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![Page 1: Biological systems are open Develop our understanding of the utility of G Introduce thermodynamic equilibrium (helps us to determine G°´) Effect of.](https://reader035.fdocuments.us/reader035/viewer/2022062804/5697bf7a1a28abf838c82fc3/html5/thumbnails/1.jpg)
Biological systems are open
• Develop our understanding of the utility of G
• Introduce thermodynamic equilibrium (helps us to determine G°´)
• Effect of T on thermodynamic equilibrium
• Develop our understanding of the utility of G
• Introduce thermodynamic equilibrium (helps us to determine G°´)
• Effect of T on thermodynamic equilibrium
![Page 2: Biological systems are open Develop our understanding of the utility of G Introduce thermodynamic equilibrium (helps us to determine G°´) Effect of.](https://reader035.fdocuments.us/reader035/viewer/2022062804/5697bf7a1a28abf838c82fc3/html5/thumbnails/2.jpg)
![Page 3: Biological systems are open Develop our understanding of the utility of G Introduce thermodynamic equilibrium (helps us to determine G°´) Effect of.](https://reader035.fdocuments.us/reader035/viewer/2022062804/5697bf7a1a28abf838c82fc3/html5/thumbnails/3.jpg)
![Page 4: Biological systems are open Develop our understanding of the utility of G Introduce thermodynamic equilibrium (helps us to determine G°´) Effect of.](https://reader035.fdocuments.us/reader035/viewer/2022062804/5697bf7a1a28abf838c82fc3/html5/thumbnails/4.jpg)
)*( PdVdwdw revrev
![Page 5: Biological systems are open Develop our understanding of the utility of G Introduce thermodynamic equilibrium (helps us to determine G°´) Effect of.](https://reader035.fdocuments.us/reader035/viewer/2022062804/5697bf7a1a28abf838c82fc3/html5/thumbnails/5.jpg)
![Page 6: Biological systems are open Develop our understanding of the utility of G Introduce thermodynamic equilibrium (helps us to determine G°´) Effect of.](https://reader035.fdocuments.us/reader035/viewer/2022062804/5697bf7a1a28abf838c82fc3/html5/thumbnails/6.jpg)
![Page 7: Biological systems are open Develop our understanding of the utility of G Introduce thermodynamic equilibrium (helps us to determine G°´) Effect of.](https://reader035.fdocuments.us/reader035/viewer/2022062804/5697bf7a1a28abf838c82fc3/html5/thumbnails/7.jpg)
![Page 8: Biological systems are open Develop our understanding of the utility of G Introduce thermodynamic equilibrium (helps us to determine G°´) Effect of.](https://reader035.fdocuments.us/reader035/viewer/2022062804/5697bf7a1a28abf838c82fc3/html5/thumbnails/8.jpg)
Thermodynamics of open systems (reaction mixes)
We need to handle systems that contain more than one component, the concentrations of which can vary (e.g. a solution containing a number of dissolved reactants). These are called open systems.
Consider: A + B <===> C + D
There are four solutes (reactants or products) and the concentrations of A, B, C and D are affected by this and other reactions. How do we calculate G for this reaction?
![Page 9: Biological systems are open Develop our understanding of the utility of G Introduce thermodynamic equilibrium (helps us to determine G°´) Effect of.](https://reader035.fdocuments.us/reader035/viewer/2022062804/5697bf7a1a28abf838c82fc3/html5/thumbnails/9.jpg)
Thermodynamics of open systems (reaction mixes)
For one component (A): GA = GA°´ + nART.ln[A]
And for 1 mole of A:
where the units are free energy per mole (J mol-1). This quantity is also known as the chemical potential (µA) and we write:
µA = µA°´ + RT.ln[A]
Previously we had for the general case: dG = Vdp - SdT
For open, multicomponent systems, we write:
dG = Vdp - SdT + i µidni
G A G Ao 'RT ln[A]
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Thermodynamics of open systems (reaction mixes)
In biological systems (constant p and T):
dG = i µidni or G = i µini
We can now calculate G for a specific reaction:
aA + bB <===> cC + dD
where the reactants are A and B, the products are C and D. a, b, c and d represent the number of moles of each that participate in the reaction. For this reaction:
G = Gproducts - Greactants
= (cµc + dµd) - (aµa + bµb)
![Page 11: Biological systems are open Develop our understanding of the utility of G Introduce thermodynamic equilibrium (helps us to determine G°´) Effect of.](https://reader035.fdocuments.us/reader035/viewer/2022062804/5697bf7a1a28abf838c82fc3/html5/thumbnails/11.jpg)
Thermodynamics of open systems (reaction mixes)
But µA = µA°´ + RT.ln[A] etc. so:
G = [(cµc°´ + dµd°´) - (aµa°´ + bµb°´) + RTln([C]c[D]d/[A]a[B]b)
which we express as:
G = G°´ + RTln([C]c[D]d/[A]a[B]b) (Joules)
To find the free energy change per mole, note that a, b, c and d will reflect the stoichiometry of the reaction (the numbers of each type of molecule involved in a single reaction). For example, a single reaction might involve the following numbers of molecules:
2A + 1B <----> 1C + 2D
which is the same as: A + A + B <----> C + D + D
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Thermodynamics of open systems (reaction mixes)
We now have an equation which allows us to calculate G in practice:
(J mol-1)
a, b, c and d are the stoichiometric coefficients.
G°´ is the standard free energy change per mole.
G Go RT lncC dD aA bB
Standard free energy change per mole is the free energy change that occurs when reactants at 1 M are completely converted to products at 1 M at standard p, T and pH.
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Thermodynamic equilibrium
We calculate G so that we can determine the spontaneous direction of a reaction (favourable or unfavourable). To do that we must determine:
G°´• the concentration of each component • the stoichiometry of the reaction.
We need G < 0 for a favourable forward reaction. We can drive the reaction forward either by:
• increasing [A] and/or [B]• decreasing [C] and/or [D]
Living cells can (sometimes) control reactant/product concentrations to ensure that G < 0 for desired reactions.
G G o 'RT lncC dD aA bB
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Thermodynamic equilibrium
In many cases there is a dynamic steady state: new reactants are made and products consumed in other reactions in order to keep concentrations steady. So G holds constant and, if it is negative, the reaction keeps going.
If the cell dies, the reaction will reach thermodynamic equilibrium and come to a halt. Let’s see what happens:
We have:
If G < 0 at time zero and the system is isolated, then G becomes less negative as the concentrations of C and D build up (and those of A and B decline). Eventually equilibrium is reached when G =0.
G G o 'RT lnC c
D d
A aB b
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Thermodynamic equilibrium
At equilibrium,
and define the equilibrium constant K:
This constant depends on the chemical natures of the reactants and products. We measure G°´ by measuring the concentrations of A, B, C and D once the reaction has reached equilibrium.
G o ' RT lnC c
D d
A aB b
eq
K C c
D d
A aB b
eq
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Thermodynamic equilibrium
Note: if G°´ < 0, then ([C][D])eq > ([A][B])eq (for a=b=c=d=1)
if G°´ > 0, then ([C][D])eq < ([A][B])eq
Thus, G°´ determines whether the reactants or products predominate at equilibrium. T
Thermodynamic equilibrium is not a static state (conversion of A and B to C and D and back again keeps going but there is no net change in their concentrations).
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The effect of temperature
We can write: G°´ = -RTlnK = H°´ - TS°´
Thus, ln K Go'
RT
Ho'
R
1
T
So'
R
We can therefore plot lnK vs 1/T to determine H°´ and S°´, the standard enthalpy and entropy of the reaction respectively.
Such a plot is known as a Van’t Hoff plot. It will give a straight-line if H°´ is independent of T (usually true for narrow ranges of T).
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Summary
(1) The sign of G tells us the spontaneous direction of a reaction:
G < 0, forwardG > 0, reverseG = 0, equilibrium
(2) G°´, the standard free energy change for a reaction determines the relative concentrations of reactants and products that will be found at thermodynamic equilibrium.
(3) Neither quantity tells us about the rate of the reaction.
K G ' RTe C c
D d
A aB b
eq
See a textbook for more details on G and G°´ - we will see this later on at transition state theory
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References
1. Biological Physics. Energy, Information, Life Philip Nelson, (Freeman and Company, New York, 2004).
2. Principles of Physical Biochemistry, chapter 2, pp. 69-89 Kensal E. van Holde, W. Curtis Johnson and P. Shing Ho (Pretice Hall, Upper Saddle River, 1992).