EQUILIBRIUM (Kc) PROBLEMS!
1. Write the general equilibrium constant expressions, Kc, for each of the following reactions:
a. N2H4 (g) <------------> N2 (g) + 2H2(g)
b. 2NOCl(g) <------------> 2NO(g) + Cl2(g)
c. 2NO(g) + 2H2(g) <------------> N2(g) + 2H2O(g)
d. 4HCl(g) + O2(g) <------------> 2Cl2(g) + 2H2O(g)
2. Write the general expression Kc for the following processes:
a. The combustion of methane gas
b. The decomposition of solid potassium chlorate
c. The reaction between solid sodium carbonate and hydrochloric acid
3. Write the general equilibrium constant expression, Kc, for carbon monoxide reacting with
hydrogen gas to form methane and water vapor. This process is used for producing natural gas.
4. Write the general equilibrium constant expression for the formation of nitrosyl chloride gas, or
NOCl, from nitrogen monoxide and chlorine.
5. An 8.00 L reaction container at 4910C contained .650 mol H2, .275 mol I2, and 3.00 mol HI.
Assuming that the substances are at equilibrium when these amounts were measured, find the
value of Kcat 4910C for the reaction of hydrogen and iodine vapor to give hydrogen iodide gas.
6. Carbon monoxide and hydrogen react in the following equation:
CO(g) + 3H2(g) <------------> CH4(g) + H2O(g)
When 1.00 mol CO and 3.00 mol H2 are placed into a 10.0 L vessel at 9270C and allowed to
come to equilibrium, the mixture is found to contain .387 mol H2O. What is the concentration
of each substance at equilibrium? What is the Kc for this reaction at 9270C?
7. The same reaction above was performed at a different time, and at equilibrium there was .30
mol CO, .10 mol H2, .020 mol H2O, and an unknown amount of CH4 in a 1 liter vessel. What
is the concentration of the CH4, if the reaction was performed at 9270C?
8. The following equilibrium concentrations were observed for the Haber process at 1270C:
[NH3] = 3.55 x 10-4 mol/L
[N2] = 8.50 x 10-1 mol/L
[H2] = 3.10 x 10-3 mol/L
a. Calculate the value of Kc at 1270C for this reaction, which is nitrogen and hydrogen
reacting to form ammonia.
b. Calculate the value of the equilibrium constant for the reverse of this reaction.
9. For the synthesis of ammonia from the elements at 5000C, the equilibrium constant is
6.0 x 10-2. Predict the direction in which the system will shift to equilibrium in each of the
following cases, by calculating the reaction quotient, or Q:
a. [NH3] = 1.00 x 10-3 M, [N2] = 1.00 x 10-5M, [H2] = 2.00 x 10-3M
b. [NH3] = 2.00 x 10-4 M, [N2] = 1.50 x 10-5M, [H2] = 3.54 x 10-1M
c. [NH3] = 1.00 x 10-4 M, [N2] = 5.00 M, [H2] = 1.00 x 10-2M
10. A mixture of .00500 moles of hydrogen gas and .0100 moles of iodine vapor are placed into a
5.00 liter container at 4480C and allowed to come to equilibrium. Analysis at equilibrium
shows that the concentration of hydroiodic acid vapor is 1.87 x 10-3M. Calculate Kc at 4480C
for this reaction.
11. Hydrogen gas reacts violently with chlorine gas to produce hydrogen chloride vapor, used to
create hydrochloric acid. Suppose 1.55 moles of hydrogen gas and 1.55 moles of chlorine gas
are placed into a 2.50 liter vessel. What are the concentrations of each substance in the gaseous
mixture when it comes to equilibrum at 4580C? The equilibrium constant at this temperature is
49.7.
12. The reaction of elemental hydrogen and fluorine to form hydrofluoric acid has an equilibrium
constant of 1.15 x 102 at a certain temperature. In one experiment, 3.00 mol of all 3
components, including the product, was added to a 1.50-liter flask. Calculate the equilibrium
concentrations of all species.
13. Using the above reaction and Kc, assume a new experiment: 3.0 mol of hydrogen and 6.0 mol
of fluorine are added into a 3.0-liter flask. What are the equilibrium concentrations of each
component?
14. A 3.00 liter flask is filled with 2.00 moles of hydrogen gas, and 3.00 moles of iodine gas at
4480C. If the Kc for this reaction is 50.5 at 4480C, what are the concentrations of all chemicals
in the flask at equilibrium, if HI gas is produced?
15. NOCl gas decomposes into nitrogen monoxide gas and chlorine gas. At 350C, the equilibrium
constant is 1.6 x 10-5. In an experiment in which 1.0 mol of NOCl is placed into a 2.0 L flask,
what are the equilibrium concentrations?
16. Carbon dioxide can degrade into carbon monoxide and oxygen. It has a Kc of 2.0 x 10-6 at
350C. If 2.0 mol of carbon dioxide are placed into a 5.0 L vessel, calculate the equilibrium
concentrations of all species.
17. The Kc for the decomposition of phosphorous pentachloride gas into phosphorous trichloride
gas and chlorine gas is 1.80 at 2500C. If .200 moles of phosphorous pentachloride is added to a
5.00 L container, what are the concentrations of each chemical at equilibrium at this
temperature?
18. For the reaction:
2 IBr(g) <---------> I2(g) + Br2(g)
Kc = 8.5 x 10-3 at 1500C. If .025 moles of IBr are placed into a 2.0 L container, what is the
concentration of IBr after equilibrium is reached?
19. When sulfur dioxide reacts with oxygen to form sulfur trioxide at 250C, the Kc is equal to
8.0 x 1035. From the size of Kc at this temperature, do you think that this reaction occurs to any
great extent at room temperature? If an equilibrium mixture contains 1.0M sulfur trioxide, and
contains oxygen and sulfur dioxide, what is the concentration of the sulfur dioxide in the
mixture? Does this result agree with what you would expect from the size of the Kc?
KP PROBLEMS!
20. The Kp at 450.00C for nitrogen gas reacting with hydrogen gas to form ammonia gas is
4.51 x 10-5. For each of the following mixtures, indicate whether the reaction is at equilibrium
at 450.00C. If the reaction is not at equilibrium, indicate which direction the reaction will shift:
a. 105 atm ammonia, 35.0 atm nitrogen, 495 atm hydrogen
b. 35.0 atm ammonia, 595 atm nitrogen, .100 atm hydrogen
c. 26.0 atm ammonia, 42.0 atm nitrogen, 202 atm hydrogen
d. 105 atm ammonia, 55.0 atm nitrogen, 5.00 atm hydrogen
21. The Kc at 300.00C for nitrogen gas reacting with hydrogen gas to form ammonia gas is 9.60.
Calculate the Kp for this reaction at this temperature.
22. HARD - .831 grams of SO3 gas is placed into a 1.00 liter container and heated to 1100.0 K.
The SO3 decomposes into sulfur dioxide gas and oxygen gas. At equilibrium the total pressure
in the container is 1.21 atm. Calculate the values of Kc and Kp for this reaction at 1100.0 K.
23. The reaction of nitrogen gas with oxygen gas in the air to form nitrogen monoxide, which is
useful for fertilizing plants, is known as “fixing” nitrogen. The Kc for this reaction at 250C is
1 x 10-30. Does this process occur easily in nature for plants in the air? If the initial pressure of
nitrogen and oxygen in the air is .8 and .1 atm, respectively, then what is the equilibrium
pressure of nitrogen monoxide in the air for plants to use?
24. Hydrogen gas and iodine vapor react to form hydrogen iodide gas. The equilibrium constant,
or Kc, is 1.00 x 102 at 250C. Suppose hydrogen at 5.0 x 10-1 atm, iodine at 1.0 x 10-1 atm, and
hydrogen iodide at 5.0 x 10-1atm are added to a 5.0 L flask. Calculate the equilibrium pressures
of all species.
25. 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. Consider
an experiment in which gaseous dinitrogen tetroxide was placed into a flask and allowed to
reach equilibrium at a temperature where Kp = .133. At equilibrium, the pressure of dinitrogen
tetroxide was found to be 2.71 atm. Calculate the equilibrium pressure of nitrogen dioxide.
26. At 1100 K, Kp = .524 for the reaction of sulfur dioxide and oxygen to form sulfur trioxide.
Calculate the equilibrium partial pressures of each gas produced from an initial mixture in
which partial pressure of sulfur dioxide and oxygen are .50 atm and the partial pressure of
sulfur trioxide is zero.
27. Sulfur dioxide gas will react with oxygen gas to produce sulfur trioxide gas. The Kp for this
reaction at 900 K is .345. At equilibrium, the partial pressure of the sulfur dioxide is .165 atm,
and the partial pressure of the oxygen is .755 atm. What is the equilibrium partial pressure of
the sulfur trioxide?
28. Consider the following reaction:
NH4HS(s) <---------> NH3 (g) + H2S (g)
0
At 22.0 C the Kp for this reaction is .0700. If NH4HS(s) is placed into a container and allowed
to decompose at 22.00C, what are the equilibrium partial pressures of the two products?
29. Calculate the Kp for the reaction of nitrogen monoxide gas and chlorine gas to produce NOCl at
25.00C, if the following pressures were measured at equilibrium:
PNOCl = 1.20 atm PNO = 5.00 x 10-2 atm Pchlorine = 3.00 x 10-1 atm
30. Using the above Kp, calculate the value of Kc at 250C for the same reaction listed above.
31. HARD - Calculate the Kp at 1100K for the reaction of sulfur dioxide and oxygen to make
sulfur trioxide, if the total pressure of the container at equilibrium is 1.35 atm. The initial
concentrations of SO2 and O2 gases are 1.00 and .500 atm, respectively. Then, calculate the Kc
for the reaction.
LE’ CHATELIER’S PRINCIPLE
32. Arsenic can be extracted from its ores by first reacting the ore with oxygen to form solid As4O6,
which is then reacted with carbon to form As4 gas and carbon monoxide. Predict the shift of
the equilibrium position in response to each of the following changes in conditions for the
second reaction of: As4O6 (g) + 6 C (s) <----------------> As4 (g) + 6 CO(g)
a. Addition of carbon monoxide
b. Addition of carbon
c. Removal of carbon
d. Addition of As4O6
e. Removal of gaseous arsenic (As4)
33. Predict the shift in equilibrium position that will occur for each of the following processes
when the volume is reduced.
a. The preparation of liquid phosphorous trichloride from gaseous chlorine and solid P4.
b. The preparation of phosphorous pentachloride gas from gaseous chlorine and liquid
phosphorous trichloride.
c. The reaction of phosphorous trichloride gas and gaseous ammonia to form hydrogen
chloride gas and gaseous P (NH2) 3.
34. For each of the following reactions, predict how the value of K changes as the temperature is
increased:
a. Nitrogen and oxygen gas form gaseous nitrogen monoxide - H = +181 kJ
b. Sulfur dioxide and oxygen form sulfur trioxide - H = -198 kJ
35. Consider the reversible reaction:
FeO (s) + CO (g) <------------> Fe (s) + CO2 (g
When carbon dioxide is removed from the equilibrium mixture (say by passing the gases
through water to absorb the CO2), what is the direction of the net reaction as the new
equilibrium is achieved?
36. What would you expect to be the effect of an increase of pressure on each of the following
reactions? Will the pressure change shift the reaction to the right or left?
a. CH4 (g) + 2S2 (g) <------------> CS2 (g) + 2H2S (g)
b. 4HCl(g) + O2(g) <------------> 2Cl2(g) + 2H2O(g)
c. CO2 (g) + C (s) <------------> 2CO (g)
37. List the four variables or factors that can affect the equilibrium of a reaction.
38. At temperatures near 800.00C, steam passed over hot coke (a form of carbon obtained from
coal)
reacts to form carbon monoxide gas and hydrogen gas. This is an important industrial reaction
to manufacture hydrogen.
a. If the Kc at this temperature is .160, what are the equilibrium concentrations of water,
carbon monoxide, and hydrogen if we start with just solid carbon and .100 moles of steam
in a 1.00 liter container?
b. What is the minimum amount of carbon needed in the container to achieve equilibrium
at these conditions?
c. What is the total pressure in the container at equilibrium?
d. At 25.00C, the Kc for this reaction is 7 x 10-23. Is this reaction endothermic or
exothermic? Why do you think this?
e. To produce the maximum amount of carbon monoxide and hydrogen at equilibrium,
should the pressure of the system be increased or decreased?