Question

Aconitase catalyzes the citric acid cycle reaction: citrate <==> isocitrate. The standard free energy change, ΔGo ’, for this reaction is +6.7 kJ/mol. However, the observed free energy change (ΔG) for this reaction in pig heart mitochondria is +0.8 kJ/mol. What is the ratio of [isocitrate]/[citrate] in these mitochondria? If [isocitrate] = 0.03 mM, what is [citrate]

Answer 1

The ratio of [isocitrate] to [citrate] can be calculated using the standard free energy change, the observed free energy change, the gas constant, and the temperature in Kelvin. Once the ratio is known, the concentration of citrate can be determined given the concentration of isocitrate.

Step-by-step explanation:

The student has asked how to calculate the ratio of [isocitrate] to [citrate] in pig heart mitochondria given the standard free energy change (ΔG°') and the observed free energy change (ΔG). To find the ratio of [isocitrate]/[citrate], the equation ΔG = ΔG°' + RTln([isocitrate]/[citrate]) is used, where R is the gas constant (8.314 J/mol·K) and T is the temperature in Kelvin.

Given ΔG°' = +6.7 kJ/mol and ΔG = +0.8 kJ/mol, we can solve for the ratio [isocitrate]/[citrate]. Assuming T is 298K (25°C), the equation becomes +800 J/mol = +6700 J/mol + (8.314 J/mol·K)(298 K)ln([isocitrate]/[citrate]). Solving for the ratio gives us the equilibrium constant for the reaction in the mitochondria. If [isocitrate] = 0.03 mM, we then use the ratio to calculate [citrate].

Answer 2

A. [isocitrate]/[citrate] = 0.724

B. [citrate] = 24.1 mM

Step-by-step explanation:

Using the equation, ∆G'° = -RTlnK'eq

Where, ∆G'° = 0.8 KJ/mol = 800 J/mol; R is molar gas constant = 8.315 J/mol; T is standard temperature = 298 K; Keq is equilibrium constant = [isocitrate]/[citrate]

Making Keq subject of formula in the above equation;

Keq = e^(-∆G'°/RT)

= e^ {-800/(8.315*298)}

= e^(-0.323)

Keq = 0.724

Therefore, [isocitrate]/[citrate] = 0.

724

B. Keq = [isocitrate]/[citrate]

Where Keq = 0.724, [isocitrate] = 0.03mM.

[citrate] = Keq/[isocitrate]

= 0.724/0.03

[citrate] = 24.1 mM