ATP hydrolysis at pH 7.0 is accompanied by release of a hydrogen ion to the medium. if delta G note for this reactionis -30.5 kJ/mol, what is the free energy change for the same reaction with all component, including H+ at a standard state
To determine the free energy change for the ATP hydrolysis reaction with all components at standard state, we need to consider the free energy change associated with the release of a hydrogen ion (H+) as well.
Given the delta G note for ATP hydrolysis at pH 7.0 as -30.5 kJ/mol, we can use the Nernst equation to calculate the change in free energy (delta G) for the release of H+.
The Nernst equation is given by:
E = E° - (RT/nF) * ln([H+])
Where:
E = Cell potential
E° = Standard cell potential
R = Gas constant (8.314 J/(mol·K) or 0.008314 kJ/(mol·K))
T = Temperature in Kelvin (room temperature is around 298 K)
n = Number of electrons transferred in the reaction (in this case, it is 1 for the release of 1 H+)
F = Faraday's constant (96,485 C/mol)
At standard state, the concentration of H+ is 1 M. Therefore, the concentration term ([H+]) becomes 1 M in the Nernst equation.
By rearranging the Nernst equation, we can solve for the change in free energy (delta G) for the release of H+:
delta G = -n * F * delta E
Where:
delta G = Change in free energy
n = Number of electrons transferred (1 in this case)
F = Faraday's constant
To calculate delta E, we need to subtract the standard cell potential for the reaction from the standard cell potential for the reduction of H+ (with all components at standard state). Since the reduction of H+ is a reduction half-reaction, we can use the values from standard reduction potentials (E°) table.
Assuming the standard cell potential for the ATP hydrolysis reaction is 0. Let's say the standard cell potential for the reduction of H+ is -0.42 V. The change in potential (delta E) can be calculated as:
delta E = E° of ATP hydrolysis - E° of H+ reduction
delta E = 0 - (-0.42) V
Now we can calculate the change in free energy for the release of H+:
delta G = -n * F * delta E
delta G = -(1) * (96485 C/mol) * (-0.42 V)
Finally, convert the units of C and V to kJ/mol:
delta G = (-1) * (96485 C/mol) * (-0.42 V) * (1 J/C) * (1 kJ/1000 J) * (1 mol/1 mol)
After performing the calculation, you will find the value of delta G for the release of H+ in kJ/mol. To obtain the total free energy change for the reaction with all components at standard state, you can sum delta G of ATP hydrolysis (-30.5 kJ/mol) and delta G for the release of H+ (calculated using the Nernst equation).
Please note that the standard reduction potential for the reduction of H+ and the standard state concentration of H+ (1 M) might vary depending on the specific conditions and context.