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Bai 3

Module by: Thang Nguyen

Internal Energy (E)

Figure 1
Figure 1 (graphics1.)

The internal energy of a biochemical system includes any kind of energy that might be changed by any chemical or biochemical reaction. Examples include the kinetic energy of motion and the energy of vibration and rotation of every atom, molecule and ion in the system. Other examples include all of the energy stored in the chemical bonds between atoms and the energy of noncovalent interactions between molecules and ions. The internal energy of a system is a function of its state. That is, the internal energy depends only on the initial and final states of the system, not on the path taken to get from the initial state to the final state. The thermodynamic state of a system is defined by prescribing the amounts of all substances and any two of the following three system variables:

1) Temperature (T)

2) Pressure (P)

3) Volume (V)

An open system can exchange energy with its surroundings and may therefore change its internal energy. This change is called

Figure 2
Figure 2 (graphics2.)
E. Internal energy exchanges can only involve heat (q) or work (w). This is the first law of thermodynamics:
Figure 3
Figure 3 (graphics3.)
E = q-w, where a positive value of q indicates heat absorbed by the system from its surroundings and a positive value of w indicates work is done by the system on its surroundings. Conversely, a negative value of q means that heat flows from the the system to its surroundings and a negative value of w means that the surroundings do work on the system.

When V is changed against a constant P, w = P

Figure 4
Figure 4 (graphics4.)
V or, using the ideal gas law,

w=

Figure 5
Figure 5 (graphics5.)
nRT.

Enthalpy

Figure 6
Figure 6 (graphics6.)

The enthalpy (H) is defined as H = E + PV. Where E is the internal energy, P is the pressure, and V is the volume.

At constant pressure,

Figure 7
Figure 7 (graphics7.)
H =
Figure 8
Figure 8 (graphics8.)
E + P
Figure 9
Figure 9 (graphics9.)
V. The same result can be obtained from the first law of thermodynamics:

Figure 10
Figure 10 (graphics10.)
E = q-w, so

q =

Figure 11
Figure 11 (graphics11.)
E + w, but w = P
Figure 12
Figure 12 (graphics12.)
V when V is changed against a constant P, so

q =

Figure 13
Figure 13 (graphics13.)
E + P
Figure 14
Figure 14 (graphics14.)
V

Thus, when the heat of a reaction is measured at constant pressure, it is really

Figure 15
Figure 15 (graphics15.)
H that is measured. Furthermore, most biological processes occur at constant pressure, so
Figure 16
Figure 16 (graphics16.)
H gives a more accurate measure of the energy available from a biological process than
Figure 17
Figure 17 (graphics17.)
E does. Finally, because E and PV are functions of state (not path), H is also a function of state. Thus,
Figure 18
Figure 18 (graphics18.)
H depends only on the initial and final states of the process for which it is calculated.

Entropy and the Second Law of Thermodynamics

Figure 19
Figure 19 (graphics19.)

Figure 20
Figure 20 (graphics20.)
E and
Figure 21
Figure 21 (graphics21.)
H describe the energy changes, but tell nothing about the favored direction for a process. To do this, one must take into account the degree of randomness or disorder of a system. The degree of randomness or disorder of a system is measured by a state function called the Entropy (S). Entropy is defined as S = kln(W), where k is the Boltzmann constant (the gas constant R divided by Avogadro's number) and W is the number of thermodynamic substates of equal energy.

The entropy of an ordered state is lower than that of a disordered state of the same system. For example, there are more ways to put a large number of molecules in a random or disorderly arrangement than there are to put them in an orderly arrangement. Thus, the increasing entropy in a system is a thermodynamic driving force.

The second law of thermodynamics states that the entropy of an isolated system will tend to increase to a maximum value. However, this form of the second law is of little use biologically because it applies only to isolated systems (systems that do not exchange energy with their surroundings). Most biological systems, however, are open - they exchange energy and matter with their surroundings. Thus, biological systems undergo changes in energy and entropy in many reactions, and both must determine the direction of thermodynamically favorable processes. The Gibbs Free Energy (G) is a function of state that includes both energy and entropy terms:

G = H-TS, where T is the absolute temperature, H (the enthalpy) measures the energy change at constant pressure, and S (the entropy) measures the randomness of the system. At constant temperature and pressure,

Figure 22
Figure 22 (graphics22.)
G =
Figure 23
Figure 23 (graphics23.)
H -T
Figure 24
Figure 24 (graphics24.)
S

A decrease in energy (-

Figure 25
Figure 25 (graphics25.)
H) and/or an increase in entropy (+
Figure 26
Figure 26 (graphics26.)
S) tends to make a process favorable. Either a negative
Figure 27
Figure 27 (graphics27.)
H or a positive
Figure 28
Figure 28 (graphics28.)
S tends to make
Figure 29
Figure 29 (graphics29.)
G negative. Thus, the second law can be restated for open systems as follows:

1.

Figure 30
Figure 30 (graphics30.)
G must be negative for a process in an open system to be favorable at constant temperature and pressure.

2. A positive

Figure 31
Figure 31 (graphics31.)
G indicates a process is not favorable.

Interplay of Enthalpy and Entropy

Figure 32
Figure 32 (graphics32.)

Table 3.3 summarizes how the balance between enthalpy and entropy determines the direction in which a process is thermodynamically favorable. However, keep in mind the following:

1. The favorability of a process (negative

Figure 33
Figure 33 (graphics33.)
) has nothing to do with reaction rate.

2. The entropy of an open system can decrease, but energy must be expended to do so, however.

Table 3.3

Figure 34
Figure 34 (graphics34.)

Figure 35
Figure 35 (graphics35.png)

Free Energy and Useful Work

Figure 36
Figure 36 (graphics36.)

The term

Figure 37
Figure 37 (graphics37.)
represents the portion of an energy change (
Figure 38
Figure 38 (graphics38.)
H) that is available to do useful work. If
Figure 39
Figure 39 (graphics39.)
H is the total energy in a reaction, then
Figure 40
Figure 40 (graphics40.)
G =
Figure 41
Figure 41 (graphics41.)
H -T
Figure 42
Figure 42 (graphics42.)
S indicates that part of
Figure 43
Figure 43 (graphics43.)
H is alway dissipated as heat (the T
Figure 44
Figure 44 (graphics44.)
S term) and is therefore unavailable for other things, such as muscle contraction, ion transport, or tissue growth. The remaining amount (
Figure 45
Figure 45 (graphics45.)
) is available for useful work, but may not actually be fully utilized for useful work because the efficiency of a process (the ratio of work actually accomplished to
Figure 46
Figure 46 (graphics46.)
, the maximum work available) is always less than 100%.

Free Energy and Concentration

Figure 47
Figure 47 (graphics47.)

Standard state represents a 1M solution. The chemical potential of a component A (GA) is equal to the chemical potential at the standard state plus RT ln[A]

Figure 48
Figure 48 (graphics48.png)

At [A] = 1M, GA = GA

Figure 49
Figure 49 (graphics49.)

Consider moving molecule A from one side of a membrane through which A can pass (region 1) to the other (region 2).

The free energy of moving A out of region 1 is given by

Figure 50
Figure 50 (graphics50.png)

The free energy of moving A into region 2 is given by

Figure 51
Figure 51 (graphics51.png)

Overall,

Figure 52
Figure 52 (graphics52.png)

Thus, if the concentration of A in region 2 is lower than in region 1,

Figure 53
Figure 53 (graphics53.)
G is negative and the process is favorable. On the other hand, if the concentration of A in region 2 is higher than in region 1,
Figure 54
Figure 54 (graphics54.)
G is positive and the process is unfavorable

Free Energy Change and the Equilibrium Constant

Figure 55
Figure 55 (graphics55.)

Free energy is a state function, so

Figure 56
Figure 56 (graphics56.)
G for a reaction depends only on the free energy of the initial state (the reactants) and the free energy of the final state (the products):

Figure 57
Figure 57 (graphics57.)
G = G(products) - G(reactants)

Consider the reaction aA + bB <=> cC + dD, where a is the number of moles of component A, b is the number of moles of component B, etc.

Using the equation for the chemical potential, and collecting the standard state terms into a single

Figure 58
Figure 58 (graphics58.)
, yields

Figure 59
Figure 59 (graphics59.)
G =
Figure 60
Figure 60 (graphics60.)
+ RT ln {([C]c[D]d)/([A]a[B]b)}

Simplifying (and remembering that each product and reactant must be raised to the appropriate power) yields the following general equation for determining

Figure 61
Figure 61 (graphics61.)
G under any set of conditions, where
Figure 62
Figure 62 (graphics62.)
is the free energy change for the standard state (1M):

Figure 63
Figure 63 (graphics63.)
G =
Figure 64
Figure 64 (graphics64.)
+ RT ln{[Products]/[Reactants]}

At equilibrium, the equilibrium constant K for the reaction is given by

K = {([C]c[D]d)/([A]a[B]b)}

Recall that

Figure 65
Figure 65 (graphics65.)
G = 0 at equilibrium, so substituting yields

0 =

Figure 66
Figure 66 (graphics66.)
+ RT ln K,

-

Figure 67
Figure 67 (graphics67.)
= RT lnK, or

Figure 68
Figure 68 (graphics68.png)

Whenever a system is displaced from equilibrium, it will spontaneously proceed in the direction necessary to reestablish the equilibrium state. Negative

Figure 69
Figure 69 (graphics69.)
G is the driving force for such a reaction.

Coupled Reactions

Figure 70
Figure 70 (graphics70.)

Reactions, such as A<=>B and C<=>D, when coupled, have a

Figure 71
Figure 71 (graphics71.)
that is the sum of the individual
Figure 72
Figure 72 (graphics72.)
s. This may be important if one of the reactions has a fairly large positive
Figure 73
Figure 73 (graphics73.)
.

Important Points about graphics74.G

Figure 74
Figure 74 (graphics75.)

1. Three important terms relating to the free energy change of a process are:

Figure 75
Figure 75 (graphics76.)
- the total free energy change for a reaction under any conditions

Figure 76
Figure 76 (graphics77.)
- free energy under standard conditions (all concentrations of 1M)

Figure 77
Figure 77 (graphics78.)
, the free energy change under standard biological conditions (all concentrations 1M, [H2O] = constant, and pH = 7.0)

Thus, a positive

Figure 78
Figure 78 (graphics79.)
may influence a reaction, but cellular conditions may make the overall
Figure 79
Figure 79 (graphics80.)
for the reaction negative.

2.

Figure 80
Figure 80 (graphics81.)
and only
Figure 81
Figure 81 (graphics82.)
determines whether a reaction is favorable as written.. Only when
Figure 82
Figure 82 (graphics83.)
is negative is a reaction favored. The sign of
Figure 83
Figure 83 (graphics84.)
or
Figure 84
Figure 84 (graphics85.)
does not determine the direction a reaction will proceed.

3.

Figure 85
Figure 85 (graphics86.)
depends on temperature (
Figure 86
Figure 86 (graphics87.)
=
Figure 87
Figure 87 (graphics88.)
H - T
Figure 88
Figure 88 (graphics89.)
S). This can be a factor for a given reaction occurring in different organisms living under very different conditions of temperature.

Factors Contributing to Large Energies of Hydrolysis of Phosphate Compounds

Figure 89
Figure 89 (graphics90.)

1. Resonance stabilization of phosphate products. Figure 3.9 depicts the resonance stabilization of the orthophosphate ion, HPO42- (abbreviated Pi). The multiple resonance forms are of equal energy, but all are not possible when the phosphate group is bound in an ester, such as ATP. Once Pi is released upon hydrolysis, however, the multiple resonance forms increase the overall entropy of the system, an energetically favorable process.

Figure 3.9: Resonance stabilization of orthophosphate, HPO42- (Pi).

Figure 90
Figure 90 (graphics91.)

Figure 91
Figure 91 (graphics92.png)

2. Additional hydration of hydrolysis products - Release of Pi allows greater opportunities for hydration. Hydration is an energetically favored state.

3. Electrostatic repulsion between charged products - When both products of hydrolysis are negatively charged (e.g., ADP and Pi in the hydrolysis of ATP), repulsion of the ionized products favors hydrolysis.

4. Enhanced resonance stabilization or tautomerization of product molecules - Hydrolysis is favored when product molecules can adopt multiple molecular forms. For example, pyruvate has two molecular forms, whereas PEP has only one.

5. Release of a proton in buffered solution - A proton is released in some hydrolysis reactions (see Figure 3.7), so hydrogen ion concentration (pH) influences the reaction.

For ATP4- + H2O <=> ADP3- + HPO42- + H+,

Figure 92
Figure 92 (graphics93.)
G =
Figure 93
Figure 93 (graphics94.)
+ RT ln {([ADP3-][HPO42-][H+])/([ATP(-4)][H2O])}, which can be rearranged as

Figure 94
Figure 94 (graphics95.)
G =
Figure 95
Figure 95 (graphics96.)
+ RTln { ([ADP3-][HPO42-]) / ([ATP4-])} + RT ln{[H+]/[H2O]}

Because RT ln{[H+] / [H2O]} is relatively constant at pH 7.0 in biological systems, it can be incorporated into

Figure 96
Figure 96 (graphics97.)
to make
Figure 97
Figure 97 (graphics98.)
. Thus,

Figure 98
Figure 98 (graphics99.)
=
Figure 99
Figure 99 (graphics100.)
+RT ln{[H+] / [H2O]}

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