Chemistry 130

Chemistry 130

Chemical Equilibrium

Dr. John F. C. Turner

409 Buehler Hall

jturner@ion.chem.utk.edu

Chemistry 130

Chemical change and equilibrium

Transition state theory shows that there are always two reactions associated with a chemical change – the forward reaction and the reverse reaction.

The forward reaction has a rate constant k1 and the reverse

reaction k-1COg NO2g CO2g NOgWe can write a rate law for

these two reactions:

and the precise concentrations at equilibrium will be determined by the activation energies for the forward and reverse reactions

forward = k1[CO][NO2]

backward = k−1[CO2][NO]

Chemistry 130

Chemical change and equilibrium

We understand the relationship between the rate constant k and the activation energy; it is given by the Arrhenius equation:

COg NO2g CO2g NOgWhen the rates of the forward and reverse reactions are equal, the rates of formation and destruction of products are equal – we say that the system is at equilibrium.

k1 = Ae−EA, forward

RT k−1 = Ae

−EA , reverse

RT

Chemistry 130

Chemical change and equilibrium

When the rates are equal,

and so

then

forward = k1[CO][NO2]

backward = k−1[CO2][NO]

forward = backward

k1[CO ][NO2] = k−1[CO2] [NO]

k1

k−1

=[CO2][NO][CO][NO2]

Chemistry 130

Chemical change and equilibrium

When the rates are equal,

and so

then

forward = k1[CO][NO2]

backward = k−1[CO2][NO]

forward = backward

k1[CO ][NO2] = k−1[CO2] [NO]

Keq =k1

k−1

=[CO2][NO][CO][NO2]

Chemistry 130

Equilibrium constants

As the rates are equal at equilibrium, then the Keq is a fundamental

constant of the particular reaction and we call it the equilibrium constant.

In general, the equilibrium constant for a reaction is

Often we do not know k1 or k-1 but we can easily measure the ratio

of the two through the concentrations of the reactants and the products.

Keq =k1

k−1

=[Products][Reactants]

Chemistry 130

Equilibrium constants

For a general reaction

the equilibrium constant is given by

In general, the equilibrium constant is written in terms of concentrations, which at their most basic are given by

Keq =k1

k−1

=[C]c[D]d

[A]a[B]b

aA bB cC dD

c = nV

Chemistry 130

Equilibrium constants

The equilibrium constant for a reaction is useful in many ways and occurs in both thermodynamics and kinetics.

The first calculation that it allows us to perform is the calculation of concentration. At 698 K, hydrogen iodide decomposes via

Given

2HIg H2g I2g

Keq =[H2][I2]

[HI ]2= 1.84 × 10−2

[H2] = 0.025 M

[I2] = 0.025 M0.0250.025

[HI ]2= 1.84 × 10−2

[HI ]2 =0.0250.0251.84 × 10−2

[HI ] = 0.0250.0251.84 × 10−2

12 = 0.184 M

Chemistry 130

Equilibrium constants

Rules for equilibrium constants

If you reverse a reaction as written, the equilibrium constant is inverted.

If you add two or more reactions together, the equilibrium constants are multiplied.

If you muliply a single reaction by a number n, you raise the equilibrium constant to the power n

Chemistry 130

Equilibrium constants

A very large or very small equilibrium constant describes a reaction that has gone to completion or one that does not perceptibly occur:

For

which means that the combustion of hydrogen and oxygen is essentially complete.

For the reverse reaction,

which implies that the reverse reaction is negligibly important.

2H2g O2g 2H2Ol

Keq = 1.4 × 1083

2H2Ol 2H2g O2g

Keq,reverse = 7.1 × 10−84

Chemistry 130