Page 271 - Thermodynamics of Biochemical Reactions

Chemical Equilibrium in One Phase Systems 271

TableForm~calcdHTsp~atpsp,C283.15,298.15,313.15},01,T~1eHeadings-
> C C "ATP-4 " , "HATP-3 'I, "H2ATP-2" 1 , "2 83.15 K" , "2 98.15 K" , "3 13.15 K" 1 1 I
{
283.15 K 298.15 K 313.15 K
ATP-4 -3619.21 -3619.21 -3619.21
HATP-3 -3612.91 -3612.91 -3612.91
H2ATP-2 -3627.91 -3627.91 -3627.91

This calculation is based on the assumption that the standard enthalpies of formation of the three species are independent of
temperature, and so this is the expected result.

TableForm[calcdHTsp[at~s~,{283.15,298.15,313.15},.l],TableHeadings-
> C C "ATP-4 'I, "HATP-3 " , "H2ATP-2 " 1, { "2 83 -15 K" , "298.15 K" , "313.15 K" 1 1 I

283.15 K 298.15 K 313.15 K
ATP-4 -3615.12 -3614.23 -3613.22
HATP-3 -3610.61 -3610.11 -3609.54

H2ATP-2 -3626.89 -3626.66 -3626.41
Even though the standard enthalpies of formation are independent of temperature at zero ionic strength, they are not indepen-
dent of temperature at a finite ionic strength. The largest effect is for the -4 ion.

TableForm[calcdHTsp[atpspr(283.15,298.15,313.15},.25l,TableHeadings-
> C I "ATP-4 'I, " IiATP-3 'I, "H2ATP-2 " 1, C "2 83 .15 K" , "2 98.15 K" , "313 .15 K" 1 1 1
283.15 K 298.15 K 313.15 K
ATP-4 -3613.8 -3612.62 -3611.29

HATP-3 -3609.86 -3609.2 -3608.46
H2ATP-2 -3626.56 -3626.26 -3625.93
3.9 There are two ways to obtain values for the enthalpy coefficient in equation 3.6-5 as a function of temperature: (a)
Calculate the derivative of the Gibbs energy coefficient divided by T. (b) Fit the enthalpy coefficients of Clarke and Glew to
AT2 + BT3. Use both of these methods and make plots to compare these functions with the values in Table 3.1

(a) According to Problem 3.5, RTa is given by

rtal~ha=9.20485*10A-3*t-l.28466*lOA-5*tA2+4.95l99*lOA-8*tA3
-8 3
0.00920485 t - 0.0000128466 t2 + 4.95199 10 t

Using the Gibbs-Helmholtz equation

rt2Dalpha=Expand[tA2*D[rtalpha/t,tll

-8 3
0. t - 0.0000128466 t2 + 9.90398 10 t

The following are the enthalpy coefficients given by Clarke and Glew.