Question

The thermodynamic properties of foods can be discussed in terms of the enthalpy of combustion per gram of food. Do you get more energy from the metabolism of one gram of sugar or one gram of fat? Answer this question quantitatively and with as much thermodynamic detail as possible. Use two of the following three methods to quantify your answer: (A) arithmetic method, (B) calorimetry, and/or (C) computational.

Answer 1

The energy from one gram of sugar is less than what we get from 1 g of fat. Therefore fats are used as storage molecules to be used when glucose is not available.

Caloimetric method:
glucose consumption eqaution = C12H22O11 + 12O2 --> 12CO2+ 11H20
DELTA H = {12(-393) + 11(-285)} - {-2226}
= -5625 kJ per mole.
Thus 1 g glucose = -5625/342 = 16 kJ of energy.
(342 is the molecular weight of sugar.)

Fatty acid equation = C18H34O2 + 251/2O2 --> 18CO2 +17 H20
DELTA H = {18(-393) + 17(-285)} - {-783}
= -11136 kJ per mole
so 1 g of fat would release = -11136/283 = 39 kJ of energy.
Hence fats release far more energy than glucose.

Arithmatic method

1 glucose = 32 ATP
1 sugar = 2 glucose
1 ATP = - 30.5 kJ per mole
therefore 32 * 2 = 64 ATP = 64*-30.5 = 976 kJ per mole = 5.7 kJ per gram of glucose

1 fatty acid breakdown = 129 ATP
so, (129 * 30.5)/283 = 13.9 kJ per gram of fatty acid.
Hence fats yield far higher energy than glucose.