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] = 1.33 mM [oxaloacetate] = 0.230 mM [NAD ] = 160 mM [NADH] = 64 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 free energy change
- 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 in this case)
- Q is the reaction quotient
First, let's calculate the reaction quotient (Q) using the concentrations provided:
Q = ([oxaloacetate] * [NADH]) / ([malate] * [NAD])
Substituting the given concentrations into the equation:
Q = (0.230 mM * 64 mM) / (1.33 mM * 160 mM)
Simplifying:
Q = 0.01472
Now, let's calculate the free energy change (ΔG) using the equation mentioned earlier:
ΔG = 29.7 kJ/mol + (8.314 J/(mol·K) * 310 K) * ln(0.01472)
Simplifying:
ΔG = 29.7 kJ/mol + (2569.54 J) * ln(0.01472)
Calculating the natural logarithm:
ΔG = 29.7 kJ/mol + (2569.54 J) * (-4.216)
Simplifying:
ΔG = 29.7 kJ/mol - 10841.83 J
Converting J to kJ:
ΔG = 29.7 kJ/mol - 10.842 kJ/mol
ΔG = 18.858 kJ/mol
Therefore, the free energy change for the malate dehydrogenase reaction at 37.0 °C (310 K) is approximately 18.858 kJ/mol.
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 (8.314 J/(mol*K)), T is the temperature in Kelvin, and Q is the reaction quotient.
In this case, the reaction quotient (Q) can be calculated using the concentrations of the reactants and products:
Q = ([oxaloacetate] * [NADH]) / ([malate] * [NAD])
Given concentrations:
[malate] = 1.33 mM
[oxaloacetate] = 0.230 mM
[NAD+] = 160 mM
[NADH] = 64 mM
First, convert the concentrations from mM to M:
[malate] = 1.33 x 10^(-3) M
[oxaloacetate] = 0.230 x 10^(-3) M
[NAD+] = 160 x 10^(-3) M
[NADH] = 64 x 10^(-3) M
Next, substitute the values into the reaction quotient equation and calculate Q:
Q = (0.230 x 10^(-3) * 64 x 10^(-3)) / (1.33 x 10^(-3) * 160 x 10^(-3))
Now we can calculate ΔG:
ΔG = 29.7 kJ/mol + (8.314 J/(mol*K)) * (310 K) * ln(Q)
Note: We converted the temperature from Celsius to Kelvin by adding 273.15.
Simplify and solve the equation to find ΔG.