Page 270 - Thermodynamics of Biochemical Reactions

270 Mathematica Solutions to Problems

Equation 3.7-6 yields the following table: These are the adjustments to be subtracted from pH,to give pH,= - log H+]

TableFonn[Trans~ose[alpha*isA.5/(Log[lO]*(l+l.6*isA.5))/.t-~{283.l5,298.l5,3l3.l5}/.~s-
>{O, .05, -1, .15, .2, .25)] ,TableHeadings->{ {110",".05", ".10t1,".15", .2O", ".25"}, {"lo
'I
C","25 C","40 C"))I
10 c 25 C 40 C
0 0 0 0
.05 0.0820433 0.0841 0.0863484

.10 0.104609 0.107232 0.110098
.I5 0.119125 0.122111 0.125376
.20 0.129867 0.133122 0.136681
.25 0.138383 0.141852 0.145644

3.8 Calculate the standard enthalpies of formation of the three species of ATP at 283.15 K, 298.15 K, and 313.15 K at ionic
strengths of 0, 0.10, and 0.25 M.

(BasicBiochemData2 has to be loaded)

Since we have a program to calculate standard Gibbs energies of formation, we can calculate the standard enthalpies of
formation by use of the Gibbs Helmholtz equation.

calcdHTsp [speciesmat,-, temp-, ionstr-1 : =
Module[{dGzero, dGzeroT,dHzero,zi, nH, gibbscoeff, istermG,gfnsp,hfnsp),(*This program
first calculates the functions of T and ionic strength for the standard Gibbs energy
of formation for all of the species in a reactant, and then uses the Gibbs Duhem
equation to calculate the functions of T and ionic strength for the standard enthalpy
of formation. The temperature, temp in &can be specified in approximately the range
273.15 K to 313.15 K, and the ionic strength, ionstr in M, can be specified in the
range 0 to 0.35 M. Lists of temperatures and ionic strengths can also be used. The
standard enthalpies of formation in the output are in kJ molA-l.
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. gfnsp is alist of the functions for the species. hfnsp is a
list of the functions for the enthalpies of the species.*)
{dGzero,dHzero,zi,nH) = Transpose[speciesmat];
gibbscoeff=9.20483*1OA-3*t-l.284668*lOA-5*tA2~4.95l99*lOA-8*t~3;
dGzeroT=dGzero*t/298.15+dH~ero*(l-t/298.15);
istermG = gibbscoeff*(ziA2)*(isA.5)/(1 + 1.6*isA.5);
gfnsp=dGzeroT - istennG;
hfnsp=-tA2*D[gfnsp/t,t] ;
hfnsp/.t->temp/.is->ionstr]

calcdHTsplatpsp,298.15,01
{-3619.21, -3612.91, -3627.91)

These are the expected values for these three species at zero ionic strength.

{{-2768.1, -3619.21, -4, 12}, {-2811.48, -3612.91, -3, 13},
{-2838.18, -3627.91, -2, 14}}