Ap chem unit 13 presentation

Chemical EquilibriumAP Chem Unit 13

Chemical Equilibrium The Equilibrium Condition The Equilibrium Constant Equilibrium Expressions Involving

Pressures Heterogeneous Equilibria Applications of the Equilibrium Constant Solving Equilibrium Problems Le Chatelier’s Principle

IntroductionTo this point, we have assumed that reactions proceed to completion, that is, until one of the reactants runs out. Most reactions stop short of completion.

In fact, the system reaches chemical equilibrium, the state where the concentrations of all reactants and products remain constant with time.

IntroductionAny chemical reactions carried out in a closed vessel will reach equilibrium Some reactions, the equilibrium position

favors the products so that the reaction appears to go to completion. The equilibrium position is said to lie “far to the right”. This reflects the direction of the products.

IntroductionSome reactions only occur to a slight extent. In this case, the equilibrium position is

said to lie “far to the left”. This reflects the direction of the reactants.

The Equilibrium Constant13.1

The Equilibrium ConditionEquilibrium is not static but a highly dynamic situation. On a molecular level many molecules are moving back and forth between reactants and products. No net change in concentration of

reactants and products.

The Equilibrium ConditionH2O(g) + CO(g) H2(g) + CO2(g)



The equilibrium positionlies far to the right. Thisreaction favors the products. But the reactants never reach a concentration of zero.


What would happenif H2O(g) was added tothe system?

First, the forward reaction would increase, then the reverse reaction would increase. A new equilibrium would occur.

Characteristics of Chemical EquilibriumThe equilibrium position is determined by many factors: initial concentrations. relative energies of the reactants and

products. relative degree of “organization” of the

reactants and products.

The Equilibrium Constant13.2

Law of Mass Action

The Law of Mass Action is a general description of the equilibrium condition.

jA + kB lC + mD

The square brackets indicate the concentrations of the the reactants and products at equilibrium. K is the equilibrium constant.

Practice Problem #1Write the equilibrium expression for the following reaction:

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

The Equilibrium ConstantThe value of the equilibrium constant at a given temperature can be calculated if we know the equilibrium concentrations of the reaction components. Equilibrium constants are typically given

without units.

Practice Problem #2

The following equilibrium concentrations were observed for the Haber process for the synthesis of ammonia at 127°C:

[NH3] = 3.1 x 10-2 mol/l

[N2] = 8.5 x 10-1 mol/l

[H2] = 3.1 x 10-3 mol/l

a) Calculate the value of K at 127°C for this reaction.

3.8 x 104

Practice Problem #2


[NH3] = 3.1 x 10-2 mol/l

[N2] = 8.5 x 10-1 mol/l

[H2] = 3.1 x 10-3 mol/l

b) Calculate the value of the equilibrium constant at 127°C for the reaction:

2NH3(g) N2(g) + 3H2(g)

2.6 x 10-5 (the reverse order reaction gives the reciprocal of K)

Practice Problem #2


[NH3] = 3.1 x 10-2 mol/l

[N2] = 8.5 x 10-1 mol/l

[H2] = 3.1 x 10-3 mol/l

c) Calculate the value of the equilibrium constant at 127°C for the reaction:

1.9 x 102 (When the coefficients are ½ of the balanced equation, new K = K1/2)

Equilibrium Expression Summary The equilibrium expression for a reaction is the

reciprocal of that for the reaction written in reverse.

When the balanced equation for a reaction is multiplied by a factor n, the equilibrium expression for the new reaction is the original expression raised to the nth power. Knew =Ko

n

K values are customarily written without units. Law of mass action can describe reactions in

the solution and gas phase.

Equilibrium Expression Summary The equilibrium expression and

constant for a reaction is the same at a given temperature, regardless of the initial amounts of the reaction components. equilibrium concentrations will not

always be the same. See Table 13.1 p600

Equilibrium ExpressionA set of equilibrium concentrations is called an equilibrium position. There is only one equilibrium constant

for a particular system at a given temperature, but there is an infinite number of equilibrium positions.

Practice Problem #3These results were collected for two experiments involving the reaction at 600°C between gaseous sulfur dioxide and oxygen to form gaseous sulfur trioxide:Show that the equilibrium constant is the same in both experiments.

Initial Equilibrium

[SO2] = 2.00 M 1.50 M

[O2] = 1.50 M 1.25 M

[SO3] = 3.00 M 3.50 M

Initial Equilibrium

[SO2] = 0.500 M

0.590 M

[O2] = 0 M 0.0450 M

[SO3] = 0.350 M

0.260 M4.36 and 4.32, within experimental error.

Equilibrium Expressions Involving Pressures

13.3

Pressure EquilibriaSo far we have described equilibria involving gases in terms of concentrations. Equilibria involving gases also can be described with pressure. C represents the molar concentration of the

gas. jA + kB lC + mD

Practice Problem #4The reaction for the formation of nitrosyl chloride:

2NO(g) + Cl2(g) 2NOCl(g)

was studied at 25°C. The presurres at equilibrium were found to be: NOCl =1.2 atm, NO = 5.0 x 10-2 atm, Cl2 = 3.0 x 10-1 atm. Calculate the value of Kp for this reaction at 25°C.

1.9 x 103

Kc vs. Kp

Kp = Kc(RT)Δn

Δn is the sum of the coefficients of the gaseous products minus the sum of the coefficients of the gaseous reactants

jA + kB lC + mD Δn=(l + m) – (j + k)

more moles of gas = more pressure

Practice Problem #5Using the value of Kp obtained in Problem #4, calculate the value of K at 25°C for the reaction: 2NO(g) + Cl2(g) 2NOCl(g)

Kp =1.9 x 103

K = 4.6 x 104

Heterogeneous Equilibria13.4

Homogenous vs. Heterogeneous Homogenous equlibria is where all the

reactants are in the same phase. Typically gases

Heterogeneous equilibria involve more than one phase. The position of a heterogeneous equilibrium

does not depend on the amounts of pure solids or liquids present.

Concentrations of pure solids and liquids cannot change.

Concentrations of pure solids and liquids are not included in the equilibrium expression for the reaction

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

This simplification only occurs with pure solids or liquids and not solutions or gases.

Practice Problem #6

Write the expressions for K and Kp for the following processes:a) Solid phosphorus pentachloride decomposes to liquid phosphorus trichloride and chloride gas.b) Deep blue solid copper (II) sulfate pentahydrate is heated to drive off water vapor to form white solid copper (II) sulfate.

Practice Problem #6

a) Solid phosphorus pentachloride decomposes to liquid phosphorus trichloride and chloride gas.

K = [Cl2] and Kp=PCl2

Practice Problem #6

b) Deep blue solid copper (II) sulfate pentahydrate is heated to drive off water vapor to form white solid copper (II) sulfate.

K = [H2O]5 Kp= (PH2O)5

Applications of the Equilibrium Constant13.5

Applications of the Equilibrium ConstantKnowing the equilibrium constant for a reaction allows us to predict several important features of the reaction The tendency for the reaction to occur

(but not the speed). Whether or not a given set of

concentrations represents an equilibrium condition.

Applications of the Equilibrium Constant

If the reaction is not at equilibrium, we can determine which way the reaction is moving by taking the current law of mass action ratio and comparing it to the equilibrium constant. The ratio of non-equilibrium concentrations

gives us the reaction quotient, Q.

Applications of the Equilibrium ConstantTo determine which direction a system will shift to reach equilibrium, we compare the values of Q and K. Q=K. The system is at equlibrium; no shift will

occur. Q>K. The initial concentrations of product to initial

reactants is too large. To reach equilibrium, the system must shift left, consuming products and forming reactants.

Q<K. The ratio of initial concentrations of products to initial concentrations of reactants is too small. The system must shift to the right to form more products.

Applications of the Equilibrium Constant

Practice Problem #7For the synthesis of ammonia at 500°C, the equilibrium constant is 6.0 x 10-2. Predict the direction in which the system will shift to reach equilibrium in each of the following cases:a) [NH3]=1.0x10-3M, [N2]=1.0x10-5M, [H2]=2.0x10-

3Mb) [NH3]=2.00x10-4M, [N2]=1.50x10-5M,

[H2]=3.54x10-1M

c) [NH3]=1.0x10-4M, [N2]=5.0M, [H2]=1.0x10-2M

a) Q>K, shift left. b)Q=K, no shift. c)Q<K, shift right.

Practice Problem #8Dinitrogen tetroxide in its liquid state was used as one of the fuels on the lunar lander for the NASA Apollo missions. In the gas phase it decomposes to gaseous nitrogen dioxide.

N2O4(g) 2NO2(g)

Consider an experiment in which gaseous N2O4 was placed in a flask and allowed to reach equilibrium at a temperature where Kp=0.133. At equilibrium, the pressure of N2O4 was found to be 2.71atm. Calculate the equilibrium pressure of NO2(g).

.600 atm

The ICE TableWhen initial concentrations and equilibrium constants are known, but none of the equilibrium positions are known it is helpful to write an ICE table.I:The Initial concentrations of products and

reactants C: The Change in concentrations needed to

reach equilibrium is summarized in terms of variables.

E: The Equilibrium values are summarized as a combination of initial and change needed.

ICE Table Example:Consider the reaction: N2(g) + 3H2(g) 2NH3(g)

K = 6.0 x 10-2 at 500°C.The initial concentration of N2 is 3.0M and H2 is 2.0M. What are the equilibrium positions of this reaction?

Initial (M) Change Equilibrium (M)

N2 3.0 -x 3.0 - x

H2 2.0 -3x 2.0 – 3x

NH3 0.0 +2x 2x

ICE Table Example:

N2(g) + 3H2(g) 2NH3(g), K = 6.0 x 10-2


N2 3.0 -x 3.0 - x

H2 2.0 -3x 2.0 – 3x

NH3 0.0 +2x 2x

Practice Problem #9 At a certain temperature a 1.00 L flask initially contained 0.298 mol PCl3(g) and 8.70x10-3 mol of PCl5(g). After the system had reached equilibrium, 2.00 x 10-3 mol Cl2(g) was found in the flask. Gaseous PCl5 decomposes according to the reaction: PCl5(g) PCl3(g) + Cl2(g). Calculate the equilibrium concentrations of all species and the value of K.

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Practice Problem #9 Initial: 0.298 mol PCl3(g). 8.70x10-3 mol of PCl5(g)in 1.00L equil: 2.00 x 10-3 mol Cl2(g)

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

Equilibrium expression:ICE Table:

k=8.96 x 10-2


PCl5(g) 0.298 -2.00 x 10-3

PCl3(g) 8.70x10-3 +2.00 x 10-3

Cl2(g) 0.0 +2.00 x 10-3 2.00 x 10-3

Practice Problem #10Carbon monoxide reacts with steam to produce carbon dioxide and hydrogen. At 700 K the equilibrium constant is 5.10. Calculate the equilibrium concentrations of all species if 1.00 mol of each component is mixed in a a 1.00L flask.

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Practice Problem #10Reaction: CO(g) + H2O(g) CO2(g) + H2(g), K= 5.10

Which way does the equilibrium need to go? Q=1.00 Q<K, shift right

ICE Table:


CO 1.0 -x 1.0 - x

H2O 1.0 -x 1.0 - x

CO2 1.0 +x 1.0 + x

H2 1.0 +x 1.0 + x

Practice Problem #10

x = 0.387 mol/L[CO] & [H2O] = .613M, [CO2] & [H2] = 1.387M

Double check K with expression.


CO 1.0 -x 1.0 - x

H2O 1.0 -x 1.0 - x

CO2 1.0 +x 1.0 + x

H2 1.0 +x 1.0 + x


Assume that the reaction for the formation of gaseous hydrogen fluoride from hydrogen and fluorine has an equilibrium constant of 1.15 x 102 at a certain temperature. In a particular experiment, 3.000 mol of each component was added to a 1.500 L flask. Calculate the equilibrium concentration of all species.

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Practice Problem #11Reaction: H2(g) + F2(g) 2HF(g), K=1.15 x 102

Which way does the equilibrium need to go? Initial concentrations:

3.000mol/1.500L = 2.00 M Q=1.00 Q<K, shift right

ICE Table: Initial (M)

Change

Equilibrium (M)

H2 2.0 -x 2.0 - x

F2 2.0 -x 2.0 - x

HF 2.0 +2x 2.0 + 2x


x=1.528[H2] & [F2]= 0.472 M

[HF] = 5.056 MCheck K with equilibrium values

Initial (M)

Change

Equilibrium (M)

H2 2.0 -x 2.0 - x

F2 2.0 -x 2.0 - x

HF 2.0 +2x 2.0 + 2x

Solving Equilibrium Problems13.6

Solving Equilibrium ProblemsStrategy:1. Write the balanced equation for the

reaction.2. Write the equilibrium expression using

law of mass action.3. List the initial concentrations.4. Calculate Q, and determine the

direction of the shift needed for equilibrium.

Solving Equilibrium ProblemsStrategy continued:5. Define the change needed to reach

equilibrium, and define the equilibrium concentrations by applying the change to the initial concentrations.

6. Substitute the equilibrium concentrations into the equilibrium expression, and solve for the unknown.

7. Check your calculated equilibrium concentrations by making sure the give the correct value of K.

Solving Equilibrium Problems

Typical systems do not produce an expression that can be solved by taking the square root of both sides. To solve some expressions, we will use

the quadratic equation.

Equilibrium ExampleSuppose for a synthesis of hydrogen fluoride from hydrogen and fluorine, 3.000 mol H2 and 6.000 mol F2 are mixed in a 3.000 L flask. Assume the equilibrium constant for the synthesis reaction at this temperature is 1.15x102. What are the equilibrium concentrations of each component.

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Equilibrium Example1. Write the balanced equation for the reaction.

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

2. What is the equilibrium expression?

3. What are the initial concentrations?[H2] = 3.00mol/3.00 L = 1.000M

[F2] = 6.00mol/3.00 L = 2.000M

[HF]= 0

Equilibrium Example4. What is Q?

Q does not need to be calculated in this example. Since HF is not present initially, we can assume that the reaction will shift to the right to reach equilibrium.5. What change is required to reach

equilibrium?

Initial (M)

Change

Equilibrium (M)

H2 1.0 -x 1.0 - x

F2 2.0 -x 2.0 - x

HF 0.0 +2x 2x

Equilibrium Example6. What is the value of K? (Use ICE in expression)

collect terms and set = 0

ax2 + bx + c = 0

a=1.11x102, b=-3.45x102, c=2.30x102

Equilibrium Example6. What is the value of K? a=1.11x102, b=-3.45x102, c=2.30x102

Substituting these values give two answers for x:

x=2.14 mol/L and 0.968 mol/L

Both of these results are not valid; the changes in concentration must be checked for validity

Equilibrium Example6. What is the value of K?

x=2.14 mol/L or 0.968 mol/L

[H2] = 1.000 – x, [F2] = 2.000 – x, [HF] = 2x

[H2] = 3.2x10-2M, [F2] = 1.032M, [HF] = 1.936M

7. Check concentrations by substituting them into the equilibrium expression.

Practice Problem #12Assume that gaseous hydrogen iodide is synthesized from hydrogen gas and iodine vapor at a temperature where the equilibrium constant is 1.00x102. Suppose HI at 5.000x10-

1 atm, H2 at 1.000x10-2 atm, and I2 at 5.000x10-3 atm are mixed in a 5.000L flask. Calculate the equilibrium pressures of all species.

Practice Problem #121. Write the balanced equation

2. What is the equilibrium expression?

3. What are the initial pressures?

4. What is the value of Q?

Practice Problem #125. What is the change required?

6. What is the value of Kp (& equilibrium pressures)?

7. Expression check.

PHI=4.29x10-1atm, PH2=4.55x10-2atm, PI2=4.05x10-

2atm

Small Equilibrium ConstantsSometimes there are simplifications that can be made to the math of some equilibrium problems. When reactions lie far to the left, the

equilibrium constants can be very small. Changes in initial concentrations can be

negligible and partially disregarded.

Small K ExampleGaseous NOCl decomposes to form the gases NO and Cl2. At 35°C the equilibrium constant is 1.6x10-5. In an experiment in which 1.0 mol NOCl is placed in a 2.0 L flask, what are the equilibrium concentrations?1. What is the equation?

2NOCL(aq) 2NO(g) + Cl2(g)

2. What is the expression?

Small K Example3. What are the initial concentrations?

[NOCl]=0.50M, [NO]=0, [Cl2] = 0

4. What is Q?Direction must lie to the right for

equilibrium.5. What is the change required?

Initial (M)

Change

Equilibrium (M)

NOCl 0.50 -2x 0.50 - 2x

NO 0.0 +2x 2x

Cl2 0.0 +x x

Small K Example6. What is the value of K (& concentrations)

x must represent a relatively small number. In order to simplify this expression, we can assume that:

0.50 – 2x ≅ .50Therefore we can simplify the expression:

x=1.0x10-2

Initial (M)

Change

Equilibrium (M)

NOCl 0.50 -2x 0.50 - 2x

NO 0.0 +2x 2x

Cl2 0.0 +x x

Small K Example[NOCl] = .50 – 2x ≈ 0.50 M[NO] = 2.0 x 10-2 M[Cl2] = 1.0 x 10-2 M

7. Check the K expression.

Le Chatelier’s Principle13.7

Le Chatelier’s Principle

Several factors can control the position of a chemical equilibrium. Changes in Concentration Temperature (removal or addition of energy) Pressure

Le Chatelier’s PrincipleLe Chatelier’s principle states that if a change is imposed on a system at equilibrium, the position of the equilibrium will shift in a direction that tends to reduce that change. It is important to realize that although

changes to the reaction may alter the equilibrium positions, they do not alter the equilibrium constant.

Le Chatelier’s PrincipleChange in Concentration: If a component (reactant or product) is

added to a reaction system at equilibrium (at constant T and P or constant T and V), the equilibrium position will shift in the direction that lowers the concentration of that component. If a component is removed, the opposite effect occurs.

Practice Problem #13Arsenic can be extracted from its ores by first reacting the ore with oxygen (called roasting) to form solid As4O6, which is then reduced using carbon:

As4O6(s) + 6C(s) As4(g) + 6CO(g)

Predict the direction of the shift of the equilibrium position in response to each of the following changes in concentration.a) Addition of carbon monoxide.b) Addition or removal of carbon or tetrarsenic

hexoxide. c) Removal of gaseous arsenic. left shift, no effect, right shift

Le Chatelier’s PrincipleChange in Pressure: There are three ways to change the pressure

of a reaction system involving gaseous components:1. Add or remove a gaseous reactant or product.2. Add an inert gas (one not involved in the

reaction).3. Change the volume of the container

Le Chatelier’s PrincipleChange in Pressure: When an inert gas is added, there is no

effect on the equilibrium position. The addition of an inert gas increases the total pressure but has no effect on the concentrations of the reactants or products. The system will remains at the original

equilibrium position

Le Chatelier’s PrincipleChange in Volume: When the volume of the container holding a

gaseous system is reduced, the system responds by reducing its own volume. This is done by decreasing the total number of gaseous molecules in the system. A reaction will shift in order to reduce the

number of gas molecules.

Practice Problem #14Predict the shift in equilibrium position that will occur for each of the following processes when the volume is reduced.a. The preparation of liquid phosphorus

trichloride by the reaction.P4(s) + 6Cl2(g) 4PCl3(l)

right shift

Practice Problem #14Predict the shift in equilibrium position that will occur for each of the following processes when the volume is reduced.b. The preparation of gaseous phosphorus

pentachloride according to the equation: PCl3(g) + Cl2(g) PCl5(g)

right shift

Practice Problem #14Predict the shift in equilibrium position that will occur for each of the following processes when the volume is reduced.c. The reaction of phosphorus trichloride with

ammonia: PCl3(g) + 3NH3(g) P(NH2)3(g) + 3HCl(g)

no effect

Le Chatelier’s PrincipleChange in Temperature: If energy is added or removed from a system

in equilibrium, the system will shift according to the heat of the reaction. Heat is a product in an exothermic reaction. Heat is a reactant in an endothermic reaction. The effect of temperature on equilibrium

changes the value of K because K changes with temperature.

Practice Problem #15For each of the following reactions, predict how the value of K changes as the temperature is increased.a. N2(g) + O2(g) 2NO(g) ΔH = 181 kJ

b. 2SO2(g) + O2(g) 2SO3(g) ΔH = -198 kJ

a) shift right b) shift left

THE END3 more units to go!!!

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Ap chem unit 13 presentation