Page 380 - Thermodynamics of Biochemical Reactions

380 Mathematica Solutions to Problems

11.1 (a) Write out the semigrand partition function I- ' for a system containing a weak acid and its basic form at a specified
pH. (b) Write out the equation for a, Go of acetate at zero ionic strength. (c) Evaluate this function for a, Go at pH 5 and
zero ionic strength. Use calcdGmat to confirm this value. (d) Calculate the semigrand partition function r ' and use it to
calculate AfGo of acetate at pH 5.

(a) The standard transformed Gibbs energy for one mole of the pseudoisomer group at zero ionic strength is given by

-(In10 NH1 pH) - pl/(r t) -(In10 NH2 pH) - p2/(r t)
-(r t Log[E +E I)
The lnlO has been put in in this way so that the partition function would print in a simple way.

r' =Expr-(i/ (r*t)) *g-]

-(ln10 NH1 pH) - pl/(r t) -(ln10 NH2 pH) - p2/(r t)
E +E
This is the semigrand partition function for the system. It was calculated from &GIo, but it could have been written down
directly.

(b) Write the equation for a, G'" of acetate at a specified pH.

For the anion

-369.31+3*r*t*Log[101 *pH
-369.31 + 3 pH r t Log[lOl

For the acid

-396.45+4*r*t*Log[lOI *gH
-396.45 + 4 pH r t Log[lOl

The standard transformed Gibbs energy of the pseudoisomer group is given by

-((-369.31 + 3 pH r t ~og[lOl)/(r t)) ,
-(r t Log[E
-((-396.45 + 4 pH r t Log[lO])/(r t))
E I)
gacetate/.r->S.31451/.t->.29815/.pH->5

-284.805

This value can be confirmed by use of calcdGmat.

calcdQnat[acetatespl/.pH->5/.is->O

-284.805