Cytochrome, a complicated molecule that we will represent as CyFe2+, reacts with the air we breathe to supply energy required to synthesize adenosine triphosphate (ATP). At pH 7.0 the following reduction potentials pertain to this oxidation of CyFe2+:
O2(g) + 4 H+(aq) + 4 e- �¨ 2 H2O(l);
E� = +0.82 V
CyFe3+(aq) + e- �¨ CyFe2+(aq);
E� = +0.22 V
a) What is delta G for the oxidation of CyFe2+ by air?
b) If the synthesis of 1.00 mol of ATP from (ADP) requires a delta G of 37.7 kJ, now many moles of ATP are synthesized per mole of O2.
To answer these questions, we can use the relationship between standard reduction potentials (E°) and the change in Gibbs free energy (ΔG°) for a reaction. The formula is:
ΔG° = -nFΔE°
Where:
- ΔG° is the change in Gibbs free energy in kJ/mol.
- n is the number of electrons transferred.
- F is the Faraday constant (96.485 C/mol).
a) To find the ΔG for the oxidation of CyFe2+ by air, we need to calculate the number of electrons transferred in the reaction. Looking at the equation:
O2(g) + 4H+(aq) + 4e- → 2H2O(l)
We can see that 4 electrons are transferred.
Now, we can calculate ΔG° using the reduction potentials:
ΔE° = E°(cathode) - E°(anode)
ΔE° = 0.82 V - (0.22 V)
ΔE° = 0.60 V
Plugging in the values, we have:
ΔG° = -nFΔE°
ΔG° = -(4)(96.485 C/mol)(0.60 V)
ΔG° = -231.564 C⋅V/mol
To convert this value from coulombs to kilojoules, we can use the conversion factor:
1 C = 1 J/C × 1 kJ/1000 J
1 C = 0.001 kJ
Therefore, the ΔG° for the oxidation of CyFe2+ by air is:
ΔG° = -231.564 C⋅V/mol × 0.001 kJ/C
ΔG° = -0.231564 kJ/mol
b) To find the number of moles of ATP synthesized per mole of O2, we need to calculate the ΔG for the synthesis of 1 mole of ATP.
From the given information, we know that the ΔG for the synthesis of 1.00 mol of ATP is 37.7 kJ.
Using the equation:
ΔG° = -nFΔE°
We can rearrange the equation to solve for n (the number of electrons transferred):
n = -ΔG° / (FΔE°)
n = -(37.7 kJ) / ((96.485 C/mol)(0.82 V))
Plugging in the values, we have:
n = -(37.7 kJ) / (78.98467 C⋅V/mol)
n ≈ -0.476 mol
Since the number of electrons transferred should always be positive, we take the absolute value: n ≈ 0.476 mol
Therefore, for every mole of O2, approximately 0.476 moles of ATP are synthesized.