the standard state free energy of hydrolysis of acetyl phosphat is G= -42.3 kJ/mol. Calculate the free energy change for the acetyl phosphate hydrolysis in a solution of 2mM acetate, 2 mM phospate and 3 nM acetyl phospahte.
To calculate the free energy change for the hydrolysis of acetyl phosphate in the given solution, we can use the equation:
ΔG = ΔG° + RTln(Q),
where:
ΔG is the free energy change for the reaction,
ΔG° is the standard state free energy of hydrolysis (-42.3 kJ/mol),
R is the gas constant (8.314 J/mol·K),
T is the temperature in Kelvin, and
Q is the reaction quotient.
To find Q, we need to determine the concentrations of reactants and products. Given that the solution contains 2 mM acetate, 2 mM phosphate, and 3 nM acetyl phosphate, we can write the balanced reaction equation for the hydrolysis of acetyl phosphate:
Acetyl phosphate + H2O ⇌ Acetate + Phosphate
From the stoichiometry of the reaction, we can see that the concentrations of acetate and phosphate will remain constant during the reaction, while the concentration of acetyl phosphate will change.
Calculating Q:
Q = [Acetate] * [Phosphate] / [Acetyl Phosphate],
Since the concentrations of acetate and phosphate are given as 2 mM, we can substitute these values into the equation:
Q = (2 mM) * (2 mM) / (3 nM),
Ensure that the units of the concentrations are consistent before performing the calculation. In this case, we can convert nM to mM by multiplying by 10^-6:
Q = (2 mM) * (2 mM) / (3 nM) = (2 * 10^-3 M) * (2 * 10^-3 M) / (3 * 10^-9 M)
= (4 * 10^-6 M^2) / (3 * 10^-9 M)
= 1.333 * 10^3.
Now that we have Q, we can substitute the values into the equation for ΔG:
ΔG = ΔG° + RTln(Q),
Plugging in the known values:
ΔG = (-42.3 kJ/mol) + (8.314 J/mol·K * temperature) * ln(1.333 * 10^3).
Since the temperature is not provided, you need to provide the temperature value in Kelvin to complete the calculation.