🎉 Announcing Numerade's $26M Series A, led by IDG Capital!Read how Numerade will revolutionize STEM Learning ## Chapter 15 ## Chemical Equilibrium ## Educators ES ### Problem 1 How does a developing fetus get oxygen in the womb? William M. Numerade Educator ### Problem 2 What is dynamic equilibrium? Why is it called dynamic? ES Eugene S. University of Minnesota - Twin Cities ### Problem 3 Give the general expression for the equilibrium constant of the following generic reaction: William M. Numerade Educator ### Problem 4 What is the significance of the equilibrium constant? What does a large equilibrium constant tell us about a reaction? A small one? ES Eugene S. University of Minnesota - Twin Cities ### Problem 5 What happens to the value of the equilibrium constant for a reaction if the reaction equation is reversed? Multiplied by a constant? William M. Numerade Educator ### Problem 6 If two reactions sum to an overall reaction, and the equilibrium constants for the two reactions are K1 and K2 what is the equilibrium constant for the overall reaction? ES Eugene S. University of Minnesota - Twin Cities ### Problem 7 Explain the difference between Kc and Kp. For a given reaction, how are the two constants related? William M. Numerade Educator ### Problem 8 What units should you use when expressing concentrations or partial pressures in the equilibrium constant? What are the units of Kp and Kc? Explain. ES Eugene S. University of Minnesota - Twin Cities ### Problem 9 Why do we omit the concentrations of solids and liquids from equilibrium expressions? William M. Numerade Educator ### Problem 10 Does the value of the equilibrium constant depend on the initial concentrations of the reactants and products? Do the equilibrium concentrations of the reactants and products depend on their initial concentrations? Explain. ES Eugene S. University of Minnesota - Twin Cities ### Problem 11 Explain how you might deduce the equilibrium constant for a reaction in which you know the initial concentrations of the reactants and products and the equilibrium concentration of only one reactant or product. William M. Numerade Educator ### Problem 12 What is the definition of the reaction quotient (Q) for a reaction? What does Q measure? ES Eugene S. University of Minnesota - Twin Cities ### Problem 13 What is the value of Q when each reactant and product is in its standard state? (See Section 9.10 for the definition of standard states.) William M. Numerade Educator ### Problem 14 In what direction does a reaction proceed for each condition: ES Eugene S. University of Minnesota - Twin Cities ### Problem 15 Many equilibrium calculations involve finding the equilibrium concentrations of reactants and products given their initial concentrations and the equilibrium constant. Outline the general procedure used in solving these kinds of problems. William M. Numerade Educator ### Problem 16 In equilibrium problems involving equilibrium constants that are small relative to the initial concentrations of reactants, we can often assume that the quantity x (which represents how far the reaction proceeds toward products) is small. When this assumption is made, we can ignore the quantity x when it is subtracted from a large number but not when it is multiplied by a large number. In other words, 2.5 - x 2.5, but 2.5x  2.5. Explain why we can ignore a small x in the first case but not in the second. ES Eugene S. University of Minnesota - Twin Cities ### Problem 17 What happens to a chemical system at equilibrium when equilibrium is disturbed? William M. Numerade Educator ### Problem 18 What is the effect of a change in concentration of a reactant or product on a chemical reaction initially at equilibrium? ES Eugene S. University of Minnesota - Twin Cities ### Problem 19 What is the effect of a change in volume on a chemical reaction (that includes gaseous reactants or products) initially at equilibrium? William M. Numerade Educator ### Problem 20 What is the effect of a temperature change on a chemical reaction initially at equilibrium? How does the effect differ for an exothermic reaction compared to an endothermic one? ES Eugene S. University of Minnesota - Twin Cities ### Problem 21 Write an expression for the equilibrium constant of each chemical equation: a. SbCl5(g) SbCl5(g) + Cl2(g) b. 2 BrNO(g) 2 NO(g) + Br2(g) c. CH4(g) + 2 H2S(g) CS2(g) + 4 H2(g) d. 2 CO(g) + O2(g) 2 CO2(g) William M. Numerade Educator ### Problem 22 Find and fix each mistake in the equilibrium constant expressions: a. 2 H2S(g) 2 H2(g) + S2(g) Kc = [H2][S2] [H2S] b. CO(g) + Cl2(g) COCl2(g) Kc = [CO][Cl2] [COCl2] ES Eugene S. University of Minnesota - Twin Cities ### Problem 23 When this reaction comes to equilibrium, will the concentrations of the reactants or products be greater? Does the answer to this question depend on the initial concentrations of the reactants William M. Numerade Educator ### Problem 24 Ethene (C2H4) can be halogenated by this reaction: where X2 can be Cl2 (green), Br2 (brown), or I2 (purple). Examine the three figures representing equilibrium concentrations in this reaction at the same temperature for the three different halogens. Rank the equilibrium constants for the three reactions from largest to smallest. ES Eugene S. University of Minnesota - Twin Cities ### Problem 25 H2 and I2 are combined in a flask and allowed to react according to the reaction: Examine the figures (sequential in time) and answer the questions: a. Which figure represents the point at which equilibrium is reached? b. How would the series of figures change in the presence of a catalyst? c. Would there be different amounts of reactants and products in the final figure (vi) in the presence of a catalyst? William M. Numerade Educator ### Problem 26 A chemist trying to synthesize a particular compound attempts two different synthesis reactions. The equilibrium constants for the two reactions are 23.3 and 2.2 * 104 at room temperature. However, upon carrying out both reactions for 15 minutes, the chemist finds that the reaction with the smaller equilibrium constant produces more of the desired product. Explain how this might be possible. ES Eugene S. University of Minnesota - Twin Cities ### Problem 27 This reaction has an equilibrium constant of Kp = 2.26 * 104 at 298 K: Calculate Kp for each reaction and predict whether reactants or products will be favored at equilibrium: a. CH3OH(g) CO(g) + 2 H2(g) b. 1 2 CO(g) + H2(g) 1 2 CH3OH(g) c. 2 CH3OH(g) 2 CO(g) + 4 H2(g) William M. Numerade Educator ### Problem 28 This reaction has an equilibrium constant of Kp = 2.2 * 106 at 298 K: Calculate Kp for each reaction and predict whether reactants or products will be favored at equilibrium: a. COF2(g) 1 2 CO2(g) + 1 2 CF4(g) b. 6 COF2(g) 3 CO2(g) + 3 CF4(g) c. 2 CO2(g) + 2 CF4(g) 4 COF2(g) ES Eugene S. University of Minnesota - Twin Cities ### Problem 29 Consider the reactions and their respective equilibrium constants: Use these reactions and their equilibrium constants to predict the equilibrium constant for the following reaction: William M. Numerade Educator ### Problem 30 Use the following reactions and their equilibrium constants to predict the equilibrium constant for this reaction: 2 A(s) 3 D(g) ES Eugene S. University of Minnesota - Twin Cities ### Problem 31 Calculate Kc for each reaction. a. I2(g) 2 I(g) Kp = 6.26 * 10-22 (at 298 K) b. CH4(g) + H2O(g) CO(g) + 3 H2(g) c. I2(g) + CI2(g) 2 IC1(g) Kp = 81.9 (at 298 K) William M. Numerade Educator ### Problem 32 Calculate Kp for each reaction. a. N2O4(g) 2 NO2(g) Kc = 5.9 10-3 (at 298 K) b. N2(g) + 3 H2(g) 2 NH3(g) Kc = 3.7 * 108 (at 298 K) c. N2(g) + O2(g) 2 NO(g) Kc = 4.10 * 10-31 (at 298 K) ES Eugene S. University of Minnesota - Twin Cities ### Problem 33 Write an equilibrium expression for each chemical equation involving one or more solid or liquid reactants or products. a. CO3 2-(aq) + H2O(I) HCO3 -(aq) + OH-(aq) b. 2 KCIO3(s) 2 KCI(s) + 3 O2(g) c. HF(aq) + H2O(I) H3O+(aq) + F-(aq) d. NH3(aq) + H2O(I) NH4 +(aq) + OH-(aq) William M. Numerade Educator ### Problem 34 Find and fix the mistake in the equilibrium expression: ES Eugene S. University of Minnesota - Twin Cities ### Problem 35 Consider the reaction: An equilibrium mixture of this reaction at a certain temperature has [CO] = 0.105 M, [H2] = 0.114 M, and [CH3OH] = 0.185 M. What is the value of the equilibrium constant (Kc) at this temperature? William M. Numerade Educator ### Problem 36 Consider the reaction: An equilibrium mixture of this reaction at a certain temperature has [NH3] = 0.278 M and [H2S] = 0.355 M. What is the value of the equilibrium constant (Kc) at this temperature? ES Eugene S. University of Minnesota - Twin Cities ### Problem 37 Consider the reaction: Complete the table. Assume that all concentrations are equilibrium concentrations in M. William M. Numerade Educator ### Problem 38 Consider the reaction: H2(g) + I2(g) 2 HI(g) Complete the table. Assume that all concentrations are equilibrium concentrations in M. ES Eugene S. University of Minnesota - Twin Cities ### Problem 39 Consider the reaction: $$2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g) \quad K_{\mathrm{p}}=28.4 \text { at } 298 \mathrm{~K}$$ In a reaction mixture at equilibrium, the partial pressure of NO is 108 torr and that of$\mathrm{Br}_{2}\$ is 126 torr. What is the partial pressure of NOBr in this mixture? William M.

### Problem 40

Consider the reaction:
In a reaction at equilibrium, the partial pressure of SO2 is
137 torr and that of Cl2 is 285 torr. What is the partial pressure
of SO2Cl2 in this mixture?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 41

For the reaction A(g) 2 B(g), a reaction vessel initially
contains only A at a pressure of PA = 1.32 atm. At equilibrium,
PA = 0.25 atm. Calculate the value of Kp. (Assume no changes in
volume or temperature.) William M.

### Problem 42

For the reaction 2 A(g)  B(g) + 2 C(g), a reaction vessel
initially contains only A at a pressure of PA = 225 mmHg. At
equilibrium, PA = 55 mmHg. Calculate the value of Kp. (Assume
no changes in volume or temperature.)

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 43

Consider the reaction:
A solution is made containing an initial [Fe3+] of 1.0 * 10-3 M
and an initial [SCN-] of 8.0 * 10-4 M. At equilibrium,
[FeSCN2+] = 1.7 * 10-4 M. Calculate the value of the
equilibrium constant (Kc). William M.

### Problem 44

Consider the reaction:
A reaction mixture is made containing an initial [SO2Cl2] of
0.020 M. At equilibrium, [Cl2] = 1.2 * 10-2 M. Calculate the
value of the equilibrium constant (Kc).

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 45

Consider the reaction:
A reaction mixture in a 3.67 L flask at a certain temperature initially
contains 0.763 g H2 and 96.9 g I2, At equilibrium, the flask
contains 90.4 g HI. Calculate the equilibrium constant (Kc) for
the reaction at this temperature. ### Problem 46

Consider the reaction:
A reaction mixture in a 5.19 L flask at a certain temperature
contains 26.9 g CO and 2.34 g H2. At equilibrium, the flask
contains 8.65 g CH3OH. Calculate the equilibrium constant (Kc)
for the reaction at this temperature.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 47

Consider the reaction:
At a certain temperature, Kc = 8.5 * 10-3. A reaction mixture at
this temperature containing solid NH4HS has [NH3] = 0.166 M
and [H2S] = 0.166 M. Will more of the solid form, or will some
of the existing solid decompose as equilibrium is reached? William M.

### Problem 48

Consider the reaction:
A reaction mixture contains 0.112 atm of H2, 0.055 atm of S2,
and 0.445 atm of H2S. Is the reaction mixture at equilibrium? If
not, in what direction will the reaction proceed?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 49

Silver sulfate dissolves in water according to the reaction:
A 1.5-L solution contains 6.55 g of dissolved silver sulfate. If additional
solid silver sulfate is added to the solution, will it dissolve? William M.

### Problem 50

Nitrogen dioxide reacts with itself according to the reaction:
A 2.25-L container contains 0.055 mol of NO2 and 0.082 mol of
N2O4 at 298 K. Is the reaction at equilibrium? If not, in what
direction will the reaction proceed?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 51

Consider the reaction and the associated equilibrium constant:
Find the equilibrium concentrations of A and B for each value of
a and b. Assume that the initial concentration of A in each case is
1.0 M and that no B is present at the beginning of the reaction.
a. a = 1; b = 1
b. a = 2; b = 2
c. a = 1; b = 2 ### Problem 52

Consider the reaction and the associated equilibrium constant:
Find the equilibrium concentrations of A, B, and C for each value
of a, b, and c. Assume that the initial concentrations of A and B
are each 1.0 M and that no product is present at the beginning of
the reaction.
a. a = 1; b = 1; c = 2
b. a = 1; b = 1; c = 1
c. a = 2; b = 1; c = 1 (set up equation for x don't solve)

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 53

For the reaction, Kc = 0.513 at 500 K.
If a reaction vessel initially contains an N2O4 concentration of
0.0500 M at 500 K, what are the equilibrium concentrations of
N2O4 and NO2 at 500 K? William M.

### Problem 54

For the reaction, Kc = 255 at 1000 K.
If a reaction mixture initially contains a CO concentration of
0.1500 M and a Cl2 concentration of 0.175 M at 1000 K, what are
the equilibrium concentrations of CO, Cl2, and COCl2 at 1000 K?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 55

Consider the reaction:
If a mixture of solid nickel (II) oxide and 0.20 M carbon monoxide
comes to equilibrium at 1500 K, what is the equilibrium concentration
of CO2? William M.

### Problem 56

Consider the reaction:
If a reaction mixture initially contains 0.110 M CO and 0.110 M
H2O, what is the equilibrium concentration of each of the
reactants and products?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 57

onsider the reaction:
If a solution initially contains 0.210 M HC2H3O2, what is the
equilibrium concentration of H3O+ at 25 degree C? William M.

### Problem 58

Consider the reaction:
If a reaction mixture initially contains 0.175 M SO2Cl2, what is
the equilibrium concentration of Cl2 at 227 C?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 59

Consider the reaction:
A reaction mixture initially contains a Br2 partial pressure of
755 torr and a Cl2 partial pressure of 735 torr at 150 K. Calculate
the equilibrium partial pressure of BrCl. William M.

### Problem 60

Consider the reaction:
A reaction mixture initially contains a CO partial pressure of
1344 torr and a H2O partial pressure of 1766 torr at 2000 K.
Calculate the equilibrium partial pressures of each of the products.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 61

Consider the reaction:
Find the equilibrium concentrations of A, B, and C for each value
of Kc. Assume that the initial concentration of A in each case is
1.0 M and that the reaction mixture initially contains no products.
Make any appropriate simplifying assumptions.
a. Kc = 1.0
b. Kc = 0.010
c. Kc = 1.0 * 10-5 William M.

### Problem 62

Consider the reaction:
Find the equilibrium partial pressures of A and B for each value
of K. Assume that the initial partial pressure of B in each case is
1.0 atm and that the initial partial pressure of A is 0.0 atm. Make
any appropriate simplifying assumptions.
a. Kc = 1.0
b. Kc = 1.0 * 10-4
c. Kc = 1.0 * 105

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 63

Consider this reaction at equilibrium:
Predict whether the reaction will shift left, shift right, or remain
unchanged after each disturbance:
a. COCl2 is added to the reaction mixture.
b. Cl2 is added to the reaction mixture.
c. COCl2 is removed from the reaction mixture. William M.

### Problem 64

Consider this reaction at equilibrium:
Predict whether the reaction will shift left, shift right, or remain
unchanged after each disturbance.
a. NO is added to the reaction mixture.
b. BrNO is added to the reaction mixture.
c. Br2 is removed from the reaction mixture.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 65

Consider this reaction at equilibrium:
Predict whether the reaction will shift left, shift right, or remain
unchanged after each disturbance.
a. O2 is removed from the reaction mixture.
b. KCl is added to the reaction mixture.
c. KClO3 is added to the reaction mixture.
d. O2 is added to the reaction mixture. William M.

### Problem 66

Consider this reaction at equilibrium:
Predict whether the reaction will shift left, shift right, or remain
unchanged after each disturbance.
a. C is added to the reaction mixture.
b. H2O is condensed and removed from the reaction mixture.
c. CO is added to the reaction mixture.
d. H2 is removed from the reaction mixture.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 67

Each reaction is allowed to come to equilibrium, and then the
volume is changed as indicated. Predict the effect (shift right,
shift left, or no effect) of the indicated volume change.
a. I2(g)2 I(g) (volume is increased)
b. 2 H2S(g)2 H2(g) + S2(g) (volume is decreased)
c. I2(g) + Cl2(g)2 ICl(g) (volume is decreased) William M.

### Problem 68

Each reaction is allowed to come to equilibrium, and then the
volume is changed as indicated. Predict the effect (shift right,
shift left, or no effect) of the indicated volume change.
a. CO(g) + H2O(g)CO2(g) + H2(g) (volume is
decreased)
b. PCl3(g) + Cl2(g)PCl5(g) (volume is increased)
c. CaCO3( s)CaO( s) + CO2(g) (volume is increased)

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 69

This reaction is endothermic:
Predict the effect (shift right, shift left, or no effect) of increasing
and decreasing the reaction temperature. How does the value of
the equilibrium constant depend on temperature? William M.

### Problem 70

This reaction is exothermic:
Predict the effect (shift right, shift left, or no effect) of increasing
and decreasing the reaction temperature. How does the value of
the equilibrium constant depend on temperature?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 71

Coal, which is primarily carbon, can be converted to natural gas,
primarily CH4, by the exothermic reaction:
Which disturbance favors CH4 at equilibrium?
a. adding more C to the reaction mixture
b. adding more H2 to the reaction mixture
c. raising the temperature of the reaction mixture
d. lowering the volume of the reaction mixture
e. adding a catalyst to the reaction mixture
f. adding neon gas to the reaction mixture William M.

### Problem 72

Coal can be used to generate hydrogen gas (a potential fuel) by
the endothermic reaction:
If this reaction mixture is at equilibrium, predict whether each
disturbance will result in the formation of additional hydrogen
gas, the formation of less hydrogen gas, or have no effect on the
quantity of hydrogen gas.
a. adding C to the reaction mixture
b. adding H2O to the reaction mixture
c. raising the temperature of the reaction mixture
d. increasing the volume of the reaction mixture
e. adding a catalyst to the reaction mixture
f. adding an inert gas to the reaction mixture

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 73

Carbon monoxide replaces oxygen in oxygenated hemoglobin
according to the reaction:
a. Use the reactions and associated equilibrium constants at
body temperature to find the equilibrium constant for the
reaction just shown.
b. Suppose that an air mixture becomes polluted with carbon
monoxide at a level of 0.10%. Assuming the air contains
20.0% oxygen and that the oxygen and carbon monoxide
ratios that dissolve in the blood are identical to the ratios in
the air, what is the ratio of HbCO to HbO2 in the bloodstream?
Comment on the toxicity of carbon monoxide. William M.

### Problem 74

Nitrogen monoxide is a pollutant in the lower atmosphere that
irritates the eyes and lungs and leads to the formation of acid
rain. Nitrogen monoxide forms naturally in the atmosphere
according to the endothermic reaction:
Use the ideal gas law to calculate the concentrations of nitrogen
and oxygen present in air at a pressure of 1.0 atm and a temperature
of 298 K. Assume that nitrogen composes 78% of air by volume
and that oxygen composes 21% of air. Find the 'natural'
equilibrium concentration of NO in air in units of
molecules>cm3. How would you expect this concentration to
change in an automobile engine in which combustion is
occurring?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 75

The reaction CO2(g) + C(s)2 CO(g) has Kp = 5.78 at 1200 K.
a. Calculate the total pressure at equilibrium when 4.45 g of CO2
is introduced into a 10.0-L container and heated to 1200 K in
the presence of 2.00 g of graphite.
b. Repeat the calculation of part a in the presence of 0.50 g of
graphite. William M.

### Problem 76

A mixture of water and graphite is heated to 600 K. When the
system comes to equilibrium, it contains 0.13 mol of H2, 0.13 mol
of CO, 0.43 mol of H2O, and some graphite. Some O2 is added to
the system, and a spark is applied so that the H2 reacts completely
with the O2. Find the amount of CO in the flask when the
system returns to equilibrium.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 77

At 650 K, the reaction MgCO3(s)MgO(s) + CO2(g) has
Kp = 0.026. A 10.0-L container at 650 K has 1.0 g of MgO(s) and
CO2 at P = 0.0260 atm. The container is then compressed to a
volume of 0.100 L. Find the mass of MgCO3 that is formed. William M.

### Problem 78

A system at equilibrium contains I2(g) at a pressure of 0.21 atm
and I(g) at a pressure of 0.23 atm. The system is then compressed
to half its volume. Find the pressure of each gas when the system
returns to equilibrium.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 79

Consider the exothermic reaction:
If you were trying to maximize the amount of C2H4Cl2 produced,
which tactic might you try? Assume that the reaction mixture
reaches equilibrium.
a. increasing the reaction volume
b. removing C2H4Cl2 from the reaction mixture as it forms
c. lowering the reaction temperature William M.

### Problem 80

Consider the endothermic reaction:
If you were trying to maximize the amount of C2H4I2 produced,
which tactic might you try? Assume that the reaction mixture
reaches equilibrium.
a. decreasing the reaction volume
b. removing I2 from the reaction mixture
c. raising the reaction temperature
d. adding C2H4 to the reaction mixture

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 81

Consider the reaction:
A reaction mixture at equilibrium at 175 K contains PH2 = 0.958 atm,
PI2 = 0.877 atm, and PHI = 0.020 atm. A second reaction
mixture, also at 175 K, contains PH2 = PI2 = 0.621 atm, and
PHI = 0.101 atm. Is the second reaction at equilibrium? If not,
what will be the partial pressure of HI when the reaction reaches
equilibrium at 175 K? William M.

### Problem 82

Consider the reaction:
A reaction mixture initially containing 0.500 M H2S and 0.500 M
SO2 contains 0.0011 M H2O at a certain temperature. A second
reaction mixture at the same temperature initially contains
[H2S] = 0.250 M and [SO2] = 0.325 M. Calculate the equilibrium
concentration of H2O in the second mixture at this temperature.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 83

Ammonia can be synthesized according to the reaction:
A 200.0-L reaction container initially contains 1.27 kg of N2 and
0.310 kg of H2 at 725 K. Assuming ideal gas behavior, calculate
the mass of NH3 (in g) present in the reaction mixture at equilibrium.
What is the percent yield of the reaction under these
conditions? ### Problem 84

Hydrogen can be extracted from natural gas according to the
reaction:
An 85.0-L reaction container initially contains 22.3 kg of CH4
and 55.4 kg of CO2 at 825 K. Assuming ideal gas behavior,
calculate the mass of H2 (in g) present in the reaction mixture at
equilibrium. What is the percent yield of the reaction under
these conditions?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 85

The system described by the reaction: CO(g) + Cl2(g)
COCl2(g) is at equilibrium at a given temperature when
PCO = 0.30 atm, PCl2 = 0.10 atm, and PCOCl2 = 0.60 atm. Pressure
of Cl2(g) = 0.40 atm is added. Find the pressure of CO when the
system returns to equilibrium. William M.

### Problem 86

A reaction vessel at 27 C contains a mixture of SO2 (P = 3.00 atm)
and O2 (P = 1.00 atm). When a catalyst is added, this reaction
takes place: 2 SO2(g) + O2(g)2 SO3(g).
At equilibrium, the total pressure is 3.75 atm. Find the value
of Kc.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 87

At 70 K, CCl4 decomposes to carbon and chlorine. The Kp for the
decomposition is 0.76. Find the starting pressure of CCl4 at this
temperature that will produce a total pressure of 1.0 atm at
equilibrium. William M.

### Problem 88

The equilibrium constant for the reaction SO2(g) + NO2(g)
SO3(g) + NO(g) is 3.0. Find the amount of NO2 that must be added
to 2.4 mol of SO2 in order to form 1.2 mol of SO3 at equilibrium.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 89

A sample of CaCO3(s) is introduced into a sealed container of
volume 0.654 L and heated to 1000 K until equilibrium is reached.
The Kp for the reaction CaCO3(s)CaO(s) + CO2(g) is
3.9 * 10-2 at this temperature. Calculate the mass of CaO(s) that
is present at equilibrium. William M.

### Problem 90

An equilibrium mixture contains N2O4, (P = 0.28) and NO2
(P = 1.1 atm) at 350 K. The volume of the container is doubled
at constant temperature. Calculate the equilibrium pressures of
the two gases when the system reaches a new equilibrium.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 91

Carbon monoxide and chlorine gas react to form phosgene:
If a reaction mixture initially contains 215 torr of CO and
245 torr of Cl2, what is the mole fraction of COCl2 when
equilibrium is reached? William M.

### Problem 92

Solid carbon can react with gaseous water to form carbon
monoxide gas and hydrogen gas. The equilibrium constant for
the reaction at 700.0 K is Kp = 1.60 * 10-3. If a 1.55 L reaction
vessel initially contains 145 torr of water at 700.0 K in contact
with excess solid carbon, find the percent by mass of hydrogen
gas of the gaseous reaction mixture at equilibrium.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 93

Consider the reaction:
a. A reaction mixture at 175 K initially contains 522 torr of NO
and 421 torr of O2. At equilibrium, the total pressure in the
reaction mixture is 748 torr. Calculate Kp at this temperature.
b. A second reaction mixture at 175 K initially contains 255 torr
of NO and 185 torr of O2. What is the equilibrium partial
pressure of NO2 in this mixture? William M.

### Problem 94

Consider the reaction:
A 2.75-L reaction vessel at 950 K initially contains 0.100 mol of
SO2 and 0.100 mol of O2. Calculate the total pressure (in atmospheres)
in the reaction vessel when equilibrium is reached.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 95

Nitrogen monoxide reacts with chlorine gas according to the
reaction:
A reaction mixture initially contains equal partial pressures of
NO and Cl2. At equilibrium, the partial pressure of NOCl is
115 torr. What were the initial partial pressures of NO and Cl2? William M.

### Problem 96

At a given temperature, a system containing O2(g) and some oxides
of nitrogen are described by these reactions:
A pressure of 1 atm of N2O4(g) is placed in a container at this
temperature. Predict which, if any, component (other than N2O4)
will be present at a pressure greater than 0.2 atm at equilibrium.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 97

A sample of pure NO2 is heated to 337 C, at which temperature
it partially dissociates according to the equation:
At equilibrium, the density of the gas mixture is 0.520 g>L
at 0.750 atm. Calculate Kc for the reaction. William M.

### Problem 98

When N2O5(g) is heated, it dissociates into N2O3(g) and O2(g)
according to the reaction:
The N2O3(g) dissociates to give N2O3(g) and O2(g) according to
the reaction:
When 4.00 mol of N2O5(g) is heated in a 1.00-L reaction vessel
to this temperature, the concentration of O2(g) at equilibrium is
4.50 mol>L. Find the concentrations of all the other species in
the equilibrium system.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 99

A sample of SO3 is introduced into an evacuated sealed container
and heated to 600 K. The following equilibrium is established:
The total pressure in the system is 3.0 atm, and the mole fraction
of O2 is 0.12. Find Kp. William M.

### Problem 100

A reaction A(g)B(g) has an equilibrium constant of
1.0 * 10-4. For which of the initial reaction mixtures is the x is
small approximation most likely to apply?
a. [A] = 0.0010 M; [B] = 0.00 M
b. [A] = 0.00 M; [B] = 0.10 M
c. [A] = 0.10 M; [B] = 0.10 M
d. [A] = 0.10 M; [B] = 0.00 M

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 101

The reaction A(g)2 B(g) has an equilibrium constant of
Kc = 1.0 at a given temperature. If a reaction vessel contains
equal initial amounts (in moles) of A and B, will the direction in
which the reaction proceeds depend on the volume of the reaction
vessel? Explain. William M.

### Problem 102

A particular reaction has an equilibrium constant of Kp = 0.50.
A reaction mixture is prepared in which all the reactants and
products are in their standard states. In which direction will the
reaction proceed?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 103

Consider the reaction:
Each of the entries in the table represents equilibrium partial
pressures of A and B under different initial conditions. What are
the values of a and b in the reaction? William M.

### Problem 104

Consider the simple one-step reaction:
Since the reaction occurs in a single step, the forward reaction
has a rate of kfor[A] and the reverse reaction has a rate of krev[B].
What happens to the rate of the forward reaction when we increase
the concentration of A? How does this explain the reason
behind Le Chatelier"s principle?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 105

The reactions shown here can be combined to sum to the overall
reaction C(s) + H2O(g)->CO(g) + H2(g) by reversing some
and/or dividing all the coefficients by a number. As a group, determine
how the reactions need to be modified to sum to the
overall process. Then have each group member determine the
value of K for one of the reactions to be combined. Finally, combine
all the values of K to determine the value of K for the overall
reaction.
a. C(s) + O2(g)->CO2(g) K = 1.363 * 1069
b. 2 H2(g) + O2(g)->2 H2O(g) K = 1.389 * 1080
c. 2 CO(g) + O2(g)->2 CO2(g) K = 1.477 * 1090 William M.

### Problem 106

Consider the reaction: N2(g) + 3 H2(g)->2 NH3(g).
a. Write the equilibrium constant expression for this reaction.
If some hydrogen is added, before the reaction shifts:
b. How will the numerator and denominator of the expression in
part a compare to the value at equilibrium?
c. Will Q be larger or smaller than K? Why?
d. Will the reaction have to shift forward or backward to retain
equilibrium? Explain.
principle? Explain.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 107

For the reaction A->B, the ratio of products to reactants at
equilibrium is always the same number, no matter how much A
or B is initially present. Interestingly, in contrast, the ratio of
products to reactants for the reaction C->2 D does depend
on how much of C and D you have initially. Explain this observation.
Which ratio is independent of the starting amounts of C
and D? Answer in complete sentences. William M.

### Problem 108

Solve each of the expressions for x using the quadratic formula
and the x is small approximation. In which of the following
expressions is the x is small approximation valid?
a. x2>(0.2 - x) = 1.3 * 104
b. x2>(0.2 - x) = 1.3
c. x2>(0.2 - x) = 1.3 * 10-4
d. x2>(0.01 - x) = 1.3 * 10-4
In a complete sentence, describe the factor(s) that tend to make
the x is small approximation valid in an expression.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 109

Have each group member explain to the group what happens if a
system at equilibrium is subject to one of the following changes
and why.
a. The concentration of a reactant is increased.
b. A solid product is added.
c. The volume is decreased.
d. The temperature is raised. William M.

### Problem 110

The atmosphere of the planet Venus is almost entirely composed
of carbon dioxide (about 96.5% carbon dioxide). The carbon
dioxide on Venus could be in equilibrium with carbonate ions in
minerals on the planet's crust. Two possible equilibrium systems
involve CaSio3 and MgSiO3:
The first graph that follows shows the expected pressures of
carbon dioxide (in atm) at different temperatures for each of
these equilibrium systems. (Note that both axes on this graph
are logarithmic.) The second graph is a phase diagram for carbon
dioxide. Examine the graphs and answer the questions.
a. The partial pressure of carbon dioxide on the surface of Venus
is 91 atm. What is the value of the equilibrium constant (Kp)
if the Venusian carbon dioxide is in equilibrium according to
system 1? According to system 2?
b. The approximate temperature on the surface of Venus is about
740 K. What is the approximate carbon dioxide concentration
for system 1 at this temperature? For system 2? (Use a point at
approximately the middle of each colored band, which
represents the range of possible values, to estimate the carbon
dioxide concentration.)
c. Use the partial pressure of carbon dioxide on the surface of
Venus given in part a to determine which of the two equilibrium
systems is more likely to be responsible for the carbon
dioxide on the surface of Venus.
d. From the carbon dioxide phase diagram, determine the minimum
pressure required for supercritical carbon dioxide to
form. If the partial pressure of carbon dioxide on the surface
of Venus was higher in the distant past, could supercritical
carbon dioxide have existed on the surface of Venus?

ES
Eugene S.
University of Minnesota - Twin Cities