36
HENRY EYRING, RICHARD P. BOYCE AND JOHN D. SPIKES
ings is heat. Note that there is nothing explicit or implied about the rates
of such spontaneous processes.
5. Refation between the Free Energy and the Equilibrium Constant
Consider the reaction
N 2 + 3H 2 ^ 2NH 3
At equilibrium, according to the law of mass action,
[NH 3 P
[N 2 ][H 2 F
In other words, there is a definite ratio of products to reactants. What
determines this ratio?
Consider a reaction chamber from which there protrudes three
evacuated cylinders. In the chamber a mixture of hydrogen, nitrogen,
and ammonia are in equilibrium so that the above reaction obtains. The
free energy change when the reactants, each at one atmosphere pressure, are combined to form NH 3 is calculated as follows: 1 mole of N 2
at one atmosphere contained in an independent cylinder is reversibly
introduced into the first evacuated cylinder without expansion of the
gas. In the process an amount of work, PV = RT, is done by the atmosphere. Similarly 3 moles of H 2 are introduced into the second
evacuated cylinder resulting in work, 3RT, being done on the H 2 . Next,
the nitrogen is reversibly expanded (or compressed) to pressure p l9 its
equilibrium partial pressure in the reaction chamber. The work done by
the gas is
f'^PdV
= RT In (1/pO
(47)
Likewise the expansion of H 2 from one atmosphere to p 2 yields an
amount of work SRTln (l/p 2 ). Now we simultaneously introduce the
1 mole of N 2 and the 3 moles of H 2 reversibly into the reaction chamber
and extract 2 moles of NH 3 into the third evacuated cylinder. In each
case this is done through a semipermeable membrane which allows only
the appropriate gas to pass between the cylinders and the reaction
chamber. In this process an amount of work, p^V x = RT, must be done
on the N 2 ; and amount 3RT on the H 2 ; and the work done by the NH 3
is 2RT. If the NH 3 is now expanded (or compressed) from its equilibrium pressure, p 3 , to one atmosphere and taken from the vacuum reversibly into the air, the work, 2RT In (p 8 /l), is done in the expansion
and the work, 2RT, must be done against the atmosphere. All these
work terms added together give the change in free energy:
AF° = -/erin-^L
(48)
P1P2
3
v
J
HENRY EYRING, RICHARD P. BOYCE AND JOHN D. SPIKES
ings is heat. Note that there is nothing explicit or implied about the rates
of such spontaneous processes.
5. Refation between the Free Energy and the Equilibrium Constant
Consider the reaction
N 2 + 3H 2 ^ 2NH 3
At equilibrium, according to the law of mass action,
[NH 3 P
[N 2 ][H 2 F
In other words, there is a definite ratio of products to reactants. What
determines this ratio?
Consider a reaction chamber from which there protrudes three
evacuated cylinders. In the chamber a mixture of hydrogen, nitrogen,
and ammonia are in equilibrium so that the above reaction obtains. The
free energy change when the reactants, each at one atmosphere pressure, are combined to form NH 3 is calculated as follows: 1 mole of N 2
at one atmosphere contained in an independent cylinder is reversibly
introduced into the first evacuated cylinder without expansion of the
gas. In the process an amount of work, PV = RT, is done by the atmosphere. Similarly 3 moles of H 2 are introduced into the second
evacuated cylinder resulting in work, 3RT, being done on the H 2 . Next,
the nitrogen is reversibly expanded (or compressed) to pressure p l9 its
equilibrium partial pressure in the reaction chamber. The work done by
the gas is
f'^PdV
= RT In (1/pO
(47)
Likewise the expansion of H 2 from one atmosphere to p 2 yields an
amount of work SRTln (l/p 2 ). Now we simultaneously introduce the
1 mole of N 2 and the 3 moles of H 2 reversibly into the reaction chamber
and extract 2 moles of NH 3 into the third evacuated cylinder. In each
case this is done through a semipermeable membrane which allows only
the appropriate gas to pass between the cylinders and the reaction
chamber. In this process an amount of work, p^V x = RT, must be done
on the N 2 ; and amount 3RT on the H 2 ; and the work done by the NH 3
is 2RT. If the NH 3 is now expanded (or compressed) from its equilibrium pressure, p 3 , to one atmosphere and taken from the vacuum reversibly into the air, the work, 2RT In (p 8 /l), is done in the expansion
and the work, 2RT, must be done against the atmosphere. All these
work terms added together give the change in free energy:
AF° = -/erin-^L
(48)
P1P2
3
v
J