The Energy Relationships in Cellular Respiration and Photosynthesis: the Balance Sheet

The respiration (or burning) 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.

Average bond energies, kcal/mole
C-H	98
O-H	110
C-C	80
C-O	78
H-H	103
C-N	65
O=O	116 (2 x 58)
C=O	187* (2 x 93.5)
C=C	145 (2 x 72.5)
(* as found in CO₂)

Conversely, the photosynthesis of a mole of glucose requires the input of 686 kcal of energy.

The reasons:

water and carbon dioxide
- the differences in electronegativity between their atoms are high
- so they have polar covalent bonds with high bond energies
- these are strong bonds
  - broken with difficulty and
  - liberating copious amounts of energy when they form
glucose and oxygen
- the differences in electronegativity between their atoms tend to be lower
- so they form covalent bonds with average bond energies on the low side
- these are broken with relative ease

The diagram shows the details.

The overall equation for each process is the same; only the direction of the arrow differs. (The actual equation is:

C₆H₁₂O₆ + 6O₂ + 6H₂O ↔ 12H₂O + 6 CO₂

but we shall ignore the six molecules of water that occur on each side as they "cancel out".)

The structural formulas are shown as well as the average bond energies for each bond involved.

Cellular Respiration

As you can see,

the 24 moles of covalent bonds in a mole of glucose require a total of 2182 kcal to be broken.
The 6 double bonds of oxygen require another 696.

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 6 moles of CO₂ involves the formation of 12 double polar covalent bonds each with a bond energy of 187 kcal/mole; total = 2244
The formation of 6 moles of H₂O involves the formation of 12 O-H bonds each with an energy of 110 kcal/mole; 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 a mole of glucose. This value holds true whether we oxidize glucose quickly by burning it or in the orderly process of cellular respiration.

The minus sign indicates that free energy has been removed from the system.

Link to discussion of free energy.

Photosynthesis

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.

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27 December 2010