Consider the malate dehydrogenase reaction from the citric acid cycle. Given the following concentrations, calculate the free energy change for this reaction at 37.0 °C (310 K). ΔG°\' for the reaction is 29.7 kJ/mol. Assume that the reaction occurs at pH 7.
[malate] = 1.39 mM [oxaloacetate] = 0.220 mM [NAD ] = 210 mM [NADH] = 84 mM
To calculate the free energy change (ΔG) for the malate dehydrogenase reaction, we can use the equation:
ΔG = ΔG°' + RT * ln(Q)
Where ΔG°' is the standard free energy change, R is the gas constant, T is the temperature, and Q is the reaction quotient.
First, we need to calculate the reaction quotient (Q). The reaction is:
Malate + NAD+ ⇌ Oxaloacetate + NADH
Q = ([Oxaloacetate] * [NADH]) / ([Malate] * [NAD+])
Plugging in the given values:
Q = (0.220 mM * 84 mM) / (1.39 mM * 210 mM)
Q = 0.000593
Next, we can calculate the free energy change using the equation:
ΔG = ΔG°' + RT * ln(Q)
The gas constant (R) is 8.31 J/(mol·K) and the temperature (T) is 310 K.
ΔG = 29.7 kJ/mol + (8.31 J/(mol·K) * 310 K) * ln(0.000593)
Finally, we convert the answer from J to kJ:
ΔG = (29.7 kJ/mol) + (8.31 J/(mol·K) * 310 K) * ln(0.000593)
ΔG = 29.7 kJ/mol + 2.56 kJ/mol * ln(0.000593)
ΔG ≈ 23.92 kJ/mol
Therefore, the free energy change for the malate dehydrogenase reaction at 37.0 °C is approximately -23.92 kJ/mol.
To calculate the free energy change (ΔG) for the malate dehydrogenase reaction, we need to use the Nernst equation and the equation for ΔG.
The Nernst equation relates the concentrations of reactants and products to the standard potential of the redox couple involved in the reaction. In this case, the redox couple is NADH/NAD+.
First, we need to calculate the concentrations of [NAD+] and [NADH] in terms of their ratios using the Nernst equation:
[E°'] = E° - (RT/nF) * ln([ox]/[red])
where
[E°'] is the standard potential of the redox couple at the desired conditions,
E° is the standard potential of the redox couple under standard conditions (0.0257 V for NADH/NAD+),
R is the gas constant (8.314 J/(mol*K)),
T is the temperature in Kelvin (310 K),
n is the number of electrons transferred in the redox reaction (2 in this case),
F is Faraday's constant (96485 C/mol),
[ox] is the concentration of the oxidized form (NAD+), and
[red] is the concentration of the reduced form (NADH).
Using the given concentrations of [NAD+] and [NADH], we have:
[NAD+] = 210 mM
[NADH] = 84 mM
Now, let's calculate the standard potential of the redox couple at the desired conditions ([E°']) using the Nernst equation:
[E°'] = E° - (RT/nF) * ln([NAD+] / [NADH])
[E°'] = 0.0257 V - (8.314 J/(mol*K) * 310 K / (2 * 96485 C/mol)) * ln(210 mM / 84 mM)
[E°'] ≈ 0.0257 V - 0.0175 V * ln(2.5)
[E°'] ≈ 0.0257 V - 0.0175 V * 0.91629
[E°'] ≈ 0.0257 V - 0.0160 V
[E°'] ≈ 0.0097 V
Now, we can calculate the free energy change (ΔG) using the equation:
ΔG = ΔG°' + RT * ln([oxaloacetate] * [NADH] / ([malate] * [NAD+]))
where
ΔG°' is the standard free energy change,
R is the gas constant (8.314 J/(mol*K)),
T is the temperature in Kelvin (310 K),
[oxaloacetate] is the concentration of oxaloacetate,
[NADH] is the concentration of NADH,
[malate] is the concentration of malate, and
[NAD+] is the concentration of NAD+.
Using the given concentrations, we have:
ΔG°' = 29.7 kJ/mol
[malate] = 1.39 mM
[oxaloacetate] = 0.220 mM
[NAD+] = 210 mM
[NADH] = 84 mM
Now, let's calculate ΔG:
ΔG = (29.7 kJ/mol) + (8.314 J/(mol*K) * 310 K) * ln((0.220 mM * 84 mM) / (1.39 mM * 210 mM))
ΔG = 29.7 kJ/mol + 2579 J * ln(0.01848)
ΔG ≈ 29.7 kJ/mol + 2579 J * (-4.011)
ΔG ≈ 29.7 kJ/mol - 10346 J
ΔG ≈ 19.35 kJ/mol
Therefore, the free energy change (ΔG) for the malate dehydrogenase reaction at 37.0 °C (310 K) is approximately 19.35 kJ/mol.