Gas Phase Equilibrium - Pennsylvania State University

Mary J. Bojan Chem 110 1

Gas Phase Equilibrium

Chemical Equilibrium

Equilibrium Constant Keq

Equilibrium constant expression

Relationship between Kp and Kc

Heterogeneous Equilibria

Meaning of Keq

Calculations of Kc

Solving Equilibrium Problems

USING AN EQUILIBRIUM CONSTANT

Information obtained from Kc 1. Predict direction of a reaction Q reaction quotien

2. Obtaining equilibrium concentrations of reactants and

products.


Equilibrium is achieved when opposing

processes proceed at equal rates.

equilibria previously discussed

Eg.

N2O4 (g) 2NO2(g)

colorless brown


In chemical equilibria, forward and reverse

reactions occur at equal rates: at a macroscopic

level, it looks like nothing is happening.


Achieving equilibrium: The relationship between the concentrations of

products and reactants at “equilibrium” will be

the same regardless of starting conditions.

Initial State: reactants only Initial state: products only


Equilibrium point of any reaction is

characterized by a single number called the

Equilibrium Constant.

In general: jA + kB pR + qS

Example:

B(g) 2 A (g) N2O4 2 NO (g)


What is the equilibrium constant

EXPRESSION (Keq) for the Haber process?

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


Summarize what we know about Keq.

The ratio of equilibrium concentrations will be constant:

Keq is the equilibrium constant for the reaction.

It is a NUMBER.

Keq (the number) DOES NOT depend on concentration

It’s a function of temperature only.

Notation:

Keq = Kc

Kc R

pS q

A jB

k

concentration […] is

expressed in M (mol/L)

Kp p

p pp

Rp

Sq

Aj

Bk

concentration is expressed

using partial pressures in atm Keq = Kp


n

cp (RT)KK

When given Keq how do I know if it is Kc or Kp?

Use context of problem.

If concentrations are given in M,

then Keq = Kc

• If concentrations are given in P,

then Keq = Kp

where n = nprod − nreact

There is a relationship between Kp and Kc.


If equilibrium concentrations are known, we

can calculate Kp and Kc.

Equilibrium concentrations of NH3, N2, and H2 were

determined at 472C.

[H2] = 0.1207M

[N2] = 0.0402M

[NH3] = 0.00272M

Find Kc and Kp.

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


Heterogeneous Equilibria involves reactants and products in more than one

phase.

3 Fe(s) + 4 H2O(g) Fe3O4(s) + 4 H2(g)

Keq =Fe3O4[ ] H2[ ]

4

Fe[ ]3

H2O[ ]4

What is [Fe]? [Fe3O4]?

Activities of pure solids and liquids = 1.


What is the equilibrium constant expression for

these reactions?

AgCl(s) Ag+(aq) + Cl−(aq)

C6H6(g) + 3H2(g) C6H12(g)

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


Is Keq large or small??? What does that mean?

Reactants Products

K ≈ 1

reactants

reactants products

products

reactants products


Try this problem.

Which one of the following has the greatest tendency to

proceed as written?

1. 4NH3(g) + 3O2(g) 2N2(g) + 6H2O(g) Kp = 11022

2. N2(g) + O2(g) 2NO(g) Kp = 5 1031

3. 2HF(g) F2(g) + H2(g) Kp = 11013

4. 2NOCl(g) 2NO(g) + Cl2(g) Kp = 4.7104


Meaning of Keq

Is Keq large or small???

Reactants Products

Cu+2(aq) + 4NH3(aq) Cu(NH3)4+2(aq) Keq =

Ni+2(aq) + 6NH3(aq) Ni(NH3)6+2(aq) Keq =


Meaning of Keq

Is Keq large or small???

Reactants Products

PbI2(s) Pb+2(aq) + 2I– (aq)

Keq = reactants

reactants products

products


More Relationships

What is Keq if the reaction is doubled??

2HI(g) H2(g) + I2(g) C

Keq =

What is Keq for the reverse reaction?

2H2(g) + 2 I2(g) 4HI(g) B

Keq =

Keq =

H2(g) + I2(g) 2HI(g) A


At a certain temperature, Kc for the following

reaction is 16.

H2(g) + I2(g) 2 HI(g)

HI(g) ½ H2(g) + ½ I2(g)

At the same temperature, what is Kc for this reaction?

1. 1/16

2. 4

3. 1/4

4. 16

5. there is not enough information to answer this

question.


General Approach to Equilibrium Constant

Problems

1. Write the balanced reaction.

2. Write the general form for Keq.

3. Set up a data table:

(may need algebraic unknowns)

initial conditions

changes in concentrations

equilibrium concentrations

4. Substitute equilibrium concentrations into the

expression for Keq and solve.


Equilibrium problem solving: calculating Keq

1.00 mole of SO2(g) and 1.00 mole of O2(g) are added to a 1.00 L

container and react until equilibrium is achieved. At equilibrium,

the container has 0.919 moles of SO3(g).

Find Kc at 1000K.


Equilibrium problem solving: calculating Keq

A one L container holds 224g of Fe and 5.00 mole of

H2O(). It is heated to 1000K and reaches equilibrium.

56g of Fe are left unreacted. What is Kc at 1000K?

3Fe(s) + 4H2O(g) Fe3O4(s) + 4H2(g)

I. initial

C. change

E. equilibrium


The reaction quotient Q can be used to

predicting the direction of a reaction.

Note: the concentrations used are NOT equilibrium

concentrations.

Reaction quotient Q

aA + bB cC + dD

Q =C[ ]

cD[ ]

d

A[ ]a

B[ ]b


We use Q to predict the direction of a

reaction.

When Q < Kc

reaction moves to right (produces product)

When Q > Kc

reaction moves to left (produces reactant)

When Q = Kc system IS at equilibrium

Q < K Q = K Q > K

K K K

Q

Q

Q


2HI(g) H2(g) + I2(g)

If we put 0.1 mole of HI in a 1L container, what will

happen?

1 reaction shifts to right

2 reaction shifts to left

3 no change occurs

Kc =H2[ ] I2[ ]HI[ ]

2 =1.25 ´10-3

If the initial concentrations of all three gases in the

vessel are 0.1 mol/L, what will happen?


We can use Keq to obtain equilibrium concentrations

of reactants and products.

Initially [IBr] = [I2] = [Br2] = 0.0500 M

What are the final concentrations of reactants and products? Kc = 2.50 10−3

2IBr(g) Br2(g) + I2(g)

I.

C.

E.


The Haber process is the

industrial process used to make ammonia

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


Factors that affect equilibrium

What happens to a system at equilibrium when it is

disturbed by changing

concentration

volume

pressure

temperature

Answer: Le Chatelier’s Principle

If a system at equilibrium is disturbed, the system will shift

its equilibrium position to minimize the effect of the

disturbance.


Le Chatelier’s Principle: To illustrate this principle

use the following chemical system in a closed 1L

container.

Hrxn = 92.4kJ/mol T = 700C

Initial conditions:

[N2] = 3.00 M [H2] = 4.50 M [NH3] = 0

At equilibrium:

[N2] = 2.00M [H2] = 1.50 M [NH3] = 1.41 M

What is Kc?

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


Use LeChatelier’s principle to answer the

following questions

1. What will happen to [NH3] if 3.0 moles of H2 are

added to the system at equilibrium?

Increase the amount of a reactant or product

2. What will happen if the volume decreases from 1.0L

to 0.5L?

Increase P by decreasing volume

3. What will happen if 5.0 moles of inert gas is added

to the system?

Increase pressure by adding an inert gas.

4. What will happen if the temperature is increased to

1000K?


1. What will happen to [NH3] if 3.0 moles of H2 are

added to the system at equilibrium?

System is no longer at equilibrium.

Which direction will it go to get to equilibrium?

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

Using LeChatelier’s principle:

Reactant or product added to a mixture at equilibrium will cause

reaction to shift in the direction that consumes part of the added

material.


2. Which direction will the reaction proceed if the

volume is decreased to 0.5L?

RTPsoVasV

n][][,][

LeChatelier’s principle:

Since pressure is increased by disturbance, reaction

will shift in direction that will reduce pressure

N2(g) + 3H2(g)

4 moles

2NH3(g)

2 moles


3. What happens when 5.0 moles of an inert gas are

added?

Inert gas: gas that does not participate in the reaction.

How does an inert gas effect the concentrations of

reactants and products?

LeChatelier’s principle:

N2(g) + 3H2(g)

4 moles

2NH3(g)

2 moles


Examples

Yellow colorless red

N2O2(g)

colorless

Fe+3(aq) + SCN– (aq) FeSCN+2(aq)

Change concentration

Change pressure

2NO2(g)

brown


changing concentration (or V so that [ ] changes) puts a

stress on the system.

Stresses do not change Keq!

Q changes; system shifts to re-establish equilibrium

Q K

Summary

WHAT IF TEMPERATURE CHANGES? • Keq changes

• change depends on whether the reaction is

exothermic or endothermic.

H +H

Mary J. Bojan Chem 110

34

4. What happens when the temperature is increased to

1000K?

Treat heat like a product (exothermic) or reactant (endothermic).

Hrxn = −92.4 kJ/mol

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

Le Chatelier’s Principle:

heat is added to a system, the reaction will shift in the

direction that absorbs heat

Reaction is exothermic (heat is a product) so adding heat

will cause reaction to shift to left.


4. What happens when the temperature is decreased?

heat + Co[H2O]62+ (aq) + 4Cl−(aq) CoCl4

2− (aq)+ 6H2O()

pink blue

Treat heat like a product (exothermic)

or reactant (endothermic).

Example: endothermic reaction


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

Problem: rate of reaction increases as T increases, BUT equilibrium

constant decreases at higher T.

To produce ammonia:

Do we want high or low temperature?

Do we want high or low pressure?

Liquefy ammonia as process

proceeds. WHY?

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Gas Phase Equilibrium - Pennsylvania State University