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Chapter 11 Chemical Equilibrium

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11.1 The Equilibrium Condition

11.2 The Equilibrium Constant

11.3 Equilibrium Expressions Involving Pressures

11.4 The Concept of Activity

11.5 Heterogeneous Equilibria

11.6 Applications of the Equilibrium Constant

11.7 Solving Equilibrium Problems

11.8 Le Chatelier's Principle

11.9 Equilibria Involving Real Gases

The Equilibrium Condition (General)

Thermal equilibrium indicates two systems in thermal contact with each do not exchange energy by heat. If two bricks are in thermal equilibrium their temperatures are the same.

Chemical equilibrium indicates no unbalanced potentials (or driving force). A system in equilibrium experiences no change over time, even infinite time.

The opposite of equilibrium systems are non-equilibrium systems that are off balance and change with time.

Example 1 atm O2 + 2 atm H2 at 298K

aA + bB cC + dD

The same equilibrium state is achieved whether starting with pure reactants or pure products.

The equilibrium state can change with temperature.

H2O (g) + CO (g) H2(g) + CO2(g)

Change

[CO] to PCO

[H2O] to PH2O

etc

As the equilibrium state is approached, the forward and backward rates of reaction approach equality. At equilibrium the rates are equal, and no further net change occurs in the partial pressures of reactants or products.

Fundamental characteristics of equilibrium states:

1. No macroscopic evidence of change.

2. Reached through spontaneous processes.

3. Show a dynamic balance of forward and backward processes.

4. Same regardless of the direction from which they are approached.

5. No change over time.

Use this in an equilibrium expression.

↔

Use this to indicate resonance.

Chemical Reactions and Equilibrium

The equilibrium condition for every reaction can be described in a single equation in which a number, the equilibrium constant (K) of the reaction, equals an equilibrium expression, a function of properties of the reactants and products.

Temperature (oC) Vapor Pressure (atm) 15.00.01683 17.00.0191219.00.0216821.00.0245423.00.0277225.00.0312630.00.0418750.00.1217

H2O(l) H2O(g) @ 25oC

K = 0.03126

H2O(l) H2O(g) @ 30oC

K = 0.04187

Partial pressures and concentrations of products appear in the numerator and those of the reactants in the denominator. Each is raised to a power equal to its coefficient in the balanced chemical equation.

aA + bB cC + dD

1. Gases enter equilibrium expressions as partial pressures, in atmospheres. E.g., PCO2

2. Dissolved species enter as concentrations, in molarity (M) moles per liter. E.g., [Na+]

3. Pure solids and pure liquids are represented in equilibrium expressions by the number 1 (unity); a solvent taking part in a chemical reaction is represented by unity, provided that the solution is dilute. E.g., I2(s) ↔ I2(aq) [I2 (aq) ] = K

PH2O

Pref

= K

The concept of Activity (i-th component)

= ai = Pi / P reference

H2O (l) H2O (g) Kp = P H2O

@ 25oC

Kp = 0.03126 atm

Pref is numerically equal to 1

K = 0.03126

The convention is to express all pressures in atmospheres and to omit factors of Pref because their value is unity. An equilibrium constant K is a pure number.

H2O (g) + CO (g) H2(g) + CO2(g)

The Equilibrium Expressions

aA + bB cC + dD

In a chemical reaction in which a moles of species A and b moles of species B react to form c moles of species C and d moles of species D,

The partial pressures at equilibrium are related through

K = PcCPdD/PaAPbB

Write equilibrium expressions for the following reactions

3 H2(g) + SO2(g) H2S(g) + 2 H2O(g)

2 C2F5Cl(g) + 4 O2(g) Cl2(g) + 4 CO2(g) + 5 F2(g)

Gases and Solids

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

K=PCO2

K is independent of the amounts

of CaCO3(s) or CaO(s)

Liquids

Solutions

H2O(l) H2O(g)

K=PH2O

I2(s) I2(aq)

K=[I2]

(PH2O)2

= K1

(PH2)2(PO2)

(PH2)2(PO2)

= K2

(PH2O)2

Relationships Among the K’s of Related Reactions

#1: The equilibrium constant for a reverse reaction is always the reciprocal of the equilibrium constant for the corresponding forward reaction.

aA + bB cC + dD

cC + dD aA + bB

versus

#1

2 H2 (g) + O2 (g) 2 H2O (g)

K1 = 1/K2

#2

2 H2O (g) 2 H2 (g) + O2 (g)

#3

H2 (g) + ½ O2 (g) H2O (g) Rxn 3 = Rxn 1 times 1/2

(PH2O)

K3 = K1½

= K3

(PH2)(PO2)½

(PH2O)2

= K1

(PH2)2(PO2)

Relationships Among the K’s of Related Reactions

# 2: When the coefficients in a balanced chemical equation are all multiplied by a constant factor, the corresponding equilibrium constant is raised to a power equal to that factor.

2 H2 (g) + O2 (g) 2 H2O (g) Rxn 1

#1

(PBr2)(PCl2)

= K1 = 0.45 @ 25oC

(PBrCl)2

(PIBr)2

= K2 = 0.051 @ 25oC

(PBr2) (PI2)

(PIBr)2

(PBr2)(PCl2)

(PBr2) (PI2)

(PBrCl)2

Relationships Among the K’s of Related Reactions

# 3: when chemical equations are added to give a new equation, their equilibrium constants are multiplied to give the equilibrium constant associated with the new equation.

2 BrCl (g) ↔ Br2 (g) + Cl2 (g)

wrong arrow

Br2 (g) + I2 (g) ↔ 2 IBr (g)

wrong arrow

2 BrCl (g) + I2 (g)↔ 2 IBr (g) + Cl2(g)

= K1K2

wrong arrow

= (0.45)(0.051)

=0.023 @ 25oC

X

= K1K2 = K3

Calculating Equilibrium Constants

Consider the equilibrium 4 NO2(g)↔ 2 N2O(g) + 3 O2(g) The three gases are introduced into a container at partial pressures of 3.6 atm (for NO2), 5.1 atm (for N2O), and 8.0 atm (for O2) and react to reach equilibrium at a fixed temperature. The equilibrium partial pressure of the NO2 is measured to be 2.4 atm. Calculate the equilibrium constant of the reaction at this temperature, assuming that no competing reactions occur.

4 NO2(g) ↔ 2 N2O(g) + 3 O2(g)

initial partial pressure (atm)

change in partial pressure (atm)

equilibrium partial pressure (atm)

Calculate the equilibrium constant of the reaction at this temperature,

assuming that no competing reactions occur.

4 NO2(g) ↔ 2 N2O(g) + 3 O2(g)

initial partial pressure (atm) 3.6 5.1 8.0

change in partial pressure (atm) – 4x+2x+3x

equilibrium partial pressure (atm) 2.4 5.1 + 2x 8.0 + 3x

5.1 + 2(0.3 atm) = 5.7 atm N2O

3.6 – 4x = 2.4 atm NO2; x = 0.3 atm

8.0 + 3(0.3 atm) = 8.9 atm O2

(PN2O)2(PO2)3

K =

=

(PNO2)4

2 GeO (g) + W2O6 (g) ↔ 2 GeWO4(g) initial partial pressure (atm)1.000 1.000 0

change in partial pressure (atm) – 2x– x+2x

equilibrium partial pressure (atm)

The compound GeWO4(g) forms at high temperature in the reaction 2 GeO (g) + W2O6(g) ↔ 2 GeWO4(g) Some GeO (g) and W2O6 (g) are mixed. Before they start to react, their partial pressures both equal 1.000 atm. After their reaction at constant temperature and volume, the equilibrium partial pressure of GeWO4(g) is 0.980 atm. Assuming that this is the only reaction that takes place, (a) determine the equilibrium partial pressures of GeO and W2O6, and (b) determine the equilibrium constant for the reaction.

2 GeO(g) + W2O6(g) ↔ 2 GeWO4(g) initial partial pressure (atm)1.000 1.000 0

change in partial pressure (atm) –2x–x+2x

equilibrium partial pressure (atm) 1.000 – 2x 1.000 – x 0.980

- determine the equilibrium partial pressures of GeO and W2O6, and
- determine the equilibrium constant for the reaction.

0 + 2x = 0.980 atm GeWO4; x = 0.490 atm

1.000 – 2(0.490) = 0.020 atm GeO

1.000 – 0.490 = 0.510 atm W2O6

(PGeWO4)2

K =

=

(PGeO)2(PW2O6)

- Skip Solving quadratic equations
- Will utilize approximation method
- Systems that have small equilibrium constants.
- Assume “x” (the change in concentration) is small (less than 5%) of the initial concentration.

A vessel holds pure CO (g) at a pressure of 1.282 atm and a temperature of 354K. A quantity of nickel is added, and the partial pressure of CO (g) drops to an equilibrium value of 0.709 atm because of the reaction

Ni (s) + 4CO (g) ↔ Ni(CO)4 (g)

Compute the equilibrium constant for this reaction at 354K.

Ni (s) + 4CO (g) ↔ Ni(CO)4 (g)

Construct an “ICE” table

P CO (atm) P Ni(CO)4 (atm)

initial partial pressure (atm) 1.282 0

change in partial pressure (atm) -4x+1x

equilibrium partial pressure (atm) 0.709 x

At equil. Pco=

x = PNi(CO)4 =

Equilibrium Calculations

At a particular temperature, K = 2.0 x 10-6 mol/L for the reaction

2CO2 (g) 2CO (g) + O2 (g)

If 2.0 mol CO2 is initially placed into a 5.0-L vessel, calculate the equilibrium concentrations of all species.

2CO2 (g) 2CO (g) + O2 (g)

initial partial pressure (mol/L) 0.4 0 0

change in partial pressure (mol/L) – 2x+2x+1x

equilibrium partial pressure (mol/L) 0.4 -2x 2x 1x

At a particular temperature, K = 2.0 x 10-6 mol/L for the reaction

2CO2 (g) 2CO (g) + O2 (g)

If 2.0 mol CO2 is initially placed into a 5.0-L vessel, calculate the equilibrium concentrations of all species.

2CO2 (g) 2CO (g) + O2 (g)

initial partial pressure (mol/L) 0.4 0 0

change in partial pressure (mol/L) – 2x+2x+1x

equilibrium partial pressure (mol/L) 0.4 -2x 2x 1x

At a particular temperature, K = 2.0 x 10-6 mol/L for the reaction

2CO2 (g) 2CO (g) + O2 (g)

If 2.0 mol CO2 is initially placed into a 5.0-L vessel, calculate the equilibrium concentrations of all species.

2CO2 (g) 2CO (g) + O2 (g)

initial partial pressure (mol/L) 0.4 0 0

change in partial pressure (mol/L) – 2x+2x+1x

equilibrium partial pressure (mol/L) 0.4 -2x 2x 1x

wrong arrow

K (the Equilibrium Constant) uses equilibrium partial pressures

Q (the reaction quotient) uses prevailing partial pressures, not necessarily at equilibrium

wrong arrow

If Q < K, reaction proceeds in a forward direction (toward products);

If Q > K, reaction proceeds in a backward direction (toward reactants);

If Q = K, the reaction is in equilibrium.

The equilibrium constant for the reaction P4(g) ↔ 2 P2(g) is 1.39 at 400oC. Suppose that 2.75 mol of P4(g) and 1.08 mol of P2(g) are mixed in a closed 25.0 L container at 400oC. Compute Q(init) (theQ at the moment of mixing) and state the direction in which the reaction proceeds.

K = 1.39 @ 400oC; nP4(init) = 2.75 mol; nP2(init) = 1.08 mol

PP4(init) = nP4(init)RT/V

=[(2.75mol)(0.08206 atm L mol-1 K-1)(273.15+400oC)]/(25.0L)

= 6.08 atm

PP2(init) = nP2(init)RT/V

=[(1.08mol)(0.08206 atm L mol-1 K-1)(273.15+400oC)]/(25.0L)

= 2.39 atm

Q =

Henri Louis Le Châtelier (1850-1936)

Highlights

- 1884 Le Chatelier's Principle: A system in equilibrium that is subjected to a stress reacts in a way that counteracts the stress
- If a chemical system at equilibrium experiences a change in concentration, temperature or total pressure the equilibrium will shift in order to minimize that change.
- Industrial chemist involved with industrial efficiency and labor-management relations
Moments in a Life

- Le Chatelier was named "chevalier" (knight) of the Légion d'honneur in 1887, decoration established by Napoléon Bonaparte in 1802.

Effects of External Stresses on Equilibria: Le Châtelier’s Principle

A system in equilibrium that is subjected to a stress reacts in a way that counteracts the stress.

Le Châtelier’s Principle provides a way to predict the response of an equilibrium system to an external perturbation, such as…

1. Effects of Adding or Removing Reactants or Products

2. Effects of Changing the Volume (or Pressure) of the System

3. Effects of Changing the Temperature

Effects of Adding or Removing Reactants or Products

PCl5(g) PCl3(g) + Cl2(g) K = 11.5 @ 300oC = Q

add extra PCl5(g)

add extra PCl3(g)

remove some PCl5(g)

remove some PCl3(g)

A system in equilibrium that is subjected to a stress reacts in a way that counteracts the stress. In this case adding or removing reactants or products

Effects of Changing the Volume of the System

PCl5(g) PCl3(g) + Cl2(g)

1 mole

1+1 = 2 moles

Let’s decrease the volume of the reaction container

Less room :: less amount (fewer moles)

Shifts reaction to restore equilibrium

Let’s increase the volume of the reaction container

More room :: more amount (greater moles)

Shifts reaction to restore equilibrium

A system in equilibrium that is subjected to a stress reacts in a way that counteracts the stress. In this case a change in volume

2 P2(g) P4 (g)

PCl5(g) PCl3(g) + Cl2(g)

CO (g) +H2O (g) CO2 (g) + H2 (g)

Boyles Law:

PV = Constant

A system in equilibrium that is subjected to a stress reacts in a way that counteracts the stress. In this case a change in volume (or pressure)

Effects of Changing the Temperature

Endothermic: heat is aborbed by a reaction

Reactants + heat gives Products

Exothermic: heat is liberated by a reaction

Reactants gives Products + heat

A system in equilibrium that is subjected to a stress reacts in a way that counteracts the stress. In this case a change in temperature

Effects of Changing the Temperature

Endothermic: absorption of heat by a reaction

Reactants + heatgives Products

Let’s increase the temperature of the reaction, what direction does the equilibrium reaction shift

Let’s decrease the temperature of the reaction

Effects of Changing the Temperature

Exothermic: heat liberated by a reaction

Reactants Products + heat

Let’s increase the temperature of the reaction

Let’s decrease the temperature of the reaction

A system in equilibrium that is subjected to a stress reacts in a way that counteracts the stress. In this case a change in temperature

If a forward reaction is exothermic,

Then the reverse reaction must be endothermic

Driving Reactions to Completion/ Increasing Yield

Industrial Synthesis of Ammonia (Haber)

N2 (g) + 3H2 (g) ↔ 2NH3 (g)

Forward reaction is exothermic

What conditions do we need to increase the yield, i.e., produce more ammonia?