Page 289 - Thermodynamics of Biochemical Reactions

Thermodynamics of Biochemical Reactions at Specified pH 289

To make the calculation at the other temperatures, we can use calcdGHT to produce the function of T, pH and ionic strength
that will give AGO and AHo at other temperatures.

calcdGHT [speciesmat-1 : =
ModuleIEdGzero, dGzeroT,dHzero,zi, nH, gibbscoeff,pHterm,
isterm,gpfnsp,dGfn,dHfn),(*This program produces the function of T (in Kelvin), pH and
ionic strength (is) that gives the standard transformed Gibbs energy of formation of a
reactant (sum of species) and the standard transformed enthalpy. The input speciesmat
is a matrix that gives the standard Gibbs energy of formation at 298.15 K, the
standard enthalpy of formation at 298.15 K, the electric charge, and the number of
hydrogen atoms in each species. There is a row in the matrix for each species of the
reactant. gpfnsp is a list of the functions for the transformed Gibbs energies of the
species. The output is in the form {dGfn,dHfn), and energies are expressed in kJ
molA-l. The values of the standard transformed Gibbs energy of formation and the
standard transformed enthalpy of formation can be calculated at any temperature in the
range 273.15 K to 313.15 K, any pH in the range 5 to 9, and any ionic strength in the
range 0 to 0.35 m by use of the assignment operator(/.).*)
{dGzero,dHzero,zi,nH}=Transpose[speciesmat];
gibbscoeff=9.20483*1OA-3*t-l.284668*lOA-5*tA2+4.95l99*lOA-8*tA3;
dGzeroT=dGzero*t/298.15+dHzero*(l-t/298.15);
pHterm nH*8.31451*(t/1000)*LOg[10A-pH];
istennG = gibbscoeff*((ziA2) - nH)*(isA.5)/(1 + 1.6*isA.5);
gpfnsp=dGzeroT - pHterm - istennG;
dGfn=-8.31451*(t/100O)*Log[A~ply[Plus,Exp[-l*gpfnsp/(8.3l45l*(t/lOOO)~lll;
dIifn=-tA2*D[dGfn/t,t];
{dGfn,dHfn)l
(b) Calculate the standard transformed Gibbs energies of of the reactants and the reaction at 283.15 K.

atp283=calcdGHT[atpspl [[111/.t->283.15;

adp283=calcdGHT[adpspl ttlIl/.t->283.15;

dGerx283=calctrGerx[at~283+h20283+de==adp283+pi283,~5,6,7,8,9~,~0,.1,.25~1
{{-34.6913, -32.9147, -32.2468}, {-35.3381, -33.4522, -32.8351}, {-36.9415, -35.8386, -:
(-41.4708, -40.4698, -40.0894}, I-46.9055, -45.7905, -45.4228}}

TableForm[Transpose[dGerx283] ,TableHeadings->{{'I = 0 M1a,"I = 0.10 M","I = 0.25
M"),{"pH 5","pH 6","pH 7","pH 8","gH 9")>1
PH 5 PH 6 PH 7 PH 8 PH 9
I = O M -34.6913 -35.3381 -36.9415 -41.4708 -46.9055

I = 0.10 M -32.9147 -33.4522 -35.8386 -40.4698 -45.7905
I = 0.25 M -32.2468 -32.8351 -35.3814 -40.0894 -45.4228

(c) Calculate the standard transformed Gibbs energies of the reactants and the reaction at 313.15 K.

atp313=calcdGHT[atpspl ~[111/.t->313.15;

adp313=calcdGHT[adpspl [[lIl/.t->313.15;