392
9 Bioenergetics
volume changes are small, so H should be no more than weakly dependent on
temperature. (Good estimates of H can be made from ‘binding enthalpies’ alone.)
The ‘law of mass action’, to be discussed later, determines the equilibrium
concentration of a product of a biochemical reaction through the value of the
‘equilibrium constant’, K = exp (− B T ), where = /T − S is
the Gibbs free energy of the products minus the Gibbs free energy of the reactants,
divided by the temperature T . The strong temperature dependence of K comes
largely through the explicit temperature T in the heat term /T = δQ/T . This
term will be negative for an exothermic reaction. However, even if the process were
endothermic, the reaction could still be spontaneous if positive entropy (disorder) is
produced and the temperature were high enough to suppress the contribution of the
heat absorption term /(K B T ).
As an example of a simple reaction, consider the oxidation of methane:
CH 4 (g) + 2 O 2 (g) → CO 2 (g) + 2 H 2 O(l) .
(9.191)
A parenthetical symbol {g, l, s} indicates a gas, liquid, or solid.
The overall enthalpy change for a reaction is often calculated by adding the
enthalpy changes to produce each molecular compound in the reaction, starting at
a standard state for this compound. This adding of heats at constant pressure was
suggested by Germain Henri Hess in 1840 and is now called Hess’ law. It follows
from the fact that the enthalpy is a state function, and so its change in value starting
from a standard state is independent of the process used to pass from the initial to the
final state. The ‘standard conditions’ for a compound is defined to be a pressure of
10 5 N/m 2 ≈ 1 atm and a temperature of T = 298.15 K= 25 ◦ C, with the compound
in its natural and most stable phase. If the compound is in solution, its standard
condition is defined to have a concentration of one mole per liter.
From tables of the standard enthalpy change needed to produce a mole of each
of the compounds involved from their elemental form, we record
CH 4 : H − − = −75 kJ
O 2 : H − − =
0 kJ
CO 2 : H − − = −393 kJ
H 2 O : H − − = −285 kJ .
(9.192)
Following Hess’ law, we find the enthalpy change for the whole reaction from
H =
J
ν j H J .
(9.193)
Implicit is the assumption that the pressure before the reaction is the same as the
pressure after. In the present case, {ν J } = {−1, −2, 1, 2}. The enthalpy change
is calculated to be H = −288 kJ. The minus sign indicates that heat would be
released (an exothermic reaction).
9 Bioenergetics
volume changes are small, so H should be no more than weakly dependent on
temperature. (Good estimates of H can be made from ‘binding enthalpies’ alone.)
The ‘law of mass action’, to be discussed later, determines the equilibrium
concentration of a product of a biochemical reaction through the value of the
‘equilibrium constant’, K = exp (− B T ), where = /T − S is
the Gibbs free energy of the products minus the Gibbs free energy of the reactants,
divided by the temperature T . The strong temperature dependence of K comes
largely through the explicit temperature T in the heat term /T = δQ/T . This
term will be negative for an exothermic reaction. However, even if the process were
endothermic, the reaction could still be spontaneous if positive entropy (disorder) is
produced and the temperature were high enough to suppress the contribution of the
heat absorption term /(K B T ).
As an example of a simple reaction, consider the oxidation of methane:
CH 4 (g) + 2 O 2 (g) → CO 2 (g) + 2 H 2 O(l) .
(9.191)
A parenthetical symbol {g, l, s} indicates a gas, liquid, or solid.
The overall enthalpy change for a reaction is often calculated by adding the
enthalpy changes to produce each molecular compound in the reaction, starting at
a standard state for this compound. This adding of heats at constant pressure was
suggested by Germain Henri Hess in 1840 and is now called Hess’ law. It follows
from the fact that the enthalpy is a state function, and so its change in value starting
from a standard state is independent of the process used to pass from the initial to the
final state. The ‘standard conditions’ for a compound is defined to be a pressure of
10 5 N/m 2 ≈ 1 atm and a temperature of T = 298.15 K= 25 ◦ C, with the compound
in its natural and most stable phase. If the compound is in solution, its standard
condition is defined to have a concentration of one mole per liter.
From tables of the standard enthalpy change needed to produce a mole of each
of the compounds involved from their elemental form, we record
CH 4 : H − − = −75 kJ
O 2 : H − − =
0 kJ
CO 2 : H − − = −393 kJ
H 2 O : H − − = −285 kJ .
(9.192)
Following Hess’ law, we find the enthalpy change for the whole reaction from
H =
J
ν j H J .
(9.193)
Implicit is the assumption that the pressure before the reaction is the same as the
pressure after. In the present case, {ν J } = {−1, −2, 1, 2}. The enthalpy change
is calculated to be H = −288 kJ. The minus sign indicates that heat would be
released (an exothermic reaction).