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2. Consider the biosynthetic reaction between glutamate and NH 4 + to form gluta

ID: 542085 • Letter: 2

Question

2. Consider the biosynthetic reaction between glutamate and NH4+ to form glutamine at T = 25o C (R = 8.3145 J / molK),

glutamate + NH4+ --> glutamine

2a. The equilibrium constant for the reaction under standard biochemical conditions is Keq = 0.00325. Calculate Go' and please give your answer in kcal/mol (assume RT = 0.6 kcal/mol).

Go' = __________ kcal/mol

2b. To make the reaction spontaneous, what would the concentration of glutamine have to be maintained at relative to the concentrations of glutamate and NH4+?

Ratio of glutamine concentration to product of glutamate and ammonium concentrations is __________

2c. Show that the biosynthesis of glutamine can be made spontaneous by the addition of ATP, assuming ATP spontaneously hydrolyzes to ADP and Pi with (Go' = -7.3 kcal / mol) at RT = 0.6 kcal/mol. In your final answer, please give your answer in kcal/mol and include all reactants and products.

Write overall reaction: __________________________________________________________________

Overall Go' = __________ kcal/mol

Explanation / Answer

The equilibrium constant, K for a reaction is related to the standard free energy change, G0 as per the expression

G0 = -R*T*ln Keq where R is the gas constant and T is the absolute temperature.

a) Given R*T = 0.6 kcal/mol, we have

G0’ = -R*T*ln Keq

====> G0’ = -(0.6 kcal/mol)*ln (0.00325) = -(0.6 kcal/mol)*(-5.72910) = 3.437460 kcal/mol 3.44 kcal/mol (ans).

b) For the reaction to be spontaneous, we must have G0 < 0. Compute the reaction quotient, Q when G0 = 0.0 kcal/mol.

We have

G0 = G0’ + RT*ln Q

===> 0.0 kcal/mol = (3.44 kcal/mol) + (0.6 kcal/mol)*ln Q

===> -(3.44 kcal/mol) = (0.6 kcal/mol)*ln Q

===> -5.73333 = ln Q

===> Q = exp(-5.73333) = 0.00323627 0.00324.

We define Q as Q = [Glutamine]/[Glutamate][Ammonium]; therefore, the ratio of the concentration of Glutamine to the product of the concentrations of Glutamate and ammonium is 0.00324 (ans).