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�‹red = +0.82 V
CyFe3+(aq) + e- �¨ CyFe2+(aq);
E�‹red = +0.22 V
a) What is ĢG for the oxidation of CyFe2+ by air?
b) If the synthesis of 1.00 mol of ATP from (ADP) requires a ĢG of 37.7 kJ, now many moles of ATP are synthesized per mole of O2.
I know for part a you have to add the two Es but after that I'm not sure
Mastering chemistry homework? Haha.
E^(zero)cell= Cathode-Anode
E^(zero)cell= 0.82V-.22V= 0.6V
Delta G= -n*F*E^(zero)cell
Delta G= -4*96485*0.6
Delta G= -231.564 J or -232 kJ
What are the funny symbols?
sorry the symbols with the f are delta G
To calculate the standard free energy change (ΔG°) for a reaction, you can use the formula:
ΔG° = -nFΔE°
Where:
- ΔG° is the standard free energy change
- n is the number of electrons transferred in the reaction
- F is Faraday's constant (96485 C/mol)
- ΔE° is the standard reduction potential difference
For part a) - the oxidation of CyFe2+ by air (O2):
We can see from the given reduction equations that the number of electrons transferred (n) is 4, as indicated by the stoichiometric coefficients of the electrons in the first equation.
ΔE° = E°(O2) - E°(CyFe2+)
= +0.82 V - (+0.22 V)
= 0.6 V
Substituting the values into the formula:
ΔG° = -nFΔE°
= -(4)(96485 C/mol)(0.6 V)
= -231,912 J/mol
To convert this to kJ/mol, divide by 1000:
ΔG° = -231,912 J/mol ÷ 1000
= -231.912 kJ/mol
Therefore, the standard free energy change (ΔG°) for the oxidation of CyFe2+ by air is -231.912 kJ/mol.
For part b):
From the previous calculation, we know that the ΔG° for the oxidation of 1 mole of CyFe2+ by air is -231.912 kJ.
Now, we have to find out how many moles of ATP can be synthesized per mole of O2.
First, we need to calculate the number of moles of O2 involved in the reaction using stoichiometry:
From the balanced equation:
4 moles of H+ + 4 moles of e- + 1 mole of O2 → 2 moles of H2O
Therefore, 1 mole of O2 requires 4 moles of H+ and 4 moles of e-.
Next, we divide the ΔG° for CyFe2+ oxidation by the number of moles of O2:
Number of moles of ATP synthesized per mole of O2 = ΔG° for CyFe2+ oxidation / ΔG° for ATP synthesis
= -231.912 kJ/mol / 37.7 kJ/mol
= -6.146 mol O2/mol ATP
Note that the negative sign indicates that the synthesis of ATP is an exergonic process.
Therefore, approximately 6.146 moles of ATP are synthesized per mole of O2.