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CHEMICAL EQUILIBRIUM
1. In doing stoichiometry calculations, we assumed that the reactions proceed to completion.
2. In fact, many stop short of completion. They have, instead, reached
______________________________.
3. This is the state where the concentrations of all reactants and products remain constant with respect to
time.
THE EQUILIBRIUM CONDITION
1. Equilibrium is not a static situation; it is a highly dynamic situation.
2. Consider this reaction:
Start with equal number of moles of H2O and CO. Since they react 1:1, the concentrations of the two gases
are always equal. Since H2 and CO2 are formed in equal amounts, they are always present in the same
concentrations.
3. When CO and H2 O are first mixed, they react and begin forming H2 and CO2. The reactant
concentrations decrease and the product concentrations increase.
4. At a certain point in time the concentrations of products and reactants no longer change and equilibrium
is reached.
5. The equilibrium position is determined by many factors:
a.
b.
c.
6. Energy and organization come into play because nature tries to achieve minimum energy and maximum
disorder.
The Characteristics of Chemical Equilibrium
1. In the production of ammonia:
Nothing appears to happen at 250C.
2. The forward reaction is so slow that the system moves toward equilibrium at a rate that cannot be
detected.
3. A catalyst is needed to speed up the forward and reverse reactions.
THE EQUILIBRIUM CONSTANT
1. The ___________________________________ is a general description of the equilibrium condition.
2. Consider the reaction:
The equilibrium expression is:
***** Write the equilibrium expression for the following reaction:
4 NH3 (g) + 7 O2 (g) ↔ 4 NO2 (g) + 6 H2O (g)
3. Equilibrium constants are given without units. This is due to corrections for the nonideal behavior of
the substances taking part in the reaction.
***** For the reaction
N2 (g) + 3 Cl2 (g) ↔ 2 NCl3 (g)
An analysis of an equilibrium mixture is performed at a certain temperature. It is found that
[NCl3(g)] = 1.9 x 10-1 M, [N2(g)] = 1.4 x 10-3 M and [Cl2(g)] = 4.3 x 10-4 M. Determine the value of K for
the reaction at this temperature.
4. Look again at:
If the reaction is reversed:
The equilibrium expression is:
If the original reaction is multiplied by some factor (n) to give:
Then:
5. The law of mass action provides a remarkably accurate description of all types of chemical equilibria.
6. The equilibrium constant always has the same value at a given temperature regardless of the amounts of
reactants that are mixed together initially.
7. But, the equilibrium concentrations _______________ always be the same.
8. Even though the individual sets of equilibrium concentrations are quite different for the different
situations, the equilibrium constant which depends on the ratio of the concentrations, remains the same.
9. Each set of equilibrium concentrations is called an ______________________________.
10. There is only __________ equilibrium constant for a particular system at a particular temperature, but
there are an ____________________ number of equilibrium positions.
11. The specific equilibrium position adopted by a system depends on the initial concentrations, but the
equilibrium constant does not.
EQUILIBRIUM EXPRESSIONS INVOLVING PRESSURES
1.
Equilibria involving gases can also be described in terms of pressures.
2.
The relationship between pressure and concentration of a gas can be seen from the ideal gas equation:
3.
For the equilibrium expression from the ammonia reaction:
Kc indicates an equilibrium expression involving concentrations. This is often left expressed as K.
4.
_______ indicates an equilibrium expression involving partial pressures.
***** The following equilibrium pressures were observed at a certain temperature for the reaction:
N2 (g) + 3 H2 (g) ↔ 2 NH3 (g)
P NH3 = 3.1 x 10-2 atm
P H2 = 3.1 x 10-3 atm
Calculate the value of the equilibrium constant, Kp, at this temperature.
P N2 = 8.5 x 10-1 atm
5.
K and Kp can be related. For the general reaction:
∆n = (sum of gaseous product coefficients – sum of gaseous reactant coefficients)
***** At 1100 K, Kp = 0.25 for the reaction:
2 SO2 (g) + O2 (g) ↔ 2 SO3 (g)
What is the value of K at this temperature?
HETEROGENEOUS EQUILIBRIA
1.
So far all of the reactants ad products have been gases. These are
______________________________.
2.
Many equilibria involve more than one phase and are called ______________________________.
3.
Look at the commercial preparation of lime:
Straightforward application of the equilibrium expression is:
4.
Experimental results show that the position of a heterogeneous equilibrium does not depend on the
amounts of pure solids or liquids present.
5.
The basic reason for this is that the concentrations of pure solids and liquids cannot change.
6.
If pure solids or pure liquids are involved in a chemical reaction, their concentrations are not included
in the equilibrium expression for the reaction.
***** Write the expressions for K and Kp for the following processes:
a.
The decomposition of solid phosphorus pentachloride to form liquid phosphorus trichloride and
chlorine gas.
b.
Deep blue solid copper (II) sulfate pentahydrate is heated to drive off water vapor to form a white
solid copper (II) sulfate.
APPLICATIONS OF THE EQUILIBRIUM CONSTANT
1.
Knowing the equilibrium constant for a reaction allows us to predict:
a.
The tendency of the reaction to occur, but not the speed.
b.
Whether or not a given set of concentrations represent an equilibrium condition.
c.
The equilibrium position that will be achieved from a given set of initial concentrations.
The Extent of a Reaction
1.
The inherent tendency for a reaction to occur is indicated by the magnitude of the equilibrium
constant.
2.
A value of K much larger than one means that at equilibrium the reaction system will consist mostly
of products – the equilibrium lies to the right.
3.
Reactions with a very large equilibrium constant go essentially to completion.
4.
A very small value of K means that the system at equilibrium will consist of mostly reactants – the
equilibrium position is far to the left. The given reaction does not occur to any significant extent.
5.
The size of K and the time required to reach equilibrium are not directly related.
Reaction Quotient
1.
When the reactants and products of a given chemical reaction are mixed, it is useful to know whether
the mixture is at equilibrium.
2.
If not, it’s useful to know the direction in which the system must shift to reach equilibrium.
3.
If the concentration of one of the products or reactants is zero, the system will shift in the direction that
produces the missing component.
4.
To determine the shift when all the initial concentrations are nonzero, we use the
___________________________________.
5.
The reaction quotient is obtained by applying the law of mass action using the initial concentrations
instead of equilibrium concentrations.
6.
There are three possible cases:
***** The equilibrium constant, Kp, is 2.4 x 103 at a certain temperature for the reaction
2 NO (g) ↔ N2 (g) + O2 (g)
For which of the following sets of conditions is the system at equilibrium? For those that are not at
equilibrium, in which direction will the system shift?
a.
P NO = 0.010 atm
P N2 = 0.11 atm
P O2 = 2.0 atm
b.
P NO = 0.0078 atm
P N2 = 0.36 atm
P O2 = 0.67 atm
c.
P NO = 0.0062 atm
P N2 = 0.51 atm
P O2 = 0.18 atm
CALCULATING EQUILIBRIUM PRESSURES AND CONCENTRATIONS
***** Dinitrogen 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) ↔ 2 NO2 (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 2.71 atm. Calculate
the equilibrium pressure of NO2 gas.
1.
We can calculate equilibrium pressures given information about both initial and equilibrium
conditions.
***** At a certain temperature a 1.000-L flask initially contained 0.298 mol PCl3 (g) and 8.70 x 10-3 mol
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 following reaction:
PCl5 (g) ↔ PCl3 (g) + Cl2 (g)
Calculate the equilibrium concentrations of all species and the value of K.
The expression for K is:
To determine K, we must determine the equilibrium concentrations. Start with the initial concentrations:
No Cl2 was initially present, but 2.00 x 10-3 M Cl2 is present at equilibrium. The mole ratio between all the
reactants and products from the balanced equation is 1:1.
Based on the stoichiometry, equilibrium is:
Apply this change to the initial concentrations:
Now find K:
2.
Sometimes we are not given any equilibrium concentrations or pressures, only the initial values.
3.
Use the stoichiometry of the reaction to express the equilibrium values in terms of the initial values.
***** 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 moles
of each component was added to a 1.5000-L flask. Calculate the equilibrium concentrations of all species.
The balanced equation is:
H2 (g) + F2 (g) ↔ 2 HF (g)
The expression for K is:
The initial concentrations of all species are:
Find Q:
__________ so the system must shift to the __________ to reach equilibrium.
Define the change needed to reach equilibrium in terms of _______. We now have:
Summarize the changes in a table as follows:
Now use the equilibrium expression to solve for x.
Check the answer:
4.
Systems where we can solve for the unknown by taking the square root of both sides are not common.
***** Suppose for a synthesis of hydrogen fluoride from hydrogen and fluorine, 3.000 mol H 2 and 6.000
mol F2 are mixed in a 3.000 L flask. The equilibrium constant for the synthesis at this temperature is 1.15 x
102. Determine the equilibrium concentration of each component.
The reaction is:
The equilibrium expression is:
The initial concentrations are:
There is no need to calculate Q because no HF is present initially, and we know that the system must shift
to the right to reach equilibrium.
Substitute into the equilibrium expression:
We cannot take the square root.
Use the quadratic formula to solve:
One of the answers is incorrect.
Check the solution.
5.
The same technique can be applied to calculating equilibrium pressures.
Treating Systems That Have Small Equilibrium constants
1.
Under certain conditions, simplifications are possible that greatly reduce some of the mathematical
difficulties.
2.
If K is very small the system won’t proceed very far before equilibrium is reached.
3.
_____ will be small; therefore when a number is either added to x or x is subtracted from a number,
you only need to include the number in the expression for K.
4.
Small vales of K and the resulting small shift to reach equilibrium allow simplification.
LE CHATELIER’S PRINCIPLE
1.
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.
The Effect of a Change in Concentration
1.
Look at the synthesis of ammonia:
At equilibrium:
What happens if 1.000 M N2 is injected into the system?
The concentrations of the species before the system adjusts are:
Calculate the value of Q
The system will shift to the _______________ to come to the new equilibrium position.
2.
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.
***** Arsenic can be extracted from its ores by first reacting the ore with oxygen to form solid As 4O6,
which is then reduced using carbon:
As4O6 (s) + 6 C (s) ↔ As4 (g) + 6 CO (g)
Predict the direction of the shift of the equilibrium position in response to each of the following changes in
conditions:
a.
Addition of carbon monoxide.
b.
Addition or removal of carbon or As4O6
c.
Removal of gaseous arsenic.
The Effect of a Change in Pressure
1.
There are three ways to change the pressure of a reaction system involving gaseous components:
a.
b.
c.
2.
We already know what happens when we add or remove a gaseous reactant or product.
3.
When an inert gas is added, there is no effect on the equilibrium position.
4.
The addition of an inert gas increases the total pressure but has no effect on the concentrations or
partial pressure of the reactants or products.
5.
When the volume of the container is changed, the concentrations (and thus the partial pressures) of
both reactants and products are changed.
6.
When the volume of a 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.
At constant T and P,
***** Predict the shift in equilibrium position that will occur for each of the following processes when the
volume is reduced.
a.
P4 (s) + 6 Cl2 (g) ↔ 4 PCl3 (l)
b.
PCl3 (g) + Cl2 (g) ↔ PCl5 (g)
c.
PCl3 (g) + 3 NH3 (g) ↔ P(NH2)3 (g) + 3 HCl (g)
The Effect of a Change in Temperature
1.
Although the previous changes alter the ___________________________________, they do not alter
the ___________________________________.
2.
The effect of temperature on equilibrium is different because the value of K changes with temperature.
3.
Treat energy as a reactant in an endothermic process and as a product in an exothermic process.
***** For each of the following reactions, predict how the value of K changes as the temperature is
increased.
a.
N2 (g) + O2 (g) ↔ 2 NO (g)
∆H0 = 181 kJ
b.
2 SO2 (g) + O2 (g) ↔ 2 SO3 (g)
∆H0 = -198 kJ