IV. Equilibrium
13.
The Nature of Chemical Equilibrium
A.
The Irreversible Reaction
Most of the reactions we have considered so far have been irreversible, as
implied by the one-way arrow: . In such a reaction, none of the
product molecules reacted again to produce the original molecules.
A non-technical example:
Chemical examples:
B.
Steady State
An open system can be in a steady state if the input rate of a
substance equals the output rate. An open system is one that loses a
substance from one “opening” and then gets that same substance
back from another source.
Non-technical examples:
Chemical Steady State Examples from the Natural World:
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IV. Equilibrium
C.
Reversible Reactions: Equilibrium
Equilibrium occurs in a closed system. Once a reaction attains equilibrium, the rate of
the forward reaction equals the rate of the reverse reaction. At the macroscopic level,
the reaction seems to have stopped, but at the molecular level it continues in both
directions.
Non-technical examples:
Chemical Equilibrium Examples:
Example 1
2 NO2(g)
N2O4(g) + heat
Macroscopic observations:
At t = 0, we have no N2O4 (invisible) and 2 moles/L of NO2. (red- brown gas). With time,
the brown colour fades. While these changes are occurring, we have not yet reached
equilibrium.
At equilibrium, the brown colour stops fading, and the concentrations of the two gases
remain constant.
Microscopically, what's happening?
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IV. Equilibrium
Example 2
A large crystal of iodine is dropped into CCl4.
a)
Describe what you would see before equilibrium is reached and after equilibrium is
attained.
b)
Also explain what occurs at the molecular level once equilibrium is established.
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IV. Equilibrium
Exercises
1.
Classify as one of the following:
(1)
Irreversible Reaction
(2)
Steady State
(3)
Reversible Reactions: Equilibrium
a)
b)
c)
d)
e)
water in an open dish left to evaporate
20 ml of alcohol in a sealed 500 ml jar
water flowing into a pool at a rate of 2 L/s and leaving the pool at that rate.
adding Mg to acid
a saturated salt solution in a closed vessel
2.
a) Sugar is added to a cup of coffee until no more sugar can dissolve. The top is sealed
so that no coffee can evaporate, and the temperature is kept constant. Hey, we have
equilibrium! Agree?
b)
Macroscopically, what would you see?
c)
Microscopically what is still going on?
3.
By burning a log, do you establish equilibrium eventually? Explain.
4.
A single drop of water placed in a closed bottle may or may not establish a state of
equilibrium between gas and liquid according to:
H2O(l)
H2O (g)
Explain. What will affect whether equilibrium is established?
5.
Given: H2(g) + Cl2(g)
2 HCl(g) + 156 kJ
Which information can you obtain from the above chemical equation? (yes/no)
a)
b)
c)
d)
e)
f)
g)
the ratio with which hydrogen and chlorine react ?
the concentrations of the gases at equilibrium ?
whether it is an equilibrium reaction?
how fast equilibrium is reached?
the physical state of the products and reactants?
whether the reaction is exothermic?
the reaction mechanism?
6.
Give 1 everyday example for each of the following. Think of something that is not
directly from your notes.
(1)
an irreversible reaction
(2)
Steady State
(3)
Reversible Reactions: Equilibrium
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IV. Equilibrium
14.
Disturbing Chemical Equilibrium: Le Chatelier's Principle
In 1888, LeChatelier gave a succinct statement of the principle he had
announced in 1884. It is:
Every change of one of the factors of an equilibrium causes a
rearrangement of the system in such a direction that the factor in question
experiences a change in a sense opposite to the original change.
Here is a different way of explaining the same concept.
Henri LeChatelier (1850-1936)
To predict how a system in equilibrium will react to a disturbance, view the
forward and reverse reactions in competition with one another. The prevailing
reaction will be the one that is getting what it needs from the disturbance. If one
reaction is being more hampered than the other, obviously it will not win out.
In Class Examples
Each of the following reactions has reached equilibrium. What will be the effect on the
equilibrium concentration of each substance when the change described is made?
Example 1
2 H2(g) +
2 NO(g)
reacting hydrogen with a metal
Example 2
SO2(g)
+
0.5 O2(g)
N2(g)
+
2 H2O(l)
SO3(g)
increasing the pressure on the system
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IV. Equilibrium
Example 3
Example 4
H2O(g)
H2O(l)
+ heat
(1)
cooling the system
(2)
decreasing the pressure
Consider the following reaction:
CaCO3(s)
limestone
CaO(s) +
CO2(g)
H = (+) or endothermic
lime
How would you maximize the amount of CaO (lime) produced?
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IV. Equilibrium
Exercises
1.
Each of the following reactions has come to equilibrium. But then you disturb the
equilibrium. Predict the effect on the concentration of each other substance involved
when the change described is made.
a)
2 H2(g) +
2 NO(g)
removing water with a drying agent
N2(g)
b)
SO2(g) +
0.5 O2(g)
using air instead of pure oxygen
SO3(g)
c)
P4(s)
+ 6 H2(g)
adding more H2
d)
FeO(s) +
CO(g)
adding more carbon dioxide
2.
In 1d, how could you decrease the amount of both FeO and CO while increasing the
amount of CO2 present?
Will the reactants be favoured (will you get less product) if pressure is increased?
Answer for each case.
3.
+
2 H2O(g)
+
CO2(g)
4PH3(s)
+
Fe(s)
a)
2 H2(g)
b)
FeO(s)
4.
Water is boiling in a pressure cooker. The temperature is at 100 C. You would like to
preserve some beans at a higher temperature, so you would like to prevent the water
from boiling. You want to favour the reverse reaction, in other words.
+
CO(g)
2 NO(g)
N2(g)
Fe(s)
+
H2O(l)
+
2 H2O (g)
CO2(g)
H2O(g)
Do you raise or lower the pressure? Explain.
5.
When an NO2 and N2O4 mixture is placed in a syringe at room temperature,
the following is observed:
As the piston is gradually pushed in, the red brown colour of NO2 first
darkens but then it gets progressively lighter. Explain.
N2O4(g)
colourless
2 NO2(g)
red-brown
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IV. Equilibrium
6.
a)
What will happen to the amount of SO3 if temperature is increased, given:
SO2(g)
b)
+
0.5 O2(g)
SO3(g) +
93 kJ
?
In what direction will equilibrium “shift” if temperature is lowered for
N2O4(g)
c)
d)
2 NO2(g) ?
What colour change will you observe in the above as you lower temperature? (see #5 for colours)
How would you change the temperature if you wanted to produce more NO 2, given:
2 NO(g)
7.
+ O2(g)
2 NO2(g)
-117 kJ
A good humidity indicator can be made by coating paper with CoCl2 and observing its colour.
Heat + [Co(H2O)6]Cl2(s)
Pink
a)
b)
8.
[Co(H2O)4]Cl2
Blue
(s)
+2 H2O(g)
If you were to observe a pink colour quickly forming at room temperature, what you
conclude about the level of humidity?
Suppose you were using the blue substance to gradually absorb moisture from your
camera case. What would you do once the substance turned pink and stopped
absorbing water? (How would you recycle the pink substance?)
Anthocyanins are pigments that are responsible for most of nature’s blue, red and purple
colours. Purple cabbage contains such pigments.
Use these equations to answer the questions that follow.
a)
X
Blue
+
H+1
Y
red
X
Blue
+
OH-1
Z
yellow
While the purple cabbage is alive, which two pigments are present
in its cells?
b) When purple cabbage is cooked, the vacuoles (microscopic bags
that contain pigment and acid ) burst, and the acid is neutralized by the rest of the cell’s alkaline
contents.
What colour will you see?
c)
If a blue anthocyanin solution is added to vinegar, what colour will it become?
d) What two colours will you see if you add base(OH-1 ), one drop at a time, to a blue solution?
e)
How do you turn a yellow solution into a purple one?
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IV. Equilibrium
15.
Law of Chemical Equilibrium
Since a reaction at equilibrium has fixed concentrations of products and reactants, we can
calculate a constant at a given temperature.
For
Kc 
aB
[ F ]e [ H ]g
[ B ]a [ D ]c
+
cD
eF
+
gH
Kc is known as the equilibrium constant. As long as temperature
remains constant, the value of K will not change regardless of the initial
amounts of reactants used.
Keep in mind: You only include concentrations of aqueous and gaseous reactants/ products, not
those of liquids or solids. Liquid and solid concentrations remain constant and so they already
are imbedded in K.
Example 1
Derive the above formula.
Example 2
Write an equilibrium law expression for the following:
a.
H2(g) + F2(g)
2 HF(g)
b.
ZnS(s)
Zn+2(aq) + S-2(aq)
c.
H2O(l)
H+(aq) + OH-(aq)
d.
6 XA(g) + Y2Z(l) + A(g)
2 X3Y(g) + A7(s)
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IV. Equilibrium
Example 3
Given: the following concentrations in moles/L at 748 oC:
H2(g)
+
0.00630
CO2(g)
0.00630
H2O(g)
+
0.00552
a.
Write an equilibrium law expression.
b.
Calculate the equilibrium constant at that temperature.
CO(g)
0.00552
Example 4
Given the following 750 oC:
Kc = 0.771
H2(g)
+
CO2(g)
H2O(g) +
CO(g)
If 0.0100 moles of hydrogen and 0.0100 moles of CO2 are mixed in a 1.00 L container, find the
equilibrium concentrations for all substances.
H2(g)
CO2(g)
H2O(g)
CO(g)
Initial amount (moles/L)
Changing
(Reacting/forming(moles/L)
Equilibrium amount(moles/L)
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IV. Equilibrium
Example 5
Given:
4 A(g)
2 B(g)
+ C(g)
a)
A student introduces 5.0 moles of A into a sealed 2.0 L flask. When the system reaches
equilibrium, only 4.0 moles of A are left behind. How many moles of B and C are there at
equilibrium?
b)
Calculate Kc for this reaction.
c)
Would a catalyst affect Kc? Explain.
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IV. Equilibrium
Example 6
Suppose 6.000 mol of F2 and 3.000 mol of H2 are mixed in a 3.000 L container to make HF . The
equilibrium constant at a certain temperature is 1.15x10 2.
Calculate the equilibrium concentrations, given:
H2(g) + F2(g)
2 HF(g)
H2(g)
F2(g)
2 HF(g)
Initial amount (moles)
Reacting/forming(moles)
Equilibrium amount(moles)
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IV. Equilibrium
Exercises
1.
For each of the following reactions, write an equilibrium law expression. Remember:
only aqueous and gaseous molecules/atoms are included in equilibrium expressions.
a.
Ag+1(aq) +
b.
c.
N2O4(g)
2 NH3(g)
d.
e.
CH3COOH(aq)
H2O(l)
f.
Cu (s)
2.
The water gas reaction:
Ag(NH3)2+1(aq)
2 NH3(g)
3 H2(g)
+
CO2(g)
2 NO2(g)
+
N2(g)
H+1(aq) + CH3CO2-1(aq)
H+1(aq) +
OH-1(aq)
2Ag+1(aq)
+
Ag(s)
H2(g)
+
Cu+2(aq)
CO (g)
+
H2O(g)
was carried out at a constant temperature (900 C) three times with the
following results.
Partial Pressure (treat like concentration in moles/L)1
TRIAL Number
1
2
3
a.
b.
3.
CO (g)
0.352
0.266
0.186
H2O(g)
0.352
0.266
0.686
CO2(g)
0.648
0.234
0.314
H2(g)
0.148
0.234
0.314
Write the equilibrium law expression.
Use the data to check if a constant is indeed obtained at 900 C.
Which are more common at equilibrium in the following: reactants ? Or products?
Cu(s)
+
Cu+2(aq)
2 Cu+1(aq)
K = 1 X 10–6
4.
In
Cu(s)
+
2 Ag+1(aq)
2 Ag(s) + Cu+2(aq) at 25 oC, there
+2
+1
is a lot more Cu than Ag at equilibrium. Which is the only reasonable value for K?
(multiple choice)
A
8.5 X 10-17
B
1.7 X 10-1
C
1.0 X 100
D
2.0 X 10 4
1
Kc, the equilibrium constant based on concentrations, is equal to Kp(for pressure) as long as the sum of
reactant-moles equals the sum of product-moles. Otherwise,
Kp = Kc (RT)n. For the derivation(not part of course), see www.emsb.qc.ca/laurenhill/science/Kp.pdf
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IV. Equilibrium
5. Calculate K for the following reaction at 40 oC:
Equation: 2 HI(g)
H2(g) + I2(g)
[HI]eq
4.0 X 10-3
[H2(g)]
7.5 X 10-3
6.
Given :
a.
f.
A student introduces 5.0 moles of A into a sealed empty one liter flask at 20 oC. When
the system reaches equilibrium, only 4.0 moles of A are present. How many moles of B
and C are at equil’m?
Calculate K for this reaction at 20 C.
Would a catalyst affect the K value?
Will the catalyst form 2 moles of B faster than without a catalyst?
A student introduces 5 moles of A into an empty 1.0 L flask at a higher temperature. This
time, 2.0 moles of A are found at equilibrium. Calculate the new K at this higher
temperature.
Was the reaction endothermic or exothermic?
7.
Given: 2 NH3(g)
a.
In an empty 2.0 L flask kept at a constant temperature, 5.0 moles of NH3 were
introduced. Only 1.5 moles of H2 and 0.5 moles of N2 were found at equilibrium. Find K
for the above reaction at this specific temperature.
The experiment was repeated at a higher temperature, again with a 2.0 L flask. Four
moles of ammonia were used initially and only 1.5 moles reacted. How much nitrogen
was formed?
b.
c.
d.
e.
b.
3 A (g)
2 B (g)
3 H2(g) +
C (g)
N2(g)
8.
Given:
a.
After placing 8 moles of A into a sealed empty one litre flask, a student found happiness
along with 4.0 moles of B and 2.0 moles of C. Find K.
The same substances were used in a similar experiment and with a 2.0 L flask. Only 4.0
moles of A were found at equilibrium after starting with 16 moles. Was the temperature
lower than that of (a)?
b.
3 A (g)
+
[I2(g)]eq
4.3 X 10-5
2 B(g)
+
C (g)
+
heat
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IV. Equilibrium
9.
A 1.00 L vessel has 7.00 g of CO(g) and 4.50 g of steam initially and nothing else. If the K
for this reaction is 3.59 under certain conditions, how many grams of carbon dioxide will
be found at equilibrium?
CO(g) + H2O(g)
10.
H2(g)
+ CO2(g)
Hydrogen (H2) and iodine (I2) react together in a 1 L flask, according to the equation:
H2(g) + I2(g)
2 HI(g)
At equilibrium, there is 7.00  10-4 mol I2, 4.13  10-3 mol H2 and a certain quantity of HI.
Given that the equilibrium constant of the reaction is 55.6 and that the pressure of the
gaseous mixture is 101 kPa, what is the temperature of the gaseous mixture?
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IV. Equilibrium
16.
Ksp = Equilibrium Constant for Solubility Products
Background Knowledge for Solubility Product constant (Ksp)
1. The solubility of CaF2(s) is 2.05 x 10-4 moles /L at
25 oC. What does that mean?
2. What actually happens to a crystal of CaF2 as it
dissolves in water? (a) draw an ionic
representation and (b) write an equilibrium
equation to represent this.
3.
How does the K for this equilibrium relate to a saturated solution?
4.
Write equilibrium equations for the following as they dissolve in water:
a) Al(OH)3(s)
b) Li3PO4(s)
c) Mg3(AsO4)2(s)
d) Hg(SCN)2(s)
e) AgCl(s)
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IV. Equilibrium
f)
Ag2C2O4(s)
The Ksp is specifically used for an equilibrium between an undissolved solid and its ions in
solution.
How to interpret Ksp
MX(s)
Ksp =
M+(aq) + X-(aq)
Low Ksp
High Ksp
Example 1
Solid silver chromate is added to pure water at 25 oC. Some of the solid remains
undissolved Ag2CrO4(s) at the bottom of the flask. The mixture is stirred for
several days to ensure that equilibrium is achieved between the undissolved
and the solution. Analysis of the equilibrated solution shows that its silver ion
concentration is 1.3 X10-4 moles/L.
Calculate Ksp for this compound.
Example 2
The Ksp for CaF2 is 3.9 X 10-11 at 25 oC. Assuming that CaF2 dissociates
completely upon dissolving and that there are no other important equilibria
affecting its solubility, calculate the solubility of CaF2 in grams per liter.
1.1 X10-12
1.7 X 10-2 g CaF2/L soln
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IV. Equilibrium
Example 3
LaF2(s)+ heat
La+2(aq) + 2 F-(aq)
In the above equilibrium, list two ways by which the solubility of LaF2 could be reduced.
Example 4
For which substance would
Ksp increase with a lower temperature?
Explain your reasoning.
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IV. Equilibrium
Exercises
1. Calculate the solubility in grams per liter of silver sulfide (Ag2S)in order to decide whether it
is accurately labeled when described as an insoluble salt. (Ag2S: Ksp = 6.3 x 10-50)
2. Determine which salt
liter?
CaCO3 or Ag2CO3
CaCO3:
is more soluble in water in units of moles per
Ksp = 2.8 x 10-9
Ag2CO3: Ksp = 8.1 x 10-12
3.
In a saturated solution of MgF2 at 18ºC, the concentration of Mg2+ is 1.21´10-3 moles/L.
The equilibrium is represented by MgF2(s)
Mg2+(aq) + 2 F-(aq)
a)
Write the expression for the solubility-product constant, Ksp, and calculate its value at
18ºC.
b)
How could you raise the solubility of magnesium fluoride?
c)
How could you lower it?
4.
Determine the Ksp of Ca(OH)2 if 0.0105 moles dissolves in 1 kg of water.
5.
Use the graph in your notes and list two substances for which Ksp will increase with
increasing temperature.
6.
At equilibrium there are only 1.7 X 10-2 moles of Pb+2 present for every liter of
solution. What is the Ksp for the following reaction?
PbCl2(s)
7.
Pb+2(aq) + 2 Cl-1(aq)
The equilibrium constant for the following is 1.0 X 10-21= Ksp
ZnS(s)
Zn+2(aq) + S-2(aq)
At equilibrium, how many moles of Zn+2 are there in every liter of solution?
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IV. Equilibrium
Tricky and Not-so-Difficult Ksp Problems From Various Tests
1.
a)
Calculate the solubility product constant(Ksp) for manganese(II) hydroxide,
Mn(OH)2, if 100.0 mL of a saturated solution of manganese(II) hydroxide was found to
contain 3.28 X 10-4 grams of manganese(II) hydroxide dissolved in it.
Manganese has a charge of +2
b)
You are concerned about disposing a saturated solution of Mn(OH)2, because of
Mn+2 ‘s effects on wildlife and humans. What could be done to lower the concentration
of Mn+2?
2.
A 100.0 ml saturated solution of what was supposed to be cadmium arsenate,
Cd3(AsO4)2 is evaporated.
0.050 grams of solidwere left behind after evaporation. Prove that it was not really
Cd3(AsO4)2
The solubility product constant (Ksp) for cadmium arsenate is 2.20 x 10-33.
3.
a)
Calculate the solubility product constant(Ksp) for PbCl2(s), if 50.0 mL of a
saturated solution of lead(II) chloride was found to contain 0.2207 g of lead(II) chloride
dissolved in it.
b)
You are concerned about disposing a saturated solution of PbCl2 because of
+2
Pb effects on wildlife and humans. What could be done to lower the concentration of
Pb+2?
c)
What could happen in the environment that would increase the concentration
of Pb+2?
4.
If 55 mg of lead (II) sulfate , PbSO4, is placed in 250.0 mL of pure water, how much
PbSO4 will remain undissolved?
The solubility product constant (Ksp) for PbSO4 is 2.53 x 10-8.
5.
Estimate the solubility of barium sulfate (BaSO4) in a solution that already has 0.020
moles/L of sulfate (SO4-2) initially.
The solubility product constant (Ksp) for barium sulfate is 1.1 x 10-10.
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