram. In the case of an exergonic
reaction depicted below the chart indicates two key things: (1) the dierence between the free energy of the
reactants and products is negative and (2) the progress of the reaction requires some input of free energy
(shown as an energy hill). This graph does not tell us how the energy in the system was redistributed,
only that the dierence between enthalpy and entropy is negative. Reactions that have a negative ∆G and
consequently are termed exergonic reactions. These reactions are occur spontaneously. Understanding
which chemical reactions are spontaneous is extremely useful for biologists that are trying to understand
whether a reaction is likely to "go" or not.
It is important to note that the term spontaneous - in the context of thermodynamics - does NOT imply anything about how fast the reaction proceeds. The change in free energy only describes the dierence
between beginning and end states NOT how fast that transition takes. This is somewhat contrary to the
everyday use of the term which usually carries the implicit understanding that something happens quickly.
As an example, the oxidation/rusting of iron is a spontaneous reaction. However, an iron nail exposed to air
does not rust instantly - it may take years.
A chemical reaction with a positive ∆G means that the products of the reaction have a higher free
energy than the reactants (see the right panel of Figure 2). These chemical reactions are called endergonic
reactions, and they are NOT spontaneous. An endergonic reaction will not take place on its own without
the transfer of energy into the reaction or increase of entropy somewhere else.
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Figure 2:
Exergonic and endergonic reactions result in changes in Gibbs free energy.
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In exergonic
reaction the free energy of the products is lower than that of the reactants; meanwhile in endergonic the
free energy of the products is higher than that of the reactants.
The building of complex molecules, such as sugars, from simpler ones is an anabolic process and is
endergonic. On the other hand, the catabolic process, such as the breaking down of sugar into simpler
molecules is generally exergonic. Like the example of rust above, while the breakdown of biomolecules is
generally spontaneous these reactions don't necessarily occur instantaneously(quickly). Figure 3 shows some
other examples of endergonic and exergonic reactions. But remember, the terms endergonic and exergonic
only refer to the dierence in free energy between the products and reactants - they don't tell you about the
rate of reaction (how fast it happens). The issue of rate will be discussed in later sections.
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Figure 3:
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Shown are some examples of endergonic processes (ones with positive changes in free energy
between products and reactants) and exergonic processes (ones with negative changes in free energy
between products and reactants). These include (a) a compost pile decomposing, (b) a chick hatching
from a fertilized egg, (c) sand art being destroyed, and (d) a ball rolling down a hill. (credit a: modication
of work by Natalie Maynor; credit b: modication of work by USDA; credit c: modication of work by
Athlex/Flickr; credit d: modication of work by Harry Malsch)
Look at each of the processes shown in gure 3 above, and decide if it is endergonic or
exergonic. In each case, does enthalpy increase or decrease, and does entropy increase or decrease?
Can you make a complete energy story for each of the processes shown?
note:
An important concept in the study of metabolism and energy is that of chemical equilibrium. Most chemical
reactions are reversible. They can proceed in both directions, often transferring energy into their environment in one direction, and transferring energy in from the environment in the other direction. The same is
true for the chemical reactions involved in cell metabolism, such as the breaking down and building up of
proteins into and from individual amino acids, respectively. Reactants within a closed system will undergo
chemical reactions in both directions until a state of equilibrium is reached. This state of equilibrium is one
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of the lowest possible free energy and a state of maximal entropy. Equilibrium in a chemical reaction, is
the state in which both reactants and products are present in concentrations which have no further tendency
to change with time. Usually, this state results when the forward reaction proceeds at the same rate as the
reverse reaction. NOTE THIS LAST STATEMENT! Equilibrium means that the relative concentrations of
reactants and products is not changing in time BUT it does NOT mean that there is no interconversion
between substrates and products - it just means that when reactant is converted to product that product is
converted to reactant at an equal rate.
Either a rebalancing of substrate of product concentrations (by adding or removing substrate or product) or
a positive change in free energy, typically by the transfer of energy from outside the reaction, is required to
move a reaction out of a state of equilibrium. In a living cell, most chemical reactions do not reach a state of
equilibrium - this would require that they reach their lowest free energy state. Energy is therefore required
to keep biological reactions out of their equilibrium state. In this way, living organisms are in a constant
energy-requiring, uphill battle against equilibrium and entropy.
Figure 4:
At equilibrium, do not think of a static unchanging system. Instead, picture molecules moving
, in equal amounts from one area to another. Here, at equilibrium, molecules are still moving from left
to right and right to left. The net movement however, is equal. There will still be about 15 molecules in
each side of this ask once equilibrium is reached.
Source: https://courses.candelalearning.com/chemistryformajorsx1xmaster/chapter/entropy/
Exercise 1: Reading Energy Diagrams
In exergonic reactions, the products have:
a.
b.
c.
d.
e.
f.
more energy than the reactants
less energy than the reactants
are always the higher energy compounds
are always the lower energy compounds
a and c
b and d
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(Solution on p. 12.)
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Exercise 2
The information in the deltaG of a reaction:
a.
b.
c.
d.
e.
f.
g.
h.
i.
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(Solution on p. 12.)
tells you the rate of the reaction
tells you if it is exergonic or endergonic
tells if the reaction has reached equilibrium
tells the the amount of energy dierence between the reactants and products
a and b
a and c
a and d
b and c
b and d
4 Activation Energy
Let's start to think a little about the rate of a reaction. Even exergonic (spontaneous)reactions typically
require a small increase in free energy before they can begin converting reactants to products. This initial
positive change in free energy is called the activation energy (or free energy of activation) and is sometimes
abbreviated EA .
The oxidation of gasoline is highly exergonic. Despite this, why do cars not spontaneously
explode in parking lots?
note:
Why do nearly all chemical reactions - even those with a very large negative ∆G - rst require some free
energy increase to proceed? The reason lies in the steps that take place during a chemical reaction. Chemical
reactions, almost by denition, require that some chemical bonds be broken and/or formed. For example,
when a glucose molecule is broken down, the glycosidic bonds are broken, bonds within water are broken and
new bonds are made between the "disassembled" water and the atoms that were involved in the glycosidic
bond. While the overall reaction (the combination of energy cost of breaking bonds, energy gained by
making bonds and the change of entropy between reactants and products) may be negative the breaking of
the bonds requires some energy input which increases the free energy of the system. The state of the reaction
at the maximum free energy of a reaction is often termed the transition state. This state is considered
to be relatively unstable where the reaction may either relax back to the reactant state or transition to the
products. The height of the activation energy "barrier" has a direct relationship to the rate of a reaction.
The higher/larger the barrier, the slower the reaction.
note: Can you propose a physical analog (or model) that can help explain why the activation
energy barrier is related to the rate of the reaction, whereas the free energy dierence between
substrate and product is not.
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Figure 5:
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Activation energy is the energy required for a reaction to proceed, and it is lower if the
reaction is catalyzed. The horizontal axis of this diagram describes the sequence of events in time.
Where does the free energy required required to overcome the activation energy barrier come from? The
sources vary. One source is the energy transferred as heat from the surroundings. This transfer changes the
kinetic energy of molecules in the system, increasing the frequency and force with which they collide and
thus the frequency that they will react. In other cases energy may be transferred from other reactions.
As noted, the activation energy of a particular reaction determines the rate at which it will proceed. The
higher the activation energy, the slower the chemical reaction will be. The example of iron rusting illustrates
an inherently slow reaction. The conversion of diamond into graphite is another spontaneous reaction that
take a LONG time. These reactions occur slowly over time because of high activation energy barriers. The
burning (oxidation) of many fossil fuels, which is an exergonic process, will take place at a negligible rate
unless their activation energy is overcome by sucient heat from a spark. Once these fuels begin to burn,
however, the chemical reactions release enough heat to help overcome the activation energy barrier for the
combustion of the rest of the fuel. Like these reactions outside of cells, the activation energy for most cellular
reactions is too high for heat energy to overcome at ecient rates. By the way, this is a very good thing
as far as living cells are concerned. Important macromolecules, such as proteins, DNA, and RNA, store
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considerable energy, and their breakdown is exergonic. If cellular temperatures alone provided enough heat
energy for these exergonic reactions to overcome their activation barriers, the essential components of a cell
would disintegrate. Therefore, in order for important cellular reactions to occur at appreciable rates (number
of reactions per unit time), their activation energies must be lowered (see gure 4). Something that helps
lower the activation energy barrier is referred to as catalysis.
note: If no activation energy were required to break down sucrose (table sugar), would you be
able to store it in a sugar bowl?
:
Exercise 3: Activation Energy
(Solution on p. 12.)
Lowering the activation energy:
a.makes the reaction happen faster
b.lowers the energy level of the transition state
c.is accomplished by adding a catalyst to the reaction
d.always causes more product to be produced
e.only reduces the transition state energy level in one direction, from reactants to
products
f.a, b and c
g.b and c
h.all of the above are true
Exercise 4
(Solution on p. 12.)
Which of the following comparisons or contrasts between endergonic and exergonic reactions is
false?
a. Endergonic reactions have a positive ∆G and exergonic reactions have a negative ∆G
b. Endergonic reactions consume energy and exergonic reactions release energy
c. Both endergonic and exergonic reactions require a small amount of energy to overcome an
activation barrier
d. Endergonic reactions take place slowly and exergonic reactions take place quickly
Exercise 5
(Solution on p. 12.)
Which of the following is the best way to judge the relative activation energies between two given
chemical reactions?
a.
b.
c.
d.
Compare the ∆G values between the two reactions
Compare their reaction rates
Compare their ideal environmental conditions
Compare the spontaneity between the two reactions
5 Appendix: Energy Units
In the International System of Units (SI), the unit of work or energy is the Joule (J). For very small amounts
of energy, the erg (erg) is sometimes used. An erg is one ten millionth of a Joule:
1
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Joule = 10, 000, 000 ergs
(1)
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Power is the rate at which energy is used. The unit of power is the Watt (W), named after James Watt,
who perfected the steam engine:
1
(2)
Watt = 1 Joule/second
Power is sometimes measured in horsepower (hp):
horsepower = 746 Watts
1
(3)
Electrical energy is generally expressed in kilowatt-hours (kWh):
1
kilowatt − hour = 3, 600, 000 Joules
(4)
It is important to realize that a kilowatt-hour is a unit of energy not power. For example, an
iron rated at 2000 Watts would consume 2x3.6x106 J of energy in 1 hour .
Heat energy is often measured in calories. One calorie (cal) is dened as the heat required
to raise the temperature of 1 gram of water from 14.5 to 15.5 ºC:
1
(5)
calorie = 4.189 Joules
An old, but still used unit of heat is the British Thermal Unit (BTU). ◦It is dened as the heat energy
required to raise the energy temperature of 1 pound of water from 63 to 64 F .
1
BTU = 1055
Joules
Physical Quantity
Force
Energy
Power
Name
Newton
Joule
Watt
Table 1
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Symbol
N
J
W
SI Unit
kg · m/s2
kg · m2 /s2
kg · m2 /s3
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Solutions to Exercises in this Module
Solution to Exercise (p. 7)
b
Solution to Exercise (p. 7)
i
Solution to Exercise (p. 10)
g
to Exercise (p. 10)
D
to Exercise (p. 10)
B
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