ADVANCED PLACEMENT CHEMISTRY

EQUILIBRIUM

Chemical equilibrium- state where concentrations of products and reactants remain constant-equilibrium is dynamic-any chemical reaction in a closed vessel will reach equilibrium-at equilibrium, forward reaction rate = reverse reaction rate

Law of Mass Action

for jA + kB lC + mDKc = [C]l[D]m [ ] = concentration in

-------- mol/L = Molarity [A]j[B]k

Kc = K = Keq = equilibrium constant (used interchangeably)

Ex. 4 NH3 + 7 O2 4 NO2 + 6 H2O

[NO2]4[H2O]6

Kc = ----------------- [NH3]4[O2]7

If we know equilibrium concentrations, we can calculate the equilibrium constant, Kc.

K changes with temperature (not with concentration or pressure).

For the reverse reaction: lC + mD jA + kB Kc' = [A]j[B]k [C]l[D]m Kc' = 1/ Kc

If the original reaction is multiplied by some factor to give: njA + nkB nlC + nmD

[C]nl[D]nm

Kc" = -------------- = Kcn

[A]nj[B]nk

For a 2-step reaction with Kc1 and Kc2 as Kc values for each step, the Kc for the overall reaction is Kc3 = Kc1 x Kc2.

The units for K depend on the reaction. They are usually not used.

Equilibrium position - a set of equilibrium concentrations. - depends on initial concentrations. (Kc doesn't)

Pressures can be used in equilibrium expressions. The equilibrium constant is called Kp. Using the same mass action equation as above, the Kp expression becomes:

(Pc)l(PD)m

Kp = ----------

(PA)j(PB)k

P = partial pressure at equilibrium in atm.

Kc involves concentrations while Kp involves pressures.

Kp and Kc can be interconverted using the

following relationship:Kp = Kc(RT) n R = 0.0821 mol/L atm T = Kelvin temperaturen = #moles gaseous product - # moles

gaseous reactantKc = Kp if # moles gaseous product =

# moles gaseous reactant

***Concentrations of pure solids and pure liquids are not included in equilibrium expressions because they are constant.

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

Kc = [CO2]

*A value for K greater than one means that the equilibrium is far to the right (mostly products).*A value for K less than one means that the equilibrium is far to the left (mostly reactants). *The size of K and the time needed to reach equilibrium are not directly related. *K values can not always be directly compared because stoichiometry differs.

If the value for K is very small, reactants are present in great excess at equilibrium.

If the value for K is very large, products are present in great excess at equilibrium. Values for K in the range of 0.001 to 1000 describe reactions where reactants and products are both present in significant quantities at equilibrium.

Consider the reaction 2NOCl(g) 2NO(g) + Cl2(g) at 35oC, when 3.00 mol NOCl(g), 1.00 mol NO(g), and 2.00 mol Cl2(g) are mixed in a 10.0 L flask. After the system has reached equilibrium the concentrations are observed to be: [Cl2] = 1.52 x 10-1 M

[NO] = 4.00 x 10-3 M[NOCl] = 3.96 x 10-1 M

Calculate the value of K for this system at 35oC.K = [NO]2[Cl2] =

[NOCl]2

(4 x 10-3)2 (1.52 x 10-1)

(3.96 x 10-1)2

= 1.55 x 10-5

Calculate the value of K for the reaction 2NO(g) + Cl2(g) 2NOCl(g).

K' = 1/K

K' = 1/1.55 x 10-5

= 6.45 x 104

Calculate the value of K for the reaction 4NOCl(g) 4NO(g) + 2Cl2(g).

K" = Kn

K" = (1.55 x 10-5)2 = 2.40 x 10-10

Calculate Kp for the first reaction.

Kp = Kc(RT) n

Kp = (1.55 x 10-5)[(0.0821)(308)]1

= 3.92 x 10-4

When working equilibrium problems, it is not always obvious which direction that equilibrium is going to shift. To determine this, solve for the reaction quotient, Q. Q only needs to be calculated when there is some of each reactant and product present.

Q = reaction quotient - calculated like Kc, but using initial concentrations instead of equilibrium concentrations1. If K = Q, then system is at equilibrium

(no shift occurs)2. If Q > K, [product]/[reactant] is too large (system shifts to left)3. If Q < K, [product]/[reactant] is too small (system shifts to the right)

Example 2. For the synthesis of ammonia, the value of K is 6 x 10-2 at 500oC. In an experiment, 0.50 mol of N2(g), 1.0 x 10-2 mol of H2(g), and 1.0 x 10-4 mol of NH3(g) are mixed at 500oC in a 1.0 L flask. In which direction will the system proceed to reach equilibrium? N2 + 3 H2 2NH3

Initial 0.50 mol/L 0.010 mol/L 1.0 x 10-4 mol/L

Q = [NH3]2 = (1.0 x 10-4)2 = 2.0 x 10-2

[N2][H2]3 (0.50)(1.0 x 10-2)3

Since Q < K, the reaction will shift to the right to reach equilibrium.

When solving equilibrium problems, it is very important to follow a series of steps. Skipping these can lead to problems (and fewer points on your AP exam).

STEPS FOR SOLVING EQUILIBRIUM PROBLEMS

1. Write a balanced equation. If a chemical reaction occurs, work out the stoichiometry and then write a second equation for the equilibrium reaction. Always do stoichiometry(in moles) first!

2. Set up the equilibrium expression. (No numbers yet!)

3. If you can't tell which way the reaction is going to shift, solve for Q.

4. Set up a chart that includes the equation, initial concentrations, changes in concentration in terms of X, and final concentrations.

5. Substitute these final concentrations into the equilibrium expression and solve for X.

6. Check your answer to make sure that it is logical!

When solving an equilibrium problem, some +x and -x values can be treated as negligible. X is considered negligible if it is less that 5% of the number that it was to be subtracted from or added to. If X is not negligible, the quadratic equation or the method of successive approximation must be used.

At 700 K, carbon monoxide reacts with water to form CO2

and H2: CO(g) + H2O(g) CO2(g) + H2(g)The equilibrium constant for this reaction at 700 K is 5.10. Consider an experiment in which 1.00 mol of CO(g) and 1.00 mol of H2O(g) are mixed together in a 1.00 L flask at 700 K. Calculate the concentrations of all species at equilibrium.

Reaction CO + H2O CO2 + H2

Initial 1.00 M 1.00 M 0 0Change -x -x +x +xEquil. 1.00-x 1.00-x x x

Keq = [CO2][H2] = 5.10 = x2 [CO][H2O] (1.00-x)2

x/(1.00-x) = 5.10 x = 0.69M[H2O]=[CO]= 1.00-0.69 = 0.31 M [CO2]=[H2]= 0.69 M

Example 4. Calculate the number of moles of Cl2 produced at equilibrium in a 10.0 L vessel when 1.00 mol of PCl5 is heated to 250oC. K = 0.041 mol/L

1.00 mol/10.0 L = 0.100 M

R PCl5(g) PCl3(g) + Cl2(g)

I 0.100 0 0

C -x +x +x

E 0.100-x x x

0.041 = x2 x2

0.100-x 0.100

x = 0.064M 0.064 is more than 5% of 0.100 so this is not a valid approximation.

Use of the quadratic equation:

x2 = 0.0041-0.041xx2 + 0.041x – 0.0041 = 0

x = 0.047 and –0.088(not possible)

[Cl2] = 0.047 moles Cl2 = 0.047M x 10.0 L = 0.47 moles Cl2

2)0041.0(4)041.0(041.0 2 x

aacbb

x2

42

Using successive approximation:When we assumed that x was

negligible, we got x = 0.064.#1 x = 0.038

#2 x = 0.050

#3 x = 0.045

#4 x = 0.047

064.0100.0041.0

2

x

038.0100.0041.0

2

x

050.0100.0041.0

2

x

045.0100.0041.0

2

x

#5 x = 0.046

#6 x = 0.047

#7 x = 0.047

047.0100.0041.0

2

x

047.0100.0041.0

2

x

046.0100.0041.0

2

x

or/ with a graphing calculator:

0.041 x 0.100 = 0.06403 (not negl) ((0.041)(0.100-ans)) = 0.038 =0.050

= 0.045 =0.047 =0.046

= 0.047 =0.047

Example 5. Consider the reaction 2HF(g) H2(g) + F2(g) where K = 1.0 x 10-2 at some very high temperature. In an experiment, 5.00 mol of HF(g), 0.500 mol of H2(g) , and 0.750 mol of F2(g) are mixed in a 5.00 L flask and allowed to react to equilibrium. Solve for the equilibrium concentrations.5.00 mol/5 L = 1.00 M HF

0.500 mol/5 L = 0.100 M H2

0.750 mol/5 L = 0.150 M F2

Q = [H2][F2] =(0.100)(0.150) = 0.015 [HF]2 (1.00)Q > K so reaction shifts left

Reaction 2HF H2 + F2

Initial 1.00 M 0.100 M 0.150 M

Change +2x -x -x

Equil. 1.00+2x 0.100-x 0.150-x

K = 1.0 x 10-2 = (0.100-x)(0.150-x)

(1.00 + 2x)2

Using the quadratic equation:0.960x2 - 0.290x + (5.00 x 10-3) = 0

)960.0(2)1000.5)(960.0(4)290.0(290.0( 32 x

x

x= 0.284 M and 0.0180 M

Since 0.284 > 0.100, it doesn't work!

x = 0.0180 M

[H2] = 0.10 - 0.0180 = 0.082 M

[F2] = 0.150 - 0.0180 = 0.132 M

[HF] = 1.00 + 2(0.0180) = 1.04 M

When K is very large, it is easier mathematically to work from completion backward to equilibrium rather than from initial concentrations forward to equilibrium. It is best to work with very large equilibria by determining what the concentrations would be at completion and then defining x to be the difference between completion and equilibrium.

The equilibrium position of the system lies very near the completion point of the reaction, so x is relatively small. Solving for x leads to the true equilibrium concentrations. In building a concentration table for a reaction with a large K, we add an additional row of information, the concentrations(or pressures) at completion. We can do this, even though the actual reaction never reaches completion, because the equilibrium position is the same no matter how it is approached.

Example 6 Nitrogen oxide reacts with oxygen to form nitrogen dioxide: 2NO(g) + O2(g) 2NO2(g)The Kc for this reaction is 3 x 106 at 200oC. Assume initial concentrations of 0.100M for NO and 0.050M for O2. Calculate the concentrations of all species present at equilibrium.

Since K is very large, this problem would be very difficult to solve in the conventional manner. The reaction will proceed almost to completion and x would be very large. We can take the reaction to completion and work backwards to find the equilibrium concentrations.

Watch out for a limiting reagent!

Reaction 2NO(g) + O2(g) 2NO2(g)

Initial Conc. 0.100 0.050 0

Change to Comp. –0.100 -0.050 +0.100

New Initial 0 0 0.100

Change to Equil +2x +x -2x

Equil Conc. 2x x 0.100-2x

RIC NICE!RIC NICE!

Kc = [NO2]2 _= 3 x 106 = (0.100-2x)2

[NO] 2[O2] (2x)2x

(0.100)2 4x3

x 9 x 10-4M

[NO2] 0.098

[NO] 1.8 x 10-3

[O2] 9 x 10-4

LeChatelier's Principle

When a stress is applied to a system, the equilibrium will shift in the direction that will relieve the stress.

Changes in concentration An increase in concentration of a reactant will cause equilibrium to shift to the right to form more products. An increase in concentration of a product will cause equilibrium to shift to the left to form more reactants.

A decrease in concentration of a product will cause equilibrium to shift to the right to form more products. A decrease in the concentration of a reactant will cause equilibrium to shift to the left to make more reactants.

A change in concentration of reactant or product will not affect the value of K.

If CO is increased, the forward reaction increases to reestablish equilibrium. Therefore the quantity of H2 will decrease and the quantity of product will increase. The value for the equilibrium constant (K) is unchanged.

If product is added to this system at equilibrium, the reverse reaction will increase to reestablish the equilibrium. Therefore quantities of both reactants (CO and H2) will increase. The value for the equilibrium constant (K) again remains unchanged.

Continuous removal of product from a reaction forces more of it to be produced, according to LeChatelier's Principle.

Metabolic reactions as well as industrial processes make use of this effect to continuously make products in equilibrium reactions.

A + B A + B C + D C + DAdd A or B -------->Add A or B -------->Remove A or B <-------Remove A or B <-------Add C or D <-------Add C or D <-------Remove C or D --------> Remove C or D -------->

Example: NExample: N22(g) + 3H(g) + 3H22(g) (g) 2NH2NH33(g)(g)

a. addition of Na. addition of N22

b. addition of NHb. addition of NH33

c. addition of Hc. addition of H22

d. removal of NHd. removal of NH33

Changes in temperature Changes in temperature may easily be treated as changes in concentration if you think of heat as a product (exothermic rxn) or a reactant (endothermic rxn).

An increase in temperature of an exothermic reaction will cause equilibrium to shift to the left. K will decrease. A decrease in temperature of an exothermic reaction will cause equilibrium to shift to the right. K will increase.

An increase in temperature of an endothermic reaction will cause equilibrium to shift to the right. K will increase. A decrease in temperature of an endothermic reaction will cause equilibrium to shift to the left. K will decrease.

EExxaammppllee:: NN22 ((gg)) ++ OO22((gg)) 22NNOO ((gg)) HH == 118811 kkJJ aa.. aaddddiittiioonn ooff hheeaatt bb.. lloowweerr tteemmppeerraattuurree EExxaammppllee:: 22SSOO22((gg)) ++ OO22 ((gg)) 22SSOO33 ((gg)) HH== --119988 kkJJ aa.. iinnccrreeaassee tteemmppeerraattuurree bb.. rreemmoovvee hheeaatt

Changes in pressureChanges in pressure only affect equilibrium systems having gaseous products and/or reactants. Increasing the pressure of a gaseous system will cause equilibrium to shift to the side with fewer gas particles.

Decreasing the pressure of a gaseous system will cause equilibrium to shift to the side with more gas particles.

If the system has the same number of moles of gas on each side, changes in pressure do not affect equilibrium.

Adding an inert gas does not affect equilibrium since the partial pressures of the gases in the reaction are not affected.

Changing pressure does not affect the value of the equilibrium constant.

Example: PExample: P44((ss) + 6Cl) + 6Cl22((gg) ) 4PCl 4PCl33((ll))

a. increase container volumea. increase container volumeb. decrease container volumeb. decrease container volumec. add argon gasc. add argon gas

Example: PClExample: PCl33((gg) + Cl) + Cl22((gg) ) PCl PCl55((gg))

a. decrease container volumea. decrease container volumeb. add helium gasb. add helium gas

Example: Example: PClPCl33((gg) + 3NH) + 3NH33((gg) ) P(NH P(NH22))33((gg) + 3HCl() + 3HCl(gg))

a. increase container volumea. increase container volume

In the production of ammonia from nitrogen and hydrogen, raising the temperature favors the reverse reaction, which absorbs heat. Temperature and pressure are carefully produced in the industrial production of ammonia, exploiting LeChatelier's Principle to maximize the amount of product obtained. The production of ammonia is of tremendous importance in feeding the world--since ammonia is used as fertilizer.

In the production of ammonia from nitrogen and hydrogen, raising the pressure favors the forward reaction because 4 moles of gas is converted to 2 moles of gas.

Addition of a catalyst Adding a catalyst does not affect equilibrium.

Example 6. Consider the reaction 2NO2(g) N2(g) + 2O2(g) which is exothermic. A vessel contains NO2(g), N2(g), and O2(g) at equilibrium. Predict how each of the following stresses will affect the concentration of O2 and the value of K.A. NO2 is added

B. N2 is removed

C. The volume is halved

D. He(g) is added

E. The temperature is increased

F. A catalyst is added