Chemical Equilibrium

Chapter 15

Chemistry the Central Science

12th Ed.

Chemical Equilibrium

The state where the concentrations of all reactants and products remain constant with time.

On the molecular level, there is frantic activity. Equilibrium is not static, but is a highly dynamic situation.

The Concept of Equilibrium

Chemical equilibrium occurs when a reaction and its reverse reaction proceed at the same rate.

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The Concept of EquilibriumAs a system approaches

equilibrium, both the forward and reverse reactions are occurring.

At equilibrium, the forward and reverse reactions are proceeding at the same rate.

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A System at Equilibrium

Once equilibrium is achieved, the amount of each reactant and product remains constant.

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Depicting Equilibrium

Since, in a system at equilibrium, both the forward and reverse reactions are being carried out, we write its equation with a double arrow:

N2O4(g) 2NO2(g)

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The Equilibrium Constant

Forward reaction:

N2O4(g) 2NO2(g)

Rate law:

Rate = kf[N2O4]

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The Equilibrium Constant

Reverse reaction:

2 NO2(g) N2O4(g)

Rate law:

Rate = kr[NO2]2

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The Equilibrium Constant

Therefore, at equilibrium

Ratef = Rater

kf[N2O4] = kr[NO2]2

Rewriting this, it becomes kf

kr [NO2]2

[N2O4]=

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The Equilibrium Constant

The ratio of the rate constants is a constant at that temperature, and the expression becomes

Keq =kf

kr [NO2]2

[N2O4]=

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The Equilibrium Constant

Consider the generalized reaction

• The equilibrium expression for this reaction would be

Kc = [C]c[D]d

[A]a[B]b

aA + bB cC + dD

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Problem

Suppose that the gas-phase reactions A B and B A are both elementary processes with rate constants of 3.8 × 10−2s−1 and 3.1 × 10−1s−1, respectively.

(a) What is the value of the equilibrium constant for the equilibrium A B.

(b) Which is greater at equilibrium, the partial pressure of A or the partial pressure of B? Explain.

Equilibrium Expression

4NH3(g) + 7O2(g) 4NO2(g) + 6H2O(g)

K NO H O

NH O2

2

24 6

34 7

Notes on Equilibrium Expressions (EE)

- The Equilibrium Expression for a reaction is the reciprocal of that for the reaction written in reverse.

- When the equation for a reaction is multiplied by n, EEnew = (EEoriginal)n

- The units for K depend on the reaction being considered.

Manipulating Equilibrium Constants

The equilibrium constant of a reaction in the reverse reaction is the reciprocal of the equilibrium constant of the forward reaction:

Kc = = 0.212 at 100 C[NO2]2

[N2O4]

Kc = = 4.72 at 100 C[N2O4][NO2]2

N2O4(g)2NO2(g)

N2O4(g) 2NO2(g)

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Manipulating Equilibrium Constants

The equilibrium constant of a reaction that has been multiplied by a number is the equilibrium constant raised to a power that is equal to that number:

Kc = = 0.212 at 100 C[NO2]2

[N2O4]

Kc = = (0.212)2 at 100 C[NO2]4

[N2O4]24NO2(g)2N2O4(g)

N2O4(g) 2NO2(g)

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Manipulating Equilibrium Constants

The equilibrium constant for a net reaction made up of two or more steps is the product of the equilibrium constants for the individual steps.

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K v. Kp

For

jA + kB lC + mD

Kp = K(RT)n

n = sum of coefficients of gaseous products minus sum of coefficients of gaseous reactants.

The Equilibrium Constant

Since pressure is proportional to concentration for gases in a closed system, the equilibrium expression can also be written

Kp =(PC

c) (PDd)

(PAa) (PB

b)

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Relationship Between Kc and Kp

From the ideal-gas law we know that

• Rearranging it, we get

PV = nRT

P = RTnV

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Relationship Between Kc and Kp

Plugging this into the expression for Kp,,for each substance, the relationship between Kc and Kp becomes

where

Kp = Kc (RT)n

n = (moles of gaseous product) (moles of gaseous reactant)

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Heterogeneous Equilibria

. . . are equilibria that involve more than one phase.

CaCO3(s) CaO(s) + CO2(g)

K = [CO2]

The position of a heterogeneous equilibrium does not depend on the amounts of pure solids or liquids present.

The Concentrations of Solids and Liquids Are Essentially

ConstantTherefore, the concentrations of solids and liquids do not appear in the equilibrium expression.

Kc = [Pb2+] [Cl]2

PbCl2(s) Pb2+(aq) + 2Cl(aq)

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CaCO3(s) CaO(s) + CO2(g)

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CaCO3 CaO CaCO3 CaO

Reaction Quotient

. . . helps to determine the direction of the move toward equilibrium.

The law of mass action is applied with initial concentrations.

The Reaction Quotient (Q)

Q gives the same ratio the equilibrium expression gives, but for a system that is not at equilibrium.

To calculate Q, one substitutes the initial concentrations on reactants and products into the equilibrium expression.

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Reaction Quotient (continued)

H2(g) + F2(g) 2HF(g)

Q HF

H F2 2

02

0 0

Reaction Quotient

Solving Equilibrium Problems

1. Balance the equation.

2. Write the equilibrium expression.

3. List the initial concentrations.

4. Calculate Q and determine the shift to equilibrium.

Solving Equilibrium Problems(continued)

5. Define equilibrium concentrations.

6. Substitute equilibrium concentrations into equilibrium expression and solve.

7. Check calculated concentrations by calculating K.

Le Châtelier’s Principle

“If a system at equilibrium is disturbed by a change in temperature, pressure, or the concentration of one of the components, the system will shift its equilibrium position so as to counteract the effect of the disturbance.”

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N2 + 3H2 2NH3

13_315

H2

NH3N2

Time

Co

nce

ntr

atio

n

Equilibrium

N2 + 3H2 2NH3

Effects of Changes on the System

1. Concentration: The system will shift away from the added component.

2. Temperature: K will change depending upon the temperature (treat the energy change as a reactant).

AN15.002

Effects of Changes on the System (continued)

3. Pressure:

a. Addition of inert gas does not affect the equilibrium position.

b. Decreasing the volume shifts the equilibrium toward the side with fewer moles.

AN15.003

END