Chemical Potential Aris Kaksis Riga Univ. docent Biochemistry

Chemical Potential µ and Homeostasis

2013. Riga Stradin’s University BioChemicalPprocesE.doc

Chemical potential show, how much change of free energy GA brings into system-reaction adding of
1 mole amount of compound A . In a fact: how great amount of free energy belongs to one 1 mol in mixture.

It means how much free energy GA has itself per 1 mole compound A , if amount of compound in molar numbers
is nA = 1 mole : µA = = G°A + R•T•ln(XA) (1-1)

chemical potential of compound A, where: G°A, kJ/mol - standard chemical potential at standard conditions
T = 298.16 K , pressure p = 101.3 kPa; R = 8.3144 J/mol/K - universal gas constant;
ln(XA) - natural logarithmic function from argument XA and XA, unless - molar fraction concentration of
compound A, expressed as XA = nA/ntotal and laying between 0<XA≤1 (absence and pure) compound A
concentrations, where nA, mol - number of moles for compound A and ntotal , mol - total number of moles
all present compounds total including water. Logarithmic function properties ln(1) = 0 yield that standard
chemical potential G°A = µA at XA = 1 is pure A compound 1 mol free energy content G°A,
assuming standard free energy of formation G°A from elements for compound A per one 1 mole.

Reaction proceeds completely forward until end only when products of reaction have hardly little disposition
to reverse change back into reactants. In other words these products of reaction have trifling remarkable or
zero value of chemical potential: µproducts = 0 , affinity turns back to reactants: A <=x= products .

Thermodynamical conditions of chemical equilibrium.

Provided chemical potential of reaction products is taking into consideration
(it has anything remarkable level of value ) , then reaction proceeds not completely until end, go not on completely
100% to reactants conversion to products, but one can observe the setting in equilibria.

In state of equilibria sum of chemical potentials for initial compounds is equal to sum of chemical potentials for
products – according chemical reaction equation reactants aA + bB and products cC + dD:

aA + bB cC + dD ; aµA + bµB = cµC + dµD (1-2)

     because compound factor-coefficients a, b, c, and d means multiply µ
    a times molecules A (A+A+A+…)= aA = amA and so on B, C, and D as
     seen on equation of reaction expression(1-2), takes a part times b,c,d:

(B+B+B+...)= bB = bµB; (C+C+C+…)= cC = cµC;

(D+D+D+…)=dD=dµD Chemical potencial µ like as amount of
compound n in mols have additive properties, e.g. summing.

The concentrations X of reactants and products at equilibrium define the equilibrium constant, Keq (see the Chemical Equilibrium). In the general reaction chemical potential sum for reactants µreactant and products µproduct at equilibrium are equal:(µreactant)= (µproduct) ; and standard free energy change Greaction = µproduct - µreactant =0 for reaction is zero and expressed negative standard free energy change is

- G°reaction = R•T•ln = R•T•ln(Keq) ; Keq = (1-3)

Kaksis 2011. Riga Stradin’s University http://aris.gusc.lv/BioThermodynamics/ChemicalPotential.doc
Greaction = G°reaction + R•T•ln ≠0 ; 0 = G°reaction + R•T•ln(Keq) at equilibrium zero (1-4)

in Homeostasis(XD^d•XC^c)/(XA^a•XB^b)≠Keqdiffers from equilibrium constant Keq =

We must be careful to distinguish between two 2 different quantities: the free-energy change, G, and the
standard free-energy change, G°. Each chemical reaction has a characteristic standard free-energy change per
one 1 mol of reactant, which maybe positive G°>0, negative G°<0, or some times zero G°=0, depending on
the equilibrium constant Keq of the reaction. The standard free-energy change G° tells us in which direction
and how far a given reaction must go to reach equilibrium when the temperature is 25 °C or
To = 298.15 K, and the pressure p is 101.3 kPa (1 atm) and component concentrations at equilibrium are X.
Thus G° is a constant: it has a characteristic, unchanging value for a given reaction. But the actual free-energy
change G, is a function of reactant and product concentrations X and of the temperature T = 310.15 °K
prevailing during the reaction in human body, which will not necessarily match the standard conditions as
defined above. Moreover, the G of any reaction proceeding => spontaneously toward its equilibrium state is
always negative G<0, becomes less negative as the reverse <= reaction proceeds, and is zero G=0 at the point
of equilibrium (XD^d•XC^c)/(XA^a•XB^b) = Keq, indicating that no more work W = -G = 0 can be done by the
reaction: aA + bB = cC + dD according expression G°reaction + R•T•ln(Keq)=0 (1-4).
Studies in „Medical chemistry”, „Biochemistry”. Studies of Gibs free energy changeΔG_reac = ΔH_reac – T ·ΔS_reac

ΔH_reac Enthalpy	ΔS_reac Entropy	T Temperature	ΔG_reac Free energy	Spontaneous ability of reaction
Dispersed energy T·ΔS_reac>0 is bound in surrounding and is lost as used free energy ΔG_reac<0	ΔS_reac>0 Positive entropy increases entropy change is positive	decomposition reaction	AB =>A + B	Biochemical catabolism in living organisms consume the free energy in spontaneous reactions maintain organisms living.
1. Endothermic Positive ΔH_reac>0		low T ΔH_reac>\|-T·ΔS_reac\|	Positive ΔG_reac>0 ΔH_reac–T·ΔS_reac>0	unfavorable reaction at low temperature
1. Endothermic Positive ΔH_reac>0	Dispersed energy is forming greater measure of chaos ΔS_reac>0 Positive . Spontaneous catabolic reactions	high T ΔH_reac<\|-T·ΔS_reac\|	Negative ΔG^°_reac< 0 ΔH_reac–T·ΔS_reac< 0	spontaneous reaction at high temperature
2. Exothermic Negative ΔH_reac<0	consume free energy change ΔG_reac<0 for life mantanance of organisms 37º C in human as well as to supply the heat for organisms as reaction Exothermic ΔH_reac<0	low T high T	Negative ΔG_reac< 0 ΔH_reac–T·ΔS_reac> 0	spontaneous reaction at any temperature
Living cell proliferations and existing conditions for Life	ΔS_reac<0 Negative entropy decreases entropy change is negative	synthesis reaction	A + B =>AB	Biochemical anabolism energy accumulates and organize in compounds as synthesized the higher order as well decreases measure of chaos ΔS_reac<0 Negative
3. Endothermic Positive ΔH_reac>0	Synthesized as well as produced free energy ΔG_reac>0 Positive accumulates in photosynthesis, in ATP synthesis, in polypeptides as well as in proteins,	any T	Positive ΔG_reac>0 ΔH_reac–T·ΔS_reac>0	unfavorable reaction thermodynamically forbidden at any temperature
4. Exothermic Negative ΔH_reac<0	in synthesized molecules, living cells live and proliferates	high T \|ΔH_reac\|<\|-T·ΔS_reac	Positive ΔG_reac>0 ΔH_reac–T·ΔS_reac>0	unfavoable rreaction at high temperature
4. Exothermic Negative ΔH_reac<0		low T \|ΔH_reac\|>\|-T·ΔS_reac\|	Negative ΔG_reac<0 ΔH_reac–T·ΔS_reac<0	spontaneous reaction at low temperature

In life important are negative change ΔS_reac<0 of entropy and positive increase ΔG_reac>0 of free energy!

Negative change ΔS_reac<0 dispersed energy TΔS

decreases and into reaction accumulates supplied +Q energy into compound macroergic bonds as increase the free energy

ΔG_reac>0.

ΔH_reac=ΔG_reac+T·ΔS_reac

Opposite to spontaneous reaction

ΔG_reac>0 negative change of free energy is lost energy.

A.Kaksis 2005. Riga Stradin’s University 4^th page http://aris.gusc.lv/BioThermodynamics/BioThermodynamics.doc

Three Reaction examples studies of Homeostasis for students Medical (Bio)Chemistry :

1. Glucose and oxygen Green plants Photosynthes
red and blue light photons energy
E=hν absorbtion heat accumulates
in glucose substance

ΔH_reac>0 EndothermicΔH_reac=+2805,27 kJ/mol

6 H₃O⁺+ 6 HCO₃^-+Q+ΔG_reac=+2970 kJ/mol
Endoergic ΔG_reac=+2970 kJ/mol

photosynthetic proces ΔG_reac>0 is
free energy accumulates
in 1 mol cytosolic glucose molecules
C₆H₁₂O₆ biochemically „combusted” by oxygen O₂
in mitochondria to combustion products
CO₂ and H₂O
along oxidative phosphorilation pathway.

direct reaction

———————=>

reverse reaction
<=———————

       Plant Enzymes
<=---Photo synthetic
<=-Reaction
<=--- Center
           oxygen
C₆H₁₂O₆+ 6 O₂
            + 6 H₂O
Glucose
biochemical
„combustion”
Glycolysis,
Oxidative
Phosphorylation

The Membrane potential 3^rd page http://aris.gusc.lv/BioThermodynamics/MembraneElektrodsAM.doc

(page 9 http://aris.gusc.lv/BioThermodynamics/OxRedBiologicalW.doc)

2. ATPase driven ATP synthesis (ATP adenosine tr

One mole of glucose C₆H₁₂O₆ produces glycolytical, mitochondrial totally 36 ATP molecules. Membrane integral enzyme ATPase nano engine to accumulate free energy ΔG_reac=+30.5 kJ/mol per produced ATP molecule under proton gradient drives in to reaction

ADP^3- +H₂PO₄^-