Page 268 - Thermodynamics of Biochemical Reactions

268 Mathematica Solutions to Problems

col3=rtalpha/.t->{0,10,20,25,30,40)+273.15
{2.56503, 2.70056, 2.84193, 2.91491, 2.98945, 3.14341)

col4=rt2Dalpha/.t->{0,10,20,25,30,40~+273.15
I1.05994, 1.21837, 1.39106, 1.48294, 1.5786, 1.78158)

{{273.15, 283.15, 293.15, 298.15, 303.15, 313.15),
{1.12942, 1.1471, 1.16597, 1.17585, 1.18603, 1.20729),
{2.56503, 2.70056, 2.84193, 2.91491, 2.98945, 3.143411,
{1.05994, 1.21837, 1.39106, 1.48294, 1.5786, 1.78158))
TableForm[Transpose[tab] ,TableHeadings->{None, {"T/K", llaa, "RTa", "RT"2 (da/dT) ''I 11

T/K a RTa RT"2 (aa/aT)
273.15 1.12942 2.56503 1.05994
283.15 1.1471 2.70056 1.21837
293.15 1.16597 2.84193 1.39106

298.15 1.17585 2.91491 1.48294
303.15 1.18603 2.98945 1.5786
313.15 1.20729 3.14341 1.78158

These values can be compared with the values in Table 3.1 in the text.

3.6 Calculate the standard Gibbs energies of formation of the three species of ATP at temperatures of 283.15 K, 298.15 K,
313.15 K and ionic strengths of 0, 0.10, and 0.25 M.

(BasicBiochemData2 has to be loaded)

ca1cdGTspCspeciesmat-,temp-,ionstr-l :=
Module[{dGzero, dGzeroT,dHzero,zi, nH, gibbscoeff, istermG,gfnsp},(*This program
calculates the functions of T and ionic strength for the standard Gibbs energy of
formation for all of the species in a reactant. The temperature, temp in K,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 Gibbs energies 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 numbers 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.*)
{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);
istennG = gibbscoeff*(ziA2)*(isA.5)/(1 + 1.6*isA.5);
gfnsp=dGzeroT - istermG;
gfnsp/.t->temp/.is->ionstr]
gat~=calcdGTsp[atpsp,298.15,0]

{-2768.1, -2811.48, -2838.18)