Page 281 - Thermodynamics of Biochemical Reactions

Thennodynamics of Biochemical Reactions at Specified pH 281

calcdI-hnat [ speciesmat-] : =
Module[{dHzero, zi, nH, dhfnsp, dGzero, pHterm, isenth, dgfnsp, dGreactant, ri},
(*This program produces the function of ionic strength (is) that gives
the standard transformed enthalpies of fonnation of the specie at
298.15 K. It then calculates the standard transformed Gibbs energy for
the reactant and the equilibrium mole fractions of the species. The
function of pH and ionic strength for the standard transformed enthalpy
of formation of the reactant is calculated by a dot product. The
input is a matrix that gives the standard Gibbs energy of formation,
the standard enthalpy of formation, the electric charge'and the number of
hydrogen atoms in the species in the reactant. There is a row in the matrix
for each species of the reactant. Energies are expressed in kJ molA-l.*)
{dGzero, dHzero, zi, nH) = Transpose[speciesmat] ;
isenth=1.4775* ((zi"2) -nH)*(isA.5) / (1+1.6*isA.5);
dhfnsp dHzero+isenth;
(*Now calculate the functions for
the standard Gibbs energies of formation of the species.*)
pHterm = nH* 8.31451 * .29815 *Log [lo A -pH] ;
gpfnsp = dGzero-pHterm-isenthe (2.91482/1.4775);
(*Now calculate the standard
transformed Gibbs energy of formation for the reactant.*)
dGreactant = -8.31451* .29815*Log[Apply[Plus, Exp[-l*gpfnsp/ (8.31451* .29815)]]];
(*Now calculate the equilibrium mole fractions of the species
in the reactant and the mole fraction-weighted average of the
functions for the standard transformed enthalpies of the species.*)
ri = Exp [ (dGreactant - gpfnsp) / (8.31451 * -29815) ] ;
ri.dhfnsp]

fnh=calcdHmat[atpspl/.is->.25/.pH->7
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calcdHTgp [speciesmat-I : =
Module[{dGzero, dGzeroT,dHzero,zi, nH, gibbscoeff,pHterm, isterm,gpfnsp,dGfnl,(*This
program first 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). It then uses the Gibbs-Helmholtz equation to calculate the function for the
standard transformed enthalpy of formation of the pseudoisomer group. 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. Energies are expressed in kJ molA-l. The value of the standard transformed
enthalpy of formation can be calculated at any temperature in the approximate 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[speciesmatl;
gibbscoeff=9.20483*1OA-3*t-l.284668*lOA-5*tA2+4.95l99*lOA-8*tA3;
dGzeroT=dGzero*t/298.15+dXizero*(l-t/298.15);
pHterm = nH*8.31451*(t/1000)*Log[1OA-pHI;
istermG = gibbscoeff*((ziA2) - nH)*(isA.5)/(1 + 1.6*isA.5);
gpfnsp=dGzeroT - pHterm - istermG;
dGfn=-8.31451*(t/100O)*Log[App~y[Plus,Exp[-l*gpfnsp/(8.3l45l*(t/lOOO~~lll;
-tA2*DtdGfn/t,tll

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