AP Chemistry
15 & 19.7  Equilibrium
NOTES
15.1 The Concept of Equilibrium
 Chemical equilibrium is a condition at which the rate of products being formed is equal to the rate
off reactants being formed.
o This is a type of dynamic equilibrium, which is any condition where processes or substances are
at equilibrium.
 Reactions at equilibrium are reversible. For example, let’s consider this equilibrium reaction, which
includes the double arrows indicating it is at equilibrium
N2O4(g) 2 NO2(g)
The rate of the reactions can be found from their equations
Forward Reaction:
N2O4(g) 2 NO2(g)
Ratef = kf[N2O4]
Reverse Reaction:
2 NO2(g) N2O4(g)
Rater = kr[NO2]2
Since they are at equilibrium, their rates must equal
kf[N2O4] = kr[NO2]2
And we can assume that
(Insert equation 15.5 from Pg. 613 in the space above)
This constant that is formed is called the equilibrium constant
*Figs 15.1 and 15.2 (Pg 612-613) shows how equilibrium is reached both pictorially and graphically.
 When substances are in an equilibrium state, it means that their amounts are no longer changing with
time.
o The reactions are still occurring (reaction going to product and product going to reactant), they
are just doing so at the same rate and so the amounts don’t change.
o It does not mean that the concentrations are equal.
 Equilibrium must occur in a closed system where neither products nor reactants can escape
15.2 The Equilibrium Constant
 Reactions that are in opposition will naturally create an equilibrium
o The Haber process is the combination of hydrogen and nitrogen at equilibrium with ammonia,
given a catalyst and specific temperature and pressure. It is the most used equilibrium example.
N2(g) + 3 H2(g) 2 NH3(g)
*Fig 15.3 (Pg 614) shows how equilibrium is reached graphically. It doesn’t matter which side you start
with, it will reach equilibrium.
 The Law of Mass Action, or Equilibrium Law, gives the relationship between the concentrations of
the reactants and the products that are there at equilibrium
o Basically, if you multiply all of the concentrations of the products and then divide that by all of
the concentrations of the reactants multiplied by each other, then you will get the equilibrium
constant.

If given the below reaction
aA + bB dD + eE
where the capital letters represent the substances and the lower case letters represent coefficients,
then according to the Law of Mass Action, the equilibrium constant could be calculated by
(Insert equation 15.8 from Pg. 614 in the space above)
This relationship between the products and reactants is called the equilibrium expression for the
reaction. The equilibrium constant, Kc, is the number we can get if we put the real concentrations
and coefficients into the equilibrium expression
o Note that solids and liquids are not included in the equilibrium expression because their
concentration changes so little that it is simply 1.
o If we were to create an equilibrium expression for the Haber process, it would look like this
(Insert equation 15.9 from Pg. 632 in the space above)
*Sample Exercise 15.1 (Pg 616) shows some examples of creating equilibrium expressions from
balanced reactions.
 Equilibrium expressions are functions of stoichiometry and not reaction mechanisms, like we used in
kinetics.
*Table 15.1 (Pg 616) shows how the equilibrium constant stays the same as the concentrations vary,
showing that the equilibrium constant is a function of a ratio.
 Kc means that we will use the concentrations, or molarities, of the substances to find the equilibrium
constant. However, it is possible to use other functions of a reaction.
o Note that equilibrium constants do not have any units
 The partial pressures of gases only can be used to determine the equilibrium constant and is denoted
by Kp. Given the same previous reaction
aA + bB dD + eE
we can use the partial pressures, in atmospheres, instead of the concentrations and get the
equilibrium expression for Kp
(Insert equation 15.11 from Pg. 617 in the space above)

where parentheses are used instead of brackets.
The ideal gas equation can be manipulated to show a relationship between Kc and Kp for a reaction.
(Insert equation 15.14 from Pg. 617 in the space above)
where ∆n = (moles of gaseous product) – (moles of gaseous reactant) and R uses the same units of
pressure as in the partial pressures of the gases.
*Sample Exercise 15.2 shows an example of how to use this equation.
 Equilibrium constants have no units because they are ratios and thusly the units cancel out.
15.3 Interpreting and Working with Equilibrium Constants
 The size of the equilibrium constant can help you to determine the direction of the reaction.
o If K> 1 then the products are favored and the reaction shifts to the right
o If K < 1, then the reactants are favored and the reaction shifts to the left
*Sample Exercise 15.3 shows how to determine the relative values of K based on the amount of product
you have. You will have to be able to order K values using this method.
 An equilibrium reaction is reversible and can go either way
o
The K value for the reverse reaction is the inverse (1/K) of the K value of the forward
reaction
*Sample Exercise 15.4 shows how to solve for the K of the reverse reaction using the reciprocal of the
forward reaction.
 If a reaction has been multiplied by a number, then the equilibrium constant will be raised to that
power. For example if a reaction
2 H2(g) + O2(g) 2 H2O(g)
Kc = [H2O]2 = 5
[H2]2[O2]
is multiplied by 3 then the K will be cubed
6 H2(g) + 3 O2(g) 6 H2O(g)
Kc = [H2O]6 = 53
[H2]6[O2]3
 If a reaction is made of up 2 or more steps, like with Hess’s Law of for a reaction mechanism, then
the K of the net reaction is equal to the product of the K’s of the individual reactions. For example
Step 1:
2 NOBr(g) 2 NO(g) + Br2(g)
Kc1 = 0.014
Step 2:
Net Rxn:
Br2(g) + Cl2(g)
2 NOBr(g) + Cl2(g)
2 BrCl(g)
Kc2 = 7.2
2 NO(g) + 2 BrCl(g)
Kc = Kc1 x Kc2 = 0.014 x 7.2 = 0.010
*Sample Exercise 15.5 shows how to combine reactions to get the K of the net reaction.
15.4 Heterogeneous Equilibria
 Homogeneous equilibria involve substances that are in the same phase. For example, they are all
gases.
 Heterogeneous equilibria involve substances that are in different phases. For example, some pure
liquid mixed in with a gas
o Remember that pure solids (s) and pure liquids (l) are not in the equilibrium expression. They
have a constant concentration and equilibrium expression only deal with substances that have a
change in concentration. Also, the concentration is a ratio and if you are dealing with a pure
liquid or solid, its concentration is itself and so the ratio would simply equal 1.
15.5 Calculating Equilibrium Constants
 If we know the concentrations of all substances at equilibrium, then we can solve for the equilibrium
constant by simply plugging in the equilibrium concentrations into the equilibrium expression.
 If we do not know the all of the concentrations of the substances at equilibrium, we must follow a
more involved procedure.
1. Put all of the known information into a table. We call it an ICE Box for short as an acronym for
the 3 different levels.
Reaction
Initial
Change
Equilibrium
A
+
B
D
+
E
2. For the substance where you know both the initial and the equilibrium, calculate the change in
concentration. If you are given the initial values for the reactants, then the initial value of the
products will be 0 and vice versa.
3. Use the balanced equation to calculate the changes in the other substances. They will have the
same molar ratio as the stoichiometry in the equation. Also, the change for reactants will be
negative since they are disappearing and the change in products will be positive since they are
being made.
4. Use the changes in each to calculate the concentrations at equilibrium. These will be the
equilibrium values for all of the substances in the reaction and can be used to solve for the
equilibrium constant.
*Sample Exercises 15.9 shows how to solve for the equilibrium constant given the initial concentrations
of substances and the equilibrium concentration of the opposite substances.
15.6 Applications of Equilibrium Constants
 We already know that we can use the value of K to determine the direction of a reaction; however
that is for the reaction in general. We can determine the direction of a reaction at any point by using
the instantaneous concentrations.
 The reaction quotient, Q, is a number found by substituting the concentrations or pressures of
reactants and products into the equilibrium expression at any time during the reaction.
 Q is found the same way K can be found. For example given the reaction
aA + bB dD + eE
(Insert equation 15.23 from Pg. 627 in the space above)

Q can be compared to K to determine the instantaneous direction of the reaction.
o If K > Q, the reaction will go to the right
o If K < Q, the reaction will go to the left
o If K = Q, the reaction is at equilibrium
*Fig 15.8 shows the relationship between K and Q graphically.
*Sample Exercise 15.10 shows how to solve for Q and then compare it to K to determine the
instantaneous direction of the reaction
 You can calculate the concentration of a substance given the concentrations of the other substances,
or at least their molar ratio from the balanced equation, and the Kc
o This involves a great deal of math and the quadratic equation may have to be used.
 You can also use this method to solve for the equilibrium amounts of any substances given the initial
concentrations and the equilibrium constant. This will require a combination of an ICEBox, using
the molar ratios to find the change, and the equilibrium constant to solve for x.
*Sample Exercise 15.12 shows how to find the equilibrium concentrations from the initial
concentrations and the equilibrium constant.
15.7 LeChâtlier’s Principle
 LeChâtlier’s Principle states: If a system at equilibrium is disturbed by a change in temperature,
pressure, or the concentration of one of the substances, the system will shift to reestablish
equilibrium.
 There are 3 main changes that occur to disturb equilibrium
o Adding or removing reactant or product
o Changing pressure by changing volume
o Changing the temperature
 Equilibrium will shift toward decreases and away from increases
o If we add a substance, some of it will be used so that we can reestablish equilibrium
o If we remove a substance, some of it will be produced to reestablish equilibrium
o For example given the Haber process
N2(g) + 3 H2(g) 2 NH3(g)
Removing NH3 would cause a shift toward NH3 so that more is produced to reestablish
equilibrium. Adding NH3 would cause more H2 and N2 to be made from the decomposition of
all of the NH3 and thusly shift away from the NH3 to reestablish equilibrium. Also, if N2 or H2 is
removed, the other increases and since one was removed, NH3 will also decrease. If N2 or H2 is
added, the other decreases and ultimately the NH3 will increase.
*Fig 15.10 (Pg 632) shows the shifting relationship graphically when H2 is added to the Haber process
system
Concentration Change
Observed Effect
Increase reactant
Favors/shifts toward
Decrease reactant
Favors/shifts toward
Increase product
Favors/shifts toward
Decrease product
Favors/shifts toward
(insert products or reactants above)

When dealing with gases, if the volume decreases or pressure increases, the equilibrium will shift
toward the side with fewer moles of gas. If the volume increases or pressure decreases, the
equilibrium will shift toward the side with more moles.
o Remember Boyle’s Law – volume and pressure are inversely proportionate.
o Pressure can also be increased by keeping the volume constant and adding more of a substance to
the system.
Δngas (nproducts – nreactants)
Increasing Pressure
Decreasing Pressure
Positive
Zero
Negative
Favors/shifts toward
Favors/shifts toward
No Effect
Favors/shifts toward
No Effect
Favors/shifts toward
(insert products or reactants above)
*Sample Exercise 15.13 shows how to use LeChâtlier’s Principle to predict equilibrium shifting
 The effect on a system of a temperature change depends on whether the reaction is endothermic or
exothermic
o In an endothermic reaction, heat is like a reactant. In an exothermic reaction, heat is like a
product.
o If the temperature is increased, the system acts like we added reactant if it is endothermic but
acts like we added product if it is exothermic.
o If the temperature is decreased, the system acts like we removed reactant if it is endothermic but
acts like we removed product if it is exothermic.
 Temperature is the only experimental variable that affects the value of the equilibrium constant
*Sample Exercise 15.14 shows how you can predict how temperature can affect the equilibrium
constant, K
Temperature Change
Reaction Type
Effect on Reaction
Effect on K
Increase
Exothermic
Favors/shifts toward
Decrease
Increase
Endothermic
Favors/shifts toward
Increase
Decrease
Exothermic
Favors/shifts toward
Increase
Decrease
Endothermic
Favors/shifts toward
Decrease

Please note that LeChâtlier’s principle is a tool used to evaluate what happens to reestablish
equilibrium but does not explain why it happens. Chemical equilibrium concepts in general explain
why shifting happens.
*Sample Integrative Exercise (Pg 638) models a potential AP Exam FRQ in which several
concepts of one topic, in this case equilibrium, are used to come to one ultimate answer.
 A catalyst changes the rate at which a reaction reaches equilibrium but does not change the
equilibrium mixture.
19.7 Free Energy and the Equilibrium Constant
 We can find ΔG, which is the free energy at nonstandard conditions by using the ΔG°, which is at
the standard conditions of 298 K and 1 atm by using the following equation
ΔG = ΔG° + RT ln Q
o R is the ideal gas constant of 8.314 J/mol·K
o T is the absolute temperature
o Q is the reaction quotient and refers to the instantaneous equilibrium expression of a specific
reaction
o Under standard conditions, Q = 1 and so ΔG = ΔG°, which makes sense
*Sample Exercise 19.11 shows how you can calculate ΔG using Q
 At equilibrium, we can solve for ΔG° using
ΔG° = -RT ln K;
where K is the equilibrium constant. We can manipulate this equation to solve for K by
K = e -ΔG° / RT
*Sample Exercise 19.12 shows how you can calculate K from the ΔG°
*Table 19.4 (Pg 813) shows the relationship between ΔG° and K
*Appendix D (Pg 1062) lists some equilibrium constants, K, for several substances
*Sample Integrative Exercise (Pg 815) models a potential AP Exam FRQ in which several
concepts of different topics are tied together using one basic equation.