For the dissociation of acetic acid, CH3COOH CH3COO- + H+, the free energy change, ΔG° = 27.26 kJ/mol. What is the free energy change, ΔG°', in the biochemical standard state? Given R = 8.315 J/mol · K. T = 25°C.
I'm not a biochemistry and have never worked with dGo' but it appears to me from reading that dGo' = dGo + RTln[(H^+)/(H2O)] and since H^+ = 10^-7 and (H2O) = 55.5 you calculate that part of it and add to dGo to solve for dGo'.
To calculate the free energy change, ΔG°', in the biochemical standard state, we can use the equation:
ΔG°' = ΔG° + RT ln(Q)
where ΔG° is the free energy change at non-standard conditions (given as 27.26 kJ/mol), R is the gas constant (8.315 J/mol · K), T is the temperature in Kelvin, and Q is the reaction quotient.
First, let's convert the temperature to Kelvin:
T = 25°C = 25 + 273.15 = 298.15 K
Now, let's calculate the reaction quotient, Q. In this case, Q is the ratio of the concentrations of the products (CH3COO-) and reactants (CH3COOH and H+).
Since we are in the biochemical standard state, Q will be equal to the equilibrium constant, K'. The equilibrium constant is the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium.
For the dissociation of acetic acid, the chemical equation is:
CH3COOH CH3COO- + H+
Since acetic acid is a weak acid, its dissociation is incomplete at equilibrium. The equilibrium constant expression can be written as:
K' = [CH3COO-] / [CH3COOH][H+]
In the biochemical standard state, the concentration of water is typically very high and remains constant. Therefore, we can consider [H2O] as a constant and incorporate it into the equilibrium constant. The reaction can then be rewritten as:
CH3COOH CH3COO- + H2O
And the equilibrium constant expression becomes:
K' = [CH3COO-] / [CH3COOH]
Now, we need to determine the values of [CH3COO-] and [CH3COOH]. In the biochemical standard state, the concentrations of the products and reactants are typically at standard conditions. Thus, we can assume that the concentrations of each species are 1 M (molar concentration) in the standard state.
Now, let's substitute the known values into the equation:
ΔG°' = ΔG° + RT ln(Q)
ΔG°' = 27.26 kJ/mol + (8.315 J/mol · K) * (298.15 K) * ln(K')
To calculate ΔG°', we need the value of ln(K'). However, we don't have the specific value for K' for the dissociation of acetic acid in the biochemical standard state. If this information is provided or if you have access to a chemical database or a table of standard equilibrium constants, you can look up the value of K' and substitute it into the equation.
Once you have the value of K', you can calculate ΔG°' using the equation above, taking care to convert the units as necessary.