Energy Relationships in Photosynthesis: The Balance Sheet
The consumption of a mole of glucose releases 686 kcal of energy. This value represents the difference between the energy needed to break the bonds of the reactants (glucose and oxygen) and the energy liberated when the bonds of the products (H2O and CO2) form. Conversely, the photosynthesis of a mole of glucose requires the input of 686 kcal of energy. The overall equation for each process is the same; only the direction of the arrow differs:
C2H12O6 + 6O2 + < - > 6H2O + 6CO2(3:5)
The average bond energies between common atoms are the following: C-H has 98 kcal/mol; O-H has 110 kcal/mol; C-C has 80 kcal/mol; C-O has 78 kcal/mol; H-H has 103 kcal/mol; C-N has 65 kcal/mol; O=O has 116 kcal/mol; C=C has 145 kcal/mol; C=O (as found in CO2) has 187 kcal/mol.
The 24 covalent bonds of glucose require a total of 2182 kcal to be broken. The six double bonds of oxygen require another 696 kcal. Thus a grand total of 2878 kcal is needed to break all the bonds of the reactants in cellular respiration.
As for the products, the formation of six molecules of CO2 involves the formation of 12 double polar covalent bonds each with a bond energy of 187 kcal; total = 2244. The formation of six molecules of H2O involves the formation of 12 O-H bonds each with an energy of 110 kcal; total = 1320. Thus a grand total of 3564 kcal is released as all the bonds of the products form.
Subtracting this from the 2878 kcal needed to break the bonds of the reactants, we arrive at -686 kcal, the free energy change of the oxidation of glucose. This value holds true whether we oxidize glucose quickly by burning it or in the orderly process of cellular respiration in mitochondria. The minus sign indicates that free energy has been removed from the system. The
details of the energy budget are just the same. The only difference is that now it takes 3564 kcal to break the bonds of the reactants and only 2878 kcal are released in forming glucose and oxygen. So we express this change in free energy (+686 kcal) with a plus sign to indicate that energy has been added to the system. The energy came from the Sun and now is stored in the form of bond energy that can power the needs of all life.
Photosynthetic reduction of CO2 can be summarized by the equations:
2H2O → O2 + 4H+ + 4e-(3:6)
CO2 + 4H+ + 4e- → (CH2O) + H2O(3:7)
Four electrons are required to be transferred fromwater, through a redox span of 1.24 eV, to reduce one molecule of CO2. The energy required for the reduction of 1 mol of CO2 is therefore
4 mol x 1.25 eV x 1.60 x 10-19 J eV-1 x 6.02 x 10-3 mol-1 = 47.77 x 104 J (115.10 kcal).
Theoretically, the energy requirement could be satisfied by the capture of 4 mol of photons of PAR light, say a red photon of 700 nm, which have an energy content of
4 mol x 2.84 x 10-19 J x 6.02 10-3 mol-1 = 68.4 x 104 J (163.40 kcal).
However, due to the thermodynamic losses during energy conversion, the fraction of absorbed photon energy converted into chemical energy seldom exceeds 0.35. Thus, eight moles of photons are required for the reduction of 1 mol of CO2
(8 mol x 2.84 x 10-19 J x 6.02 x 10-3 mol-1 = 136.82 x 104 J x 0.35 = 48.20 x 104 J (115.20 Kcal)
A mole of glucose (formed by the addition of six CO2 molecules) requires 6 x 115.20 kcal equal to 691.20 kcal. This value is calculated by taking in account the balance of the energy of bonds previously described.