Page 290 - Thermodynamics of Biochemical Reactions

290 Mathematica Solutions to Problems

dGerx313=ca1ctrGerx[atg313+h20313+h2o313+de==adp313+p~313,~5,6,7,8,9~,~0,.1,.25~1

{{-35.9046, -33.6656, -32.8677}, {-36.4876, -34.2845, -33.58951, 1-38.272, -37.1598, -3f
{-43.5265, -42.482, -42.0518}, {-49.6803, -48.4002, -47.973611

TableFonn[Transpose[dGerx313] ,TableHeadings->{{~'I = 0 M","I = 0.10 M","I = 0.25
M"),{"pH 5","pH 6","pH 7","pH 8","pH 9"))l

PH 5 PH 6 PH 7 PH 8 PH 9
I=OM -35.9046 -36.4876 -38.272 -43.5265 -49.6803
I = 0.10 M -33.6656 -34.2845 -37.1598 -42.482 -48.4002
I = 0.25 M -32.8677 -33.5895 -36.6852 -42.0518 -47.9736

Since the hydrolysis of ATP evolves heat, Le Chatelier's principle says raising the temperature will cause the reaction to go
less far to the right. But at 3 13 K the transformed Gibbs energy of reaction is more negative. To apply Le Chatelier we have
to look at the apparent equilibrium constants. At pH 7 and ionic strength 0, we obtain

6
6.63414 10

6
3.9283 10
k313=Exg[38.31/(8.31451*.31315)1
6
2.45525 10

These apparent equilibrium constants are in accord with what we expect.

4.7 Calculate the standard transformed Gibbs energies of reaction at 298.15 K and the experimental pH and ionic strength
for the reactions in the Goldberg and Tewari series of six critical reviews for which all the reactants are in BasicBiochem-
Data2. Compare the calculated standard transformed Gibbs energies of reaction with the experimental values. At present
there is not enough information to calculate the effects of temperature and metal ions, and so these effects are ignored. The
three steps in this process are: (a) Make a table of the calculated standard transformed Gibbs energies of reaction. (b) Make
a table of the relevant data in the Goldberg and Tewari Tables. (c) Make a table of the differences between the values of the
standard transformed Gibbs energies of reaction calculated in part (a) and the experimental values inthe Goldberg and
Tewari Tables.

(BasicBiochemData has to be loaded)

(a) Make a table of the calculated standard transformed Gibbs energies of reaction.
calcrow[eg, pHlist-, islist-, rx-] :=
Module[{energy, do, gvector}, (*Calculates the standard transformed Gibbs energy
of reaction for a specified reaction at specified pHs and a single
ionic strength. It then prepends the reaction without the +de=.
This second form of the reaction must be in quotation marks.*)
energy = Solve [eq, de] ;
dG=energy[[l, 1, 211 /. pH-tpHliSt /. is+islist;
gvector = Flatten[Map[NumberForm[#, {a, 2}] &, {dG}, {2}]];
Prepend [gvector, 1x1 3