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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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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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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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Exercises 1. Classify as one of the following: (1) Irreversible Reaction (2) Steady State (3) Reversible Reactions: Equilibrium a) water in an open dish left to evaporate b) 20 ml of alcohol in a sealed 500 ml jar c) water flowing into a pool at a rate of 2 L/s and leaving the pool at that rate. d) adding Mg to acid e) 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) the ratio with which hydrogen and chlorine react ? b) the concentrations of the gases at equilibrium ? c) whether it is an equilibrium reaction? d) how fast equilibrium is reached? e) the physical state of the products and reactants? f) whether the reaction is exothermic? g) 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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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.

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) N2(g) + 2 H2O(l)

reacting hydrogen with a metal

Example 2 SO2(g) + 0.5 O2(g) SO3(g) increasing the pressure on the system

Henri LeChatelier (1850-1936)

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Example 3 H2O(g) H2O(l) + heat

(1) cooling the system

(2) decreasing the pressure Example 4 Consider the following reaction:

CaCO3(s) CaO(s) + CO2(g)

H = (+) or endothermic limestone lime

How would you maximize the amount of CaO (lime) produced?

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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) N2(g) + 2 H2O(g) removing water with a drying agent

b) SO2(g) + 0.5 O2(g) SO3(g) using air instead of pure oxygen

c) P4(s) + 6 H2(g) 4PH3(s) adding more H2

d) FeO(s) + CO(g) Fe(s) + CO2(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? 3. Will the reactants be favoured (will you get less product) if pressure is increased?

Answer for each case.

a) 2 H2(g) + 2 NO(g) N2(g) + 2 H2O (g)

b) FeO(s) + CO(g) Fe(s) + CO2(g) 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.

H2O(l) 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) 2 NO2(g) colourless red-brown

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6. a) What will happen to the amount of SO3 if temperature is increased, given:

SO2(g) + 0.5 O2(g) SO3(g) + 93 kJ ? b) In what direction will equilibrium “shift” if temperature is lowered for

N2O4(g) 2 NO2(g) ? c) What colour change will you observe in the above as you lower temperature? (see #5 for colours) d) How would you change the temperature if you wanted to produce more NO2, given:

2 NO(g) + O2(g) 2 NO2(g) -117 kJ

7. A good humidity indicator can be made by coating paper with CoCl2 and observing its colour.

Heat + [Co(H2O)6]Cl2(s) [Co(H2O)4]Cl2 (s) +2 H2O(g) Pink Blue a) If you were to observe a pink colour quickly forming at room temperature, what you

conclude about the level of humidity? b) 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?)

8. 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.

X + H+1 Y Blue red

X + OH-1 Z Blue yellow

a) 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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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 aB + 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)

ca

ge

cDB

HFK

][][

][][

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Example 3 Given: the following concentrations in moles/L at 748 oC:

H2(g) + CO2(g) H2O(g) + CO(g) 0.00630 0.00630 0.00552 0.00552 a. Write an equilibrium law expression. b. Calculate the equilibrium constant at that temperature. 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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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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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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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) + 2 NH3(g) Ag(NH3)2

+1(aq)

b. N2O4(g) 2 NO2(g)

c. 2 NH3(g) 3 H2(g) + N2(g)

d. CH3COOH(aq) H+1(aq) + CH3CO2

-1(aq)

e. H2O(l) H+1(aq) + OH-1

(aq)

f. Cu (s) + 2Ag+1(aq) Ag(s) + Cu+2

(aq) 2. The water gas reaction:

CO2(g) + H2(g) 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 CO (g) H2O(g) CO2(g) H2(g)

1 0.352 0.352 0.648 0.148

2 0.266 0.266 0.234 0.234

3 0.186 0.686 0.314 0.314

a. Write the equilibrium law expression. b. Use the data to check if a constant is indeed obtained at 900 C.

3. 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 is a lot more Cu+2 than Ag+1 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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5. Calculate K for the following reaction at 40 oC:

Equation: 2 HI(g) H2(g) + I2(g)

[HI]eq [H2(g)] [I2(g)]eq

4.0 X 10-3 7.5 X 10-3 4.3 X 10-5

6. Given : 3 A (g) 2 B (g) + C (g) a. 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?

b. Calculate K for this reaction at 20 C. c. Would a catalyst affect the K value? d. Will the catalyst form 2 moles of B faster than without a catalyst? e. 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.

f. Was the reaction endothermic or exothermic?

7. Given: 2 NH3(g) 3 H2(g) + N2(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.

b. 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?

8. Given: 3 A (g) 2 B(g) + C (g) + heat

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. b. 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)?

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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) H2(g) + CO2(g)

10. 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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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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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) M+(aq) + X-

(aq)

Ksp =

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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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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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 CaCO3 or Ag2CO3 is more soluble in water in units of moles per liter?

CaCO3: 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) Pb+2(aq) + 2 Cl-1(aq)

7. 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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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 Pb+2 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.