the equilibrium state

2. The Equilibrium State,
The Equilibrium Constant Kc,
The Equilibrium Constant Kp
Chemistry 7th Ed
By
J.E. McMurry

3. Introduction
• We raised three key questions about chemical reactions:
• What happens?
• How fast and by what mechanism does it happen?
• To what extent does it happen?
• The answer to the third question: How far does a reaction proceed
toward completion before it reaches a state of chemical
equilibrium—A state in which the concentrations of reactants and
products no longer change.
• Chemical Equilibrium The state reached when the concentrations
of reactants and products remain constant over time.

4. Cont.
• When a liquid evaporates in a closed container, it soon
gives rise to a constant vapor pressure because of a
dynamic equilibrium in which the number of molecules
leaving the liquid equals the number returning from the
vapor.
• Chemical reactions behave similarly. They can occur in
both forward and reverse directions, and when the
rates of the forward and reverse reactions become
equal, the concentrations of reactants and products
remain constant. At that point, the chemical system is
at equilibrium.

5. Cont.
• A mixture of reactants and products in the equilibrium state is
called an equilibrium mixture.
• we’ll address a number of important questions about the
composition of equilibrium mixtures:
• What is the relationship between the concentrations of reactants and
products in an equilibrium mixture?
• How can we determine equilibrium concentrations from initial
concentrations?
• What factors can we exploit to alter the composition of an equilibrium
mixture?

6. The Equilibrium State
• We’ve generally assumed that chemical reactions result in
complete conversion of reactants to products. Many reactions,
however, do not go to completion.
• Take, for example, the decomposition of the colorless gas
dinitrogen tetroxide (N2O4) to the dark brown gas nitrogen dioxide
(NO2).

7. Cont.

8. Cont.
• To indicate that the reaction can proceed in both forward and
reverse directions, we write the balanced equation with two
arrows, one pointing from reactants to products and the other
pointing from products to reactants.
• Strictly speaking, all chemical reactions are reversible. What we
sometimes call irreversible reactions are simply those that
proceed nearly to completion, so that the equilibrium mixture
contains almost all products and almost no reactants.
• For such reactions, the reverse reaction is often too slow to be
detected.

9. Cont.
• The reason why chemical reactions
reach an equilibrium state follows from
chemical kinetics.
• Consider again the interconversion of
N2O4 and NO2. The rate of the forward
reaction (N2O4 2NO2) and the
reverse reaction (N2O4 2NO2) are
given by the following rate laws:
Rate forward = kf[N2O4]
Rate reverse = kr[NO2]2

10. Cont.
• The rate of the forward reaction decreases as the concentration of
the reactant N2O4 decreases, while the rate of the reverse
reaction increases as the concentration of the product NO2
increases. Eventually, the decreasing rate of the forward reaction
and the increasing rate of the reverse reaction become equal.
• At that point, there are no further changes in concentrations not
because the reactions stop but because N2O4 and NO2 both
disappear as fast as they’re formed. Thus, chemical equilibrium is
a dynamic state in which forward and reverse reactions continue
at equal rates so that there is no net conversion of reactants to
products

11. The Equilibrium Constant KC
The last column of Table 14.1 shows that, at equilibrium, the expression [NO2]2/[N2O4] has a constant
value of, 4.64 x 10-3 M, within experimental error.

12. Cont.
• The expression [NO2]2/[N2O4] appears to be related to the
balanced equation for the reaction N2O4(g) ⇌ 2NO2(g) in that the
concentration of the product is in the numerator, raised to the
power of its coefficient in the balanced equation, and the
concentration of the reactant is in the denominator.
• let’s consider a general reversible reaction:
• where A and B are the reactants, C and D are the products, and a,
b, c, and d are their respective stoichiometric coefficients in the
balanced chemical equation.

13. Cont.
• the Norwegian chemists Cato Maximilian Guldberg and Peter
Waage proposed that the concentrations in an equilibrium mixture
are related by the following equilibrium equation, where Kc is the
equilibrium constant and the expression on the right side is called
the equilibrium constant expression.

14. Cont.
• As usual, square brackets indicate the molar concentration of the
substance within the brackets, hence the subscript c for
“concentration” in Kc.
• The equilibrium equation is also known as the law of mass action
because in the early days of chemistry, concentration was called
“active mass.”
• The equilibrium constant Kc is the number obtained by
multiplying the equilibrium concentrations of all the products and
dividing by the product of the equilibrium concentrations of all
the reactants, with the concentration of each substance raised to
the power of its coefficient in the balanced chemical equation.

15. Cont.
• No matter what the individual equilibrium concentrations may be
in a particular experiment, the equilibrium constant for a
reaction at a particular temperature always has the same value.
Thus, the equilibrium equation for the decomposition reaction
N2O4(g) ⇌ 2NO2(g) is:

16. Cont.
• Values of Kc are generally reported without units because the
concentrations in the equilibrium constant expression are
considered to be concentration ratios in which the molarity of
each substance is divided by its molarity (1 M) in the
thermodynamic standard state.
• Because the units cancel, the concentration ratios and the values
of Kc are dimensionless.
• Equilibrium constants are temperature-dependent, so the
temperature must be given when citing a value of Kc.

17. Cont.
• The form of the equilibrium constant expression and the numerical value
of the equilibrium constant depend on the form of the balanced
chemical equation.
• Look again at the chemical equation and the equilibrium equation for a
general reaction:
• If we write the chemical equation in the reverse direction, the new
equilibrium constant expression is the reciprocal of the original
expression and the new equilibrium constant Kc′ is the reciprocal of the
original equilibrium constant Kc.

18. Cont.
• If a chemical equation is multiplied by a common factor n, the new
equilibrium constant expression is the original expression raised to
the power of n and the new equilibrium constant Kc′ is equal to (Kc)n.
• Because the equilibrium constants Kc and Kc′ have different
numerical values, it’s important to specify the form of the balanced
chemical equation when quoting the value of an equilibrium
constant.

19. Cont.
• Whenever chemical equations for two (or more) reactions are added to get the
equation for an overall reaction, the equilibrium constant for the overall reaction
equals the product of the equilibrium constants for the individual reactions.
• When the Kc values for the two added reactions are multiplied, the resulting
quantity is the equilibrium constant for the overall reaction.

20. The Equilibrium Constant Kp
• Because gas pressures are easily measured, equilibrium equations
for gas-phase reactions are often written using partial pressures
rather than molar concentrations.
• For example, the equilibrium equation for the decomposition of
N2O4 can be written as
• where PN2O4 and PNO2 are the partial pressures (in atmospheres) of
reactants and products at equilibrium, and the subscript p on K
reminds us that the equilibrium constant Kp is defined using
partial pressures.

21. Cont.
• As for Kc, values of Kp are dimensionless because the partial pressures in
the equilibrium equation are actually ratios of partial pressures in
atmospheres to the standard-state partial pressure of 1 atm.
• Note that the equilibrium equations for Kp and Kc have the same form
except that the expression for Kp contains partial pressures instead of
molar concentrations.
• The constants Kp and Kc for the general gas-phase reaction
• are related because the pressure of each component in a mixture of
ideal gases is directly proportional to its molar concentration.

22. Cont.
• For component A, for example,
PAV = nART
• So
• Similarly, PB = [B]RT, PC = [C]RT, and PD = [D]RT. The equilibrium
equation for Kp is therefore given by

23. Cont.
• Because the first term on the right side equals Kc, the values of Kp
and Kc are related by the equation
• Here, R is the gas constant, 0.08206 (L . atm)/(K . mol), T is the
absolute temperature, and Δn = (c + d) – (a + b) is the number of
moles of gaseous products minus the number of moles of gaseous
reactants.

24. Cont.
• For the decomposition of 1 mol of N2O4 to 2 mol of NO2, Δn = 2 - 1 = 1, and Kp
= Kc(RT):
• For the reaction of 1 mol of hydrogen with 1 mol of iodine to give 2 mol of
hydrogen iodide, Δn = 2 – (1 + 1) = 0, and Kp = Kc(RT)0 = Kc:
• In general, Kp equals Kc only if the same number of moles of gases appear on
both sides of the balanced chemical equation so that Δn = 0.