The answer is -11.1 kcal/mol. I don\'t know why. Can you show me your solution?

Question

The answer is -11.1 kcal/mol. I don't know why. Can you show me your solution?

The relationship of free-energy change (DG) to the concentrations of reactants and products is important because it predicts the direction of spontaneous chemical reactions. In the hydrolysis of ATP to ADP and inorganic phosphate (Pi), the standard free-energy change (DG°) is -7.3 kcal/mole. The free-energy change depends on concentrations according to the following equation: DG = DG° + 1.42 log10 ([ADP] [Pi]/[ATP]) In a resting muscle, the concentrations of ATP, ADP, and Pi are approximately 0.005 M, 0.001 M, and 0.010 M, respectively. What is the DG for ATP hydrolysis in resting muscle? Correct Response (a) -11.1 kcal/mole (b) -8.72 kcal/mole (c) 6.01 kcal/mole (d) -5.88 kcal/mole

Explanation / Answer

Answer

It is easy one.

Lets write the relationship between DG and concentration of various terms

DG = DGo + 1.42 log10 ([ADP] [Pi] / [ATP])

DG = -7.3 + 1.42 log10 ( 10-3 x 10 x 10-3/ 5 x 10-3)

DG = -7.3 + 1.42 { log10 (10x10-6 ) / (5 x 10-3) }

Using log M/N relation

DG = -7.3 + 1.42 { log10 (10x10-6 ) - log10 (5 x 10-3) }   

DG = - 7.3 + 1.42 { log 10 - 6 log 10 - (log 5 -3 log10)}

DG = - 7.3 + 1.42 { 1- 6 - (0.698 - 3)}

DG = - 7.3 + 1.42 { 1 - 6 - ( -2.3)}

DG = - 7.3 + 1.42 { 1 - 6 + 2.3 }

DG = - 7.3 + 1.42 ( - 2.7 )

DG = - 7.3 - 3.834

DG = 11.1 Kcal/mol

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