(3.17)
Multiplying both sides by −T yields:
−TΔS tot = −TΔS + ΔH
(3.18)
Since the temperature is always a positive number, the reaction is spontaneous if the term −TΔS tot is negative. If the process is in equilibrium then this
term is equal to zero. The product of temperature and entropy has units of
energy and is related to the amount of energy available to do work. This term,
−TΔS tot , is usually called the Gibbs energy difference, ΔG, and is written as:
ΔG = ΔH − TΔS
(3.19)
In summary, the Gibbs energy represents the energy available for the
reaction as it includes both enthalpy and entropy contributions. Since
biochemical reactions operate at constant temperature and pressure, the
Gibbs energy difference is the energy term that will be calculated to determine how a reaction will proceed:
• if ΔG is a positive then the reaction is unfavorable and the initial state
is favored,
• if ΔG is zero the reaction is in equilibrium, and
• only if ΔG is negative will the reaction occur spontaneously.
RELATIONSHIP BETWEEN THE GIBBS ENERGY AND THE
EQUILIBRIUM CONSTANT
For any given reaction A ↔ B with an equilibrium constant K, the value
of the equilibrium constant can be written in terms of the change in the
Gibbs energy:
K = e
−ΔG/kT
(3.20)
Thus, the equilibrium constant for a reaction is simply an alternative representation of the Gibbs energy change. This relationship can be divided into
three regions (Table 3.1). First, spontaneous reactions occur when the Gibbs
energy change is negative; in this case, the association constant is a positive
number greater than one. Second, at equilibrium the Gibbs energy is equal
to zero, corresponding to a value of one for the equilibrium constant. Third,
reactions that are favored to proceed in the reverse direction rather than
moving forward correspond to a positive value for the Gibbs energy change,
or correspondingly, a value less than one for the equilibrium constant.
Δ
Δ
Δ
S
S
H
T
tot =
−
CHAPTER 3
SECOND LAW OF THERMODYNAMICS
55
9781405124362_4_003.qxd 4/29/08 10:40 Page 55
Multiplying both sides by −T yields:
−TΔS tot = −TΔS + ΔH
(3.18)
Since the temperature is always a positive number, the reaction is spontaneous if the term −TΔS tot is negative. If the process is in equilibrium then this
term is equal to zero. The product of temperature and entropy has units of
energy and is related to the amount of energy available to do work. This term,
−TΔS tot , is usually called the Gibbs energy difference, ΔG, and is written as:
ΔG = ΔH − TΔS
(3.19)
In summary, the Gibbs energy represents the energy available for the
reaction as it includes both enthalpy and entropy contributions. Since
biochemical reactions operate at constant temperature and pressure, the
Gibbs energy difference is the energy term that will be calculated to determine how a reaction will proceed:
• if ΔG is a positive then the reaction is unfavorable and the initial state
is favored,
• if ΔG is zero the reaction is in equilibrium, and
• only if ΔG is negative will the reaction occur spontaneously.
RELATIONSHIP BETWEEN THE GIBBS ENERGY AND THE
EQUILIBRIUM CONSTANT
For any given reaction A ↔ B with an equilibrium constant K, the value
of the equilibrium constant can be written in terms of the change in the
Gibbs energy:
K = e
−ΔG/kT
(3.20)
Thus, the equilibrium constant for a reaction is simply an alternative representation of the Gibbs energy change. This relationship can be divided into
three regions (Table 3.1). First, spontaneous reactions occur when the Gibbs
energy change is negative; in this case, the association constant is a positive
number greater than one. Second, at equilibrium the Gibbs energy is equal
to zero, corresponding to a value of one for the equilibrium constant. Third,
reactions that are favored to proceed in the reverse direction rather than
moving forward correspond to a positive value for the Gibbs energy change,
or correspondingly, a value less than one for the equilibrium constant.
Δ
Δ
Δ
S
S
H
T
tot =
−
CHAPTER 3
SECOND LAW OF THERMODYNAMICS
55
9781405124362_4_003.qxd 4/29/08 10:40 Page 55