Chap 15
CHEMICAL EQUILIBRIUM
- Reactions that can go in both directions are called reversible reactions.
- These reactions seem to stop before they go to completion.
- When the rate of the forward and reverse reactions become equal, an equilibrium system is established.
Stepwise view to an equilibrium system
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No Reaction
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| Step 4 | RATE OF FORWARD REACTION = RATE OF REVERSE REACTION | ||||||
Rate of forward reaction Equilibrium condition
CHEMICAL EQUILIBRIUM
Characteristics of a Chemical Equilibrium System:
- A mixture of Reactants and Products is present
- The composition of the reaction mixture no longer changes:
- Concentration of reactants is constant
- Concentration of products is constant
NOTE:
Concentration of reactants
3. A Chemical Equilibrium is a Dynamic Equilibrium; both reactions (forward and reverse) are still going on
4. The Dynamic Equilibrium may be controlled (shifted to the right to favor products, or shifted to the left to favor reactants) by changing the conditions for the reaction.
Concentration of reactants
3. A Chemical Equilibrium is a Dynamic Equilibrium; both reactions (forward and reverse) are still going on
4. The Dynamic Equilibrium may be controlled (shifted to the right to favor products, or shifted to the left to favor reactants) by changing the conditions for the reaction.
Definition of Chemical Equilibrium:
- A state reached by a reaction mixture when the rate of forward reaction and the rate of reverse reactions become equal.
THE EQUILIBRIUM CONSTANT
- Concentrations of reactants and products are not equal at equilibrium, but can be quantified by use of the equilibrium constant (K).
- Consider the general chemical equation below:
where A and B are reactants and C and D are products, and
Law of Mass Action
[C], [D] = molar concentrations (molarities) of the products at equilibrium [A], [B] = molar concentrations (molarities) of the reactants at equilibrium
- When writing an equilibrium constant expression for a chemical equation, the balanced chemical equation is examined and the law of mass action is applied. For example, for the reaction shown below:
the equilibrium constant can be written as:
- Note that the coefficients of the chemical equation become the exponents in the expression of the equilibrium constant.
- The equilibrium constant expressed in terms of the concentration of the reactants and products is designated as
. - It is common practice to write K without units.
THE EQUILIBRIUM CONSTANT
Examples:
- Write the equilibrium constant expression for the equation shown below:
- Write the equilibrium constant expression for the combustion of propane:
SIGNIFICANCE OF THE EQUILIBRIUM CONSTANT
- The magnitude of the equilibrium constant indicates the extent to which the forward and reverse reactions take place.
K >>> 1:
Products are favored at equilibrium
K <<< 1:
- Reactants are favored at equilibrium
- Neither reactants, nor products are predominant at equilibrium
Summary:
- K >>1: Forward reaction is favored; forward reaction proceeds essentially to completion.
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: Neither direction is favored; forward reaction proceeds about halfway. -
: Reverse reaction is favored; forward reaction does not proceed very far.
Examples:
- The equilibrium constant for the reaction
is 10 . A reaction mixture initially contains and . Which statement below is true at equilibrium?
a) The reaction mixture will containand .
b) The reaction mixture will containand .
c) The reaction mixture will contain equal concentrations of A and B .
MANIPULATING EQUILIBRIUM CONSTANTS
- If a chemical equation is modified in some way, then the equilibrium constant for the equation also changes because of the modification. Three common modifications are discussed below:
A) If an equation is reversed, then the equilibrium constant is inversed. For example, the equilibrium constant for the reaction below and its reverse can be written as shown:
B) If the coefficients in an equation are multiplied by a factor, then the equilibrium constant should also be multiplied by that factor. For example, consider the equilibrium below and when it is doubled:
Examples:
- The reaction
has an equilibrium constant of . What is the equilibrium constant for the reaction ?
a) 1
b) 10
c) 100
d) 0.0010
MANIPULATING EQUILIBRIUM CONSTANTS
C) If a given chemical equation can be obtained by taking the sum of other equations, the Equilibrium Constant for the overall equation equals the product of the equilibrium constants of the other equations.
For example, the following equilibria occur at 1200 K
The equilibrium constant for an overall equation is equal to the product of the equilibrium constants of the individual equations.
Examples:
- Predict the equilibrium constant for the first reaction shown below, given the two equilibrium constants given:
GAS-PHASE EQUILIBRIA (
- Gas-Phase Equilibria refers to equilibrium systems where all reactants and products are gases.
- Concentrations of gases can be expressed in terms of partial pressures, since the concentration of a gas is proportional to its partial pressure.
Constant at a given temperature
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is the equilibrium constant for a gaseous reaction expressed in terms of partial pressures. -
has a value different from
Examples:
- The reaction shown below has
at 1200 K . Calculate for this reaction at this temperature.
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for the formation of NO at is . What is the value of at this temperature?
CLASSIFICATION OF CHEMICAL EQUILIBRIA
- Chemical Equilibria can be classified according to the physical state of the reactants and products present:
A) Homogeneous Equilibrium
An equilibrium that involves reactants and products in a single phase. For example:
B) Heterogeneous Equilibrium
An equilibrium involving reactants and products in more than one phase For example
NOTE: The concentrations of solids are omitted.
Reason: The concentration of a pure solid or pure liquid is a constant at a given temperature.
Reason: The concentration of a pure solid or pure liquid is a constant at a given temperature.
- Equilibrium Constant expression can be written with pure solids included:
- The concentrations of pure solids and liquids are incorporated in the value of
. - The concentration of solvent is also omitted from the expression of
for a homogeneous reaction (if constant). - The equilibrium is not affected by pure solids, pure liquids, or solvents.
A Heterogeneous Equilibrium
CLASSIFICATION OF CHEMICAL EQUILIBRIA
Examples:
Identify each of the following equilibriums as homogeneous or heterogeneous and write Kc expressions for each:
Identify each of the following equilibriums as homogeneous or heterogeneous and write Kc expressions for each:
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- For which reaction below does
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a)
b)
c)
CALCULATING
- The most direct way to obtain an experimental value for the equilibrium constant of a reaction is to measure the concentration of the reactants and products in a reaction mixture in equilibrium.
- For example, for the reaction shown below, suppose a mixture of
and are allowed to come to equilibrium at .
- If at equilibrium, the concentrations are
and , what is the value of the equilibrium constant at this temperature?
- For any reaction, the equilibrium concentrations of the reactants and products depend on the initial concentrations, and commonly vary for each case. However, the equilibrium constant is always the same at a given temperature, regardless of the initial concentrations.
| TABLE 14.1 Initial and Equilibrium Concentrations for the Reaction
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| Initial Concentrations | Equilibrium Concentrations | Equilibrium Constant | ||||
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[
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[HI] | [
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[
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[HI] |
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| 0.50 | 0.50 | 0.0 | 0.11 | 0.11 | 0.78 |
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| 0.0 | 0.0 | 0.50 | 0.055 | 0.055 | 0.39 |
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| 0.50 | 0.50 | 0.50 | 0.165 | 0.165 | 1.17 |
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| 1.0 | 0.50 | 0.0 | 0.53 | 0.033 | 0.934 |
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| 0.50 | 1.0 | 0.0 | 0.033 | 0.53 | 0.934 |
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© 2014 Pearson Education, Inc.
CALCULATING
- When equilibrium concentrations are not given, they can be determined from the initial concentrations and the stoichiometric relationships in the equation. For example, consider the simple reaction below:
- If a reaction mixture with an initial concentration of
and is allowed to come to equilibrium, and if the concentration of A at equilibrium equals 0.75 M , then the following information can be determined for this reaction.
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| Initial | 1.00 | 0.00 |
| Change | -0.25 | +0.50 |
| Equilibrium | 0.75 | 0.50 |
- The equilibrium constant for this reaction can then be calculated as shown below:
- For any reaction, the ICE table (shown above) can be used to determine the equilibrium concentrations of reactants and products from the initial concentrations given.
Examples:
- When 2.00 mole each of
and are mixed in a flask and allowed to come to equilibrium, 3.5 mol of HI is produced. What is the value of the equilibrium constant for this reaction?
Examples (cont'd):
- Consider the reaction below. A reaction mixture at
initially contains [CO]= 0.500 M and . At equilibrium, the CO concentration is found to be 0.15 M . What is the value of the equilibrium constant?
| Initial | 0.500 | 1.00 | 0.00 |
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| Equilibrium | 0.15 |
- Consider the reaction below. A reaction mixture at
initially contains . At equilibrium, the mixture contains . What is the value of the equilibrium constant?
| Initial | 0.115 | 0.00 | 0.00 |
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| Equilibrium | 0.035 |
Examples (cont'd):
- Consider the reaction shown below. A reaction mixture is made containing an initial [
] of 0.020 M . At equilibrium, . Calculate the value of the equilibrium constant .
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- A sample of
is placed in an evacuated sealed container and heated to 600 K . The following equilibrium is established:
The total pressure in the system at equilibrium is found to be 3.0 atm and the mole fraction of
PREDICTING THE DIRECTION OF CHANGE
- When the reactants in a chemical reaction mix, they generally form products, and the reaction is said to proceed in the forward direction. The amount of products formed depends on the magnitude of the equilibrium constant.
- What direction would the reaction proceed if the initial reaction mixture contains both reactants and products? To gauge the progress of a reaction relative to equilibrium, a quantity called the reaction quotient is used.
- The reaction quotient (
) has the same definition as the equilibrium constant, except that the concentrations are not at equilibrium. Therefore, for the general reaction:
the reaction quotient is:
- The reaction quotient is useful because the value of Q relative to K is a measure of the progress of reaction towards equilibrium. At equilibrium, the reaction quotient (Q) is equivalent to the equilibrium constant (K).
PREDICTING THE DIRECTION OF CHANGE
- Shown below is a plot of Q as a function of the concentrations of A and B for the simple reaction
, which has an equilibrium constant of .
Concentration (M)
© 2014 Pearson Education, Inc.
© 2014 Pearson Education, Inc.
- The three conditions highlighted above are represented by the 3 data points shown below:
| Q |
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Predicted Direction of Reaction |
| 0.55 | 1.45 | To the right (toward products) |
| 2.55 | 1.45 | To the left (toward reactants) |
| 1.45 | 1.45 | No change (at equilibrium) |
- The reaction quotient ( Q ) relative to the equilibrium constant ( K ) is a measure of the progress of the reaction toward equilibrium, and can be summarized as:
- When:
Reaction proceeds the left (towards the reactants) - When:
Reaction proceeds to the right (towards the products) - When:
Reaction mixture is at equilibrium
PREDICTING THE DIRECTION OF CHANGE
Examples:
- The following reaction has an equilibrium constant,
, equal to 3.59 at , and the following composition of reaction mixture:
(a) Is the reaction mixture at equilibrium?
(b) If not at equilibrium, in which direction will the reaction go to reach equilibrium?
2. Nitrogen dioxide dimerizes according to the reaction:
2. Nitrogen dioxide dimerizes according to the reaction:
A 2.25-L container contains 0.055 mol of
CALCULATING EQUILIBRIUM CONCENTRATIONS
- We can use equilibrium constant to calculate the equilibrium concentration of all the substances in the mixture.
- At times, the equilibrium concentration of one substance is determined from equilibrium constant and the equilibrium concentration of the other substances.
Examples:
- Nitric oxide, NO, is formed in automobile exhaust by the reaction of
and (from air):
- The equilibrium shown below has a
value of at . In an equilibrium mixture of the three gases at this temperature, the partial pressure of is 0.928 atm and that of is 0.432 atm . What is the partial pressure of in this mixture?
CALCULATING EQUILIBRIUM CONCENTRATIONS
- At times, the equilibrium concentrations of all substances are determined from equilibrium constant and the initial concentration of the reactants. When solving these problems, we use an ICE table with the known initial concentrations and then represent the unknown changes with the variable x .
- For example, consider the simple reaction below:
- If a reaction mixture with an initial concentration of
and is allowed to come to equilibrium, and the equilibrium constant is found to be 0.33 , the equilibrium concentration of each substance can be found as shown below: - The equilibrium concentration of each substance can then be found by setting up the equilibrium constant expression and solving for x .
- Examples below show some of the variations
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| Initial | 1.0 | 0.00 |
| Change |
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© 2014 Person Educaton, ke
for this type of problems.
Examples:
- For the reaction shown below, initially a mixture contains
and . Find the equilibrium concentration of the reactants and products in this reaction.
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| Initial | 0.200 | 0.200 | 0.00 |
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-x | -x | +2 x |
| Equilibrium |
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2 x |
Taking square roots of both sides:
Simplifying:
Rearranging & solving for x :
Simplifying:
Rearranging & solving for x :
Equilibrium concentrations are:
Examples:
- Ammonium hydrogen sulfide decomposes at room temperature as shown below:
A sample of ammonium hydrogen sulfide is placed in a flask at
- At relatively high temperatures, the following reaction can be used to produce methyl alcohol:
If the concentration of CO at equilibrium were found to be 0.010 M , what would be the equilibrium concentration of
CALCULATIONS INVOLVING QUADRATIC EQUATIONS
- Some of the problems involving equilibrium require use of the quadratic equation in order to determine the unknown variable. The example below shows one such problem.
Examples:
-
decomposes when heated:
If the initial concentration of
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| Initial | 1.00 M | 0 | 0 |
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-x | +x | +x |
| Equilibrium |
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x | x |
- In theory: There are two mathematical solutions
- In practice: Only one solution makes physical sense
(concentration cannot be negative)
Equilibrium Concentrations are:
LE CHATELIER'S PRINCIPLE
- The effect of changes on the equilibrium can be predicted using the Le Chatelier's principle.
- Le Chatelier's principle states that:
"If a stress is applied to a system at equilibrium, the system will respond in such a way as to relieve the stress and restore a new equilibrium under a new set of conditions". - Note sequence of events:
- Stress applied
- Equilibrium system response (equilibrium shift)
- New equilibrium
- Stress is a change in any of the following:
A) Concentration of Reactants or Products
B) Pressure
C) Temperature
A) Effect of Concentration Change on Equilibrium
(Adding or Removing Reactants or Products)
Consider:
Stress:
Response:
- Forward reaction speeds up
- Equilibrium shifts to the right
- Products are favored
New Equil.:
| decreased | increased | increased | increased |
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EFFECT OF CONCENTRATION CHANGE ON EQUILIBRIUM
In General:
- Adding Reagent
- Equilibrium always shifts in the direction that tends to reduce the concentration of the added reacting species.
- When concentration of reactant is increased equilibrium shifts forward (
). - When concentration of product is increased equilibrium shifts reverse (
). - Removing Reagent
- Equilibrium always shifts in the direction that tends to increase the concentration of the removed reacting species.
- When concentration of reactant is decreased equilibrium shifts reverse (
). - When concentration of product is decreased equilibrium shifts forward (
).
Example 1:
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(700K)
Response: - Equilibrium shifts forward to use up added reactant
(700K)
New Equil.
Conc's:
New Equil.
Conc's:
Example 2:
| Reagent Species | Change in concentration | Equilibrium Shift |
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increase | |
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decrease | |
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increase | |
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decrease | |
| HOCl | increase | |
| HOCl | decrease | |
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increase | |
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decrease |
Example 3:
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0.613 mol | 1.839 mol | 0.387 mol | 0.387 mol |
What changes in the amount of reagents would produce more
- increase amount of CO or
- remove
or - Most practical and least expensive solution is to remove
(cool reaction mixture to condense water vapor)
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| Molar Equil. Composition: | 0.613 mol | 1.839 mol | 0.387 mol | 0.387 mol | |
| Stress: | -0.387 mol | ||||
| Response: | Equilibrium shifts |  |
New Equilibrium Composition:
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- Equilibrium shift can also be predicted from an evaluation of
(Reaction Quotient)
EFFECT OF PRESSURE CHANGE ON EQUILIBRIUM
- A change in pressure has an effect on equilibrium only when the following two conditions exist:
- At least one of the reacting species (reactant or product) is a gas.
- Total number of moles of
Total number of moles of gaseous reactants gaseous products
- The Pressure of a gas may be:
- increased by decreasing the volume, at constant temperature (achieved by decreasing the size of the reaction vessel)
- decreased by increasing the volume, at constant temperature (achieved by increasing the size of the reaction vessel)
- To predict the equilibrium shift caused by a change in pressure, consider the following:
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| Increasing the concentration of |
| gaseous reacting species |
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Examples:
- Complete the table for the reaction shown below:
| Stress |
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Amounts of Reacting Species | ||||||
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EFFECT OF PRESSURE CHANGE ON EQUILIBRIUM
Examples (cont'd):
- Complete the table for the reaction shown below:
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Amounts of Reacting Species | ||||||
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- Complete the table for the reaction shown below:
| Stress | Pressure Change | Direction of Equilibrium shift | Amounts of Reacting Species | ||
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CO | |||
| Decrease in volume | |||||
| Increase in volume | |||||
EFFECT OF PRESSURE CHANGE ON EQUILIBRIUM
CONCLUSIONS:
At constant temperature:
- If the pressure is increased (volume is decreased), the reaction shifts in the direction of fewer moles of gas.
- If the pressure is decreased (Volume is increased), the reaction shifts in the direction of more moles of gas.
Le Châtelier's Principle: Changing Pressure
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EFFECT OF TEMPERATURE CHANGE ON EQUILIBRIUM
- According to Le Chatelier's principle, if the temperature of a system at equilibrium is changed, then the system will shift in a direction to counter that change. Therefore, if the temperature is increased, the reaction will shift in the direction that tends to decrease the temperature and vice versa.
- Recall that exothermic reactions
emit heat. Therefore, heat can be represent heat as a product:
- Similarly, since endothermic reactions
absorb heat, we can be represent heat as a reactant:
- At constant pressure, raising the temperature of an exothermic reaction-thought of as adding heat-shifts the reaction to the left (similar to adding products). For example:
- Conversely, lowering the temperature of an exothermic reaction-thought of as removing heat-shifts the reaction to the right (similar to removing products). For example:
EFFECT OF TEMPERATURE CHANGE ON EQUILIBRIUM
- In contrast, raising the temperature of an endothermic reaction-thought of as adding heatshifts the reaction to the right to absorb the heat. On the other hand, lowering the temperature-thought of as removing heat-shifts the reaction to the left.
Summary of Effect of Temperature on Equilibrium:
In an exothermic reaction (heat is a product):
- Increasing temperature causes reaction to shift left, decreasing equilibrium constant.
- Decreasing temperature causes reaction to shift right, increasing equilibrium constant.
In an endothermic reaction (heat is a reactant):
- Increasing temperature causes reaction to shift right, increasing equilibrium constant.
- Decreasing temperature causes reaction to shift left, decreasing equilibrium constant.
Examples:
- Complete the table below for the reaction of formation of
from and gases:
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Amounts of Reacting Species |
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Examples (cont'd):
- Coal can be used to generate hydrogen gas by the endothermic reaction shown below:
If this reaction mixture is at equilibrium, predict how each change below will affect the production of hydrogen gas:
a) adding more C to the reaction mixture
b) adding more
c) raising the temperature of the reaction mixture
d) decreasing the volume of the reaction mixture
e) adding a catalyst to the reaction mixture
3. Consider the reaction shown below:
a) adding more C to the reaction mixture
b) adding more
c) raising the temperature of the reaction mixture
d) decreasing the volume of the reaction mixture
e) adding a catalyst to the reaction mixture
3. Consider the reaction shown below:
A reaction mixture at equilibrium at 175 K contains
a) Is the second reaction at equilibrium?
b) If not, what will be the partial pressure of HI when the reaction reaches equilibrium at 175 K ?
a) Is the second reaction at equilibrium?
b) If not, what will be the partial pressure of HI when the reaction reaches equilibrium at 175 K ?
Answers to In-Chapter Problems:
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| 11 | 1 | heterogeneous;
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| 2 | homogeneous;
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| 13 | 1 | 196 | ||
| 14 | 2 | 26 | ||
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