* AP Chemistry by Satellite Lectureguide
* Student Edition

Chemical Equilibrium

Chapter 14

Objectives

Following your study of this chapter, you should be able to

- describe the macroscopic properties which characterize equilibrium reactions.
- describe the microscopic properties of equilibrium reactions.
- define the term
*chemical equilibrium*. - write the equilibrium expression given a chemical equation which describes an equilibrium reaction.
- calculate the magnitude of the equilibrium constant for a chemical reaction.
- calculate the concentration of each component in an equilibrium reaction given the initial concentration of each component and the equilibrium constant.
- state Le Chatelier's principle and identify the factors which will affect a reaction at equilibrium.
- predict the direction a reaction must proceed to establish, or re-establish, equilibrium, under a given set of conditions.
- write and use the mathematical equation which relates the equilibrium constant for a chemical reaction to temperature.
- describe the difference between an equilibrium constant and a rate constant for a chemical reaction.

Initially (before any reaction occurs) a 1.00 liter reaction vessel at 25 ºC contains
0.300 moles of NO_{2} and no nitrogen monoxide or dioxygen. Consider the
following:

a) If 0.100 moles of NO_{2} react, how many moles of NO and O_{2 }are formed? How
many moles of NO_{2}, NO, and O_{2} remain after completion of the reaction?

b) If 0.0873 moles of NO_{2} react, how many moles of NO and O_{2 }are formed?
How many moles of NO_{2}, NO, and O_{2} remain after completion of the reaction?

c) If '**2x**' moles of NO_{2} react, how many moles of NO and O_{2 }are formed (in terms
of '**x**')? How many moles of NO_{2}, NO, and O_{2} remain after completion of the
reaction?

1. Complete the equation for each reaction demonstrated in lecture and describe your observations.

Observations:

Observations:

Observations:

Observations:

Discuss the differences between the completeness of reactions in a) and b) and in
reactions c) and d).

2. Complete each of the sections according to the computer experiments performed
in lecture.

2. (Continued)

For each of the guesses listed in Experiment #7 above, provide an explanation
why it may be a reasonable answer or not.

3. Define the term *chemical equilibrium*.

4. Write the equilibrium expression, given the following general equation.

Distinguish between the K_{p} and K_{c} for the reaction.

5a. Distinguish between the equilibrium constant and the equilibrium constant
expression for a chemical reaction.

b. The following reaction is at equilibrium at a particular temperature

and the [H_{2}]_{eq} = 0.012 M, [I_{2}]_{eq} = 0.15 M and [HI]_{eq} = 0.30 M. Calculate the
magnitude of K_{c} for the reaction.

** Ans: K**_{c}** = 50**

c. Using the equilibrium constant calculated in b, calculate the magnitude of the equilibrium constant for the following reactions at the same temperature.

** Ans: K**_{c}** = 0.02**

** Ans: K**_{c}** = 7.07**

c. The initial concentration of both H_{2} and I_{2} is 0.250 M. The reaction occurs as
shown below,

When equilibrium is achieved the concentration of HI is 0.393 M. Calculate the
magnitude of K_{c} for the reaction.

** Ans: K**_{c}** = 53**

d. A vessel initially has a partial pressure of NO equal to 0.526 atm and a partial
pressure of Br_{2} equal to 0.329 atm. At equilibrium the partial pressure of Br_{2} is
0.203 atm. Calculate K_{p} for the reaction

** Ans: K**_{p}** = 4.17**

Problem Set #24

*AP Chemistry by Satellite*^{ Name___________________________________}

ALL work must be shown in all problems for full credit.

PS24.1. Given the reaction

Initially (before any reaction occurs) a 1.00 liter reaction vessel at 400 ºC
contains 0.502 moles of O_{2} and 0.791 moles of NH_{3 }and no water or nitrogen.
Consider the following:

a) If 0.0873 moles of O_{2} react, how many moles of NH_{3} must react and how
many moles of H_{2}O and N_{2 }are formed? How many moles of O_{2}, NH_{3}, H_{2}O
and N_{2} remain after completion of the reaction?

b) If 0.234 moles of NH_{3} react, how many moles of O_{2 }must react and how many
moles of H_{2}O and N_{2 }are formed? How many moles of O_{2}, NH_{3}, H_{2}O and N_{2
} remain after completion of the reaction?

c) If '**3x**' moles of O_{2} react, how many moles of NH_{3} must react and how many
moles of H_{2}O and N_{2 }are formed(in terms of '**x**')? How many moles of O_{2},
NH_{3}, H_{2}O and N_{2} remain after completion of the reaction?

d) If 0.875 moles of H_{2}O are formed, how many moles of N_{2 }are formed and how
many moles of O_{2} and NH_{3 }must react? How many moles of O_{2}, NH_{3}, H_{2}O
and N_{2} remain after completion of the reaction?

PS24.2. Write the equilibrium expression for each of the following chemical equations;

PS24.3. Equilibrium constants for the following reactions have been determined at 550 ºC:

Calculate K (at the same temperature) for the commercially important water gas shift reaction

PS24.4. Calculate K_{c} for the reaction

if K_{c }for the reaction

is 1.3 x 10^{4}.

PS24.5. A 1.00 liter container initially holds 0.257 moles of NOBr at a given temperature. The reaction which occurs is:

At equilibrium analysis shows 0.240 moles of NO and 0.120 moles of Br_{2}.

a) Which direction did the reaction proceed to establish (reach) equilibrium?

b) How many moles of NOBr reacted in order to form 0.240 moles of NO and
0.120 moles of Br_{2}?

c) How many moles of NOBr remain after equilibrium was established?

d) What is the magnitude of K_{c}?

PS24.6. In a container, the partial pressure of NOCl is initially 0.340 atm at a given
temperature. The reaction which occurs is:

At equilibrium analysis shows the partial pressure of NO is 0.0916 atm.

a) Which direction did the reaction proceed to establish (reach) equilibrium?

b) What is the partial pressure of NOCl which reacted in order for the partial
pressure of NO to be 0.0916 atm?

c) What is the partial pressure of Cl_{2} at equilibrium?

d) What is the partial pressure of NOCl at equilibrium?

e) What is the magnitude of K_{p}?

PS24.7. A 1.00 liter container holds 1.06 moles of H_{2} and 1.57 moles of CO at a
temperature of 162 ºC. At this temperature, the following reaction occurs,

After equilibrium is established, analysis shows 0.200 moles of CH_{3}OH in the
container. Calculate the [CO]_{eq}, [H_{2}]_{eq} and K_{c}.

PS24.8. The following reaction,

occurs at 298K. If 2.00 mol of HI are placed into a 1.00 liter container and
permitted to react, at equilibrium it is found that 20.0 % of the HI has
decomposed. Calculate K_{c} and K_{p}.

PS24.9 The equation which describes the preparation of ammonia is:

A 3.000 L reaction vessel initially contains 0.3000 moles N_{2} and 0.4500 moles
H_{2}. When the reaction is allowed to attain equilibrium at a given temperature,
analysis determines 0.09992 M N_{2}. Calculate K_{c} for the reaction.

6a. Setup the ICE table for the following general chemical equation. (Assume the reaction proceeds from left to right to establish equilibrium.)

b. The equilibrium constant, K_{p}, for the reaction

is 0.0202. If the initial partial pressure of H_{2} = I_{2} = 0.350 atm, calculate the
equilibrium partial pressures of all species.

** Ans: [H**_{2}**]**_{eq}** = [I**_{2}**]**_{eq}** = 0.327 atm, [HI]**_{eq}** = 4.64 x 10**^{-2}** atm**

c. The equilibrium constant, K_{c}, for the reaction

is 33.3 at 760 ºC. If 0.400 mol of PCl_{5} are placed in a 2.00 liter container, calculate
the equilibrium concentrations of all species.

** Ans: [PCl**_{3}**]**_{eq}** = [Cl**_{2}**]**_{eq}** = 0.195 M, [PCl**_{5}**]**_{eq}** = 0.005 M**

d. The equilibrium constant, K_{c}, for the reaction

is 33.3 at 760 ºC. If 0.400 mol of PCl_{5} and 1.0 mol of Cl_{2 }are placed in a 2.00 liter
container, calculate the equilibrium concentrations of all species.

** Ans: [PCl**_{3}**]**_{eq}** = 0.196 M, [Cl**_{2}**]**_{eq}** = 0.70 M, [PCl**_{5}**]**_{eq}** = 0.004 M**

7a. State Le Chatelier's principle.

b. Identify three factors which can affect a reaction at equilibrium. Using examples
discussed in lecture, briefly describe how each factor can affect a reaction at
equilibrium.

b. (Continued)

c. The reaction

has a DH = -1036 kJ. Given the reaction is at equilibrium, predict the direction the reaction will shift when disrupted by each of the following

i) the amount of H_{2}O is increased

ii) the temperature of the reaction is increased

iii) the volume of the container is decreased

iv) the amount of H_{2}S is decreased

8. Define the non-equilibrium reaction quotient, Q, and explain how it can be used to predict the direction a reaction will proceed to establish equilibrium.

c. The reaction

has been carefully studied at 350 ºC and the K_{c} is 0.079. Which direction will the
reaction proceed to establish equilibrium under each of the following initial
conditions?

i) [NOBr]_{o }= 0.100 M : [NO]_{o} = 0 : [Br_{2}]_{o} = 0

ii) [NOBr]_{o }= 0 : [NO]_{o} = 0.100 M : [Br_{2}]_{o} = 0.100 M

iii) [NOBr]_{o }= 0.100 M : [NO]_{o} = 0 : [Br_{2}]_{o} = 0.100 M

iv) [NOBr]_{o }= 0.100 M : [NO]_{o} = 0.100 M : [Br_{2}]_{o} = 0.100 M

v) [NOBr]_{o }= 0.200 M : [NO]_{o} = 0.0500 M : [Br_{2}]_{o} = 0.100 M

9a. Write the general mathematical equation which relates the equilibrium constant for a chemical reaction to temperature.

b. Define each of the variables in this equation.

c. In the reaction

DH = -57.2 kJ at 25 ºC. The equilibrium constant, K_{p}, at this temperature is 8.8.
Calculate K_{p} at 0 ºC.

** Ans: K**_{1}** = 72.9**

d. In the reaction

DH = 26.9 kJ at 25 ºC. The equilibrium constant, K_{c}, at this temperature is 4.9 x
10^{-6}. Calculate K_{c} at 100 ºC.

** Ans: K**_{1}** = 4.3 x 10**^{-5}

10a. Describe the difference between an equilibrium constant and a rate constant for a
chemical reaction.

b. How does adding a catalyst to a chemical reaction affect the magnitude of the
equilibrium constant for the reaction?

Problem Set #25

*AP Chemistry by Satellite*^{ Name___________________________________}

ALL work must be shown in all problems for full credit.

PS25.1. A 0.622 gram quantity of COBr_{2 }is sealed in a glass bulb of 0.100 L volume
and heated to a temperature of 73 ºC. At 73 ºC the COBr_{2 }partially decomposes
according to the equation

for which K_{c} = 0.190. Calculate the concentration of each species at 73 ºC.

PS25.2. The equilibrium constant, K_{p}, for the reaction

is 7.31. Calculate the partial pressure of all species at equilibrium for each of the following original mixtures:

a) 1.0 atm of CO and 1.0 atm of H_{2}O.

b) 1.0 atm of CO, 1.0 atm of H_{2}O and 1.00 atm of H_{2}.

c) 1.0 atm of H_{2} and 1.0 atm of CO_{2}.

PS25.3. At 1000 K the equilibrium constant, K_{c}, for the reaction

is 0.833. Calculate the concentrations of all species at equilibrium when 0.200
moles of NO_{2} are placed in a 2.00 L container at 1000 K.

PS25.4. At 25 ºC, 0.560 mol of O_{2} and 0.20 mol of N_{2}O were placed in a 1.00 liter
vessel and allowed to react according to the equation

When the system reached equilibrium, the concentration of NO_{2} was found to

be 0.020 M.

a) What were the equilibrium concentrations of N_{2}O and O_{2}?

PS25.4. (Continued)

b) What is the value of K_{c} for this reaction at 25 ºC?

PS25.5. The reaction

has been carefully studied at 350 ºC and the K_{c} is 0.079. Which direction (left-to-right or
right-to-left) will the reaction proceed to establish equilibrium under each of the
following initial conditions?

PS25.6. Consider the reaction

for which DH_{rxn} = -1036 kJ. Predict how the [SO_{2}] will change when the
equilibrium is disturbed by;

a) Addition of O_{2
} b) Addition of H_{2}O

c) Addition of a catalyst

d) Increase in temperature

e) Decrease in the volume of the reaction container

PS25.7. The equilibrium constant, K_{p}, for the reaction

is 6.25 at 25 ºC and DHº = 34.4 kJ. Calculate the magnitude of the equilibrium constant at 50 ºC.

PS25.8. Given the reaction

A 10.0 liter vessel at 298 K initially contains a sample of XeF_{4} at 0.750 atm.
After the reaction achieves equilibrium, the total pressure in the vessel is 1.95
atm. Calculate K_{p} from this data.

PS25.9. The equilibrium constant, K_{c}, for the reaction

is 2.50 x 10^{-6} at a particular temperature. If the [N_{2}]_{o }= 2.00 M_{,} the [O_{2}]_{o} = 1.00 M and
the [NO]_{o} = 0 M, calculate the equilibrium concentration of all species.

PS25.4. A 0.383 gram quantity of crystalline PCl_{5 }is sealed in a glass bulb of 0.100 L
volume and heated to a temperature of 250 ºC, at which temperature all of the
PCl_{5} has vaporized. At 250 ºC the PCl_{5} partially decomposes according to the
equation

If the [PCl_{3}]_{eq } = 1.4 x 10^{-2} M, calculate K_{c} at 250 ºC.