AP Chemistry (General Equilibrium) Notes (Chapter 10)
Chemical equilibrium is when two opposing reactions occur simultaneously and at the same rate.
For example:
A + B → C + D
and C + D → A + B
This is usually written as a reversible equation using double arrows:
A + B ⇌ C + D
What equilibrium is not:
• equal amounts of products and reactants
• permanent
• instantly establish
• a stop in the chemical reaction
• for reactions that go to completion (like dissociation of a strong acid)
• the same for every condition of T
Example case 1:
in a 1 L vessel
R 2SO2 + O2 ⇌ 2SO3
I 0.400 mol 0.200 mol 0
C -0.056 mol -0.028 mol + 0.056 mol
E 0.344 mol 0.172 mol 0.056 mol
in 1 L vessel the above mols are also M
Describe what occurred here. ______
Example case 2:
in a 1 L vessel
R 2SO2 + O2 ⇌ 2SO3
I 0 0 0.500 mol
C +0.424 mol +0.212 mol -0.424 mol
E 0.424 mol 0.212 mol 0.076 mol
in 1 L vessel the above mols are also M
Describe what occurred here.
______
Suppose we want a rate law:
for case 1 (forward reaction)
ratef = kf [SO2]2[O2]
for case 2 (reverse reaction)
rater = kr [SO3]2
(for only 1 step it is the slow step, so the coefficients = order)
At equilibrium ratef = rater (by definition)
kf / = Kc = / [SO3]2kr / [SO2]2[O2]
If ratef = rater
then kf [SO2]2[O2] = kr [SO3]2
rearranging to group terms…
What is on top, and what is on bottom, in relationship to the forward reaction?
______
Kc is called the equilibrium (concentration) constant (capitol K) and the c is sometimes left off
What is the value of the equilibrium constant, Kc, for case 1?
Kc = / (0.056)2 / = 0.15(0.344)2 (0.172)
Kc is unitless, so be sure the units on all your numbers match!
What is the value of the equilibrium constant, Kc, for case 2?
Kc = / (0.076)2 / = 0.15(0.424)2 (0.212)
What do you notice?
______
Did you notice for both cases we used the forward reaction? If we used the reverse reaction, we would have gotten a different K, but it would still be related to the forward K, it is just the inverse.
So Kforward = 1/Kreverse or Kreverse = 1/Kforward
Let’s try it…
Example case 2:
in a 1 L vessel
R 2SO3 ⇌ 2SO2 + O2
I 0.500 mol 0 0
C -0.424 mol +0.424 mol +0.212 mol
E 0.076 mol 0.424 mol 0.212 mol
What is Kc and what is 1/Kc for this reaction?
______
One other thing, if perhaps many equilibrium reactions are involved in a mechanism, and you are given the K for each step, the total can be found as…
Ktotal = K1 K2 K3…
In general for aA + bB ⇌ cC + dD
Kc = / [C]c[D]d[A]a[B]b
How would this change if the number of products or reactants was different?
______
Remember, the assumption is this is the only step in the mechanism or is the slow step; otherwise the coefficients don’t necessarily match the exponents.
So Kc is a measure of how much the reaction has occurred (the activity of the reaction).
The bigger the Kc the more products and less reactants. Explain.
______
What would be Kc for no reaction?
______
What would be Kc for a strong acid/base?
______
Practice:
in a 5 L vessel
R N2 + 3H2 ⇌ 2NH3
I
C
E 3.01 mol 2.10 mol 0.565 mol
Find Kc
______
Practice:
in a 2 L vessel
R 2N2O ⇌ 2N2 + O2
I 10.0 mol 0 0
C
E 2.20 mol
Find Kc
______
In the previous example the reactant and products were gases, but we used Molarity anyway. Sometimes when all the substances are gases it is easier to use their partial pressures instead of concentrations, so…
Kp = / (PC)c(PD)d(PA)a(PB)b
Why call it Kp? What would the units be?
______
Kp is not the same as Kc, because [] is only dependent on the moles and volume where P is also dependent on temperature and the gas constant, but if these are accounted for, then…
Kp = Kc(RT)Δn
where Δn = ngas products - ngas reactants
When would Kp = Kc ?
______
What if we don’t know if a reaction is at equilibrium yet?
We then determine the reaction quotient, Q
Q = / [C]c[D]d[A]a[B]b
if Q < Kc , then it is not yet at equilibrium
forward reaction will still be faster
if Q > Kc, then it is past equilibrium
reverse reaction will now be faster
if Q = Kc, then it is at equilibrium
Practice:
For 2HI ⇌ H2 + I2 the Kc = 65.0
if E 0.500M 0.280 M 3.40 M
is this at equilibrium?
______
______
______
Typically Kc is used to find the concentration of reactants and products at equilibrium. For example, what is the equilibrium concentrations if Kc = 49.0
R A + B ⇌ C + D
I 0.200 M 0.200 M 0 0
______
______
______
What is the equilibrium concentrations if Kc = 49.0
R A + B ⇌ C + D
I 0.300 M 0.100 M 0 0
______
______
Changes to equilibrium:
• if [] or pressure/volume changes or a catalyst is added, then Q changes, but Kc will not change, so the reaction rates will change to get Q = Kc again (LeChatelier’s can tell you how it will change, shifting right or left means speeding up forward or reverse reaction)
• if T changes then Kc will change, so Q = Kc will happen, but it will be a new Kc
Let’s practice using LeChatelier’s Principle
If 2A(g) + 3B(g) ⇌ C(g) + 2D(g)
Then for each change, state how it will shift (forward or reverse) and why it will shift (Q less than K or Q greater than K)
If 2A(g) + 3B(g) ⇌ C(g) + 2D(g)
Pressure is increased:
What affect does that have? ______
How will the equilibrium shift?
______
Why will the equilibrium shift? ______
If 2A(g) + 3B(g) ⇌ C(g) + 2D(g)
Pressure is decreased:
What affect does that have?
______
How will the equilibrium shift? ______
Why will the equilibrium shift?
______
If 2A(g) + 3B(g) ⇌ C(g) + 2D(g)
Volume is increased:
What affect does that have? ______
How will the equilibrium shift? ______
Why will the equilibrium shift? ______
If 2A(g) + 3B(g) ⇌ C(g) + 2D(g)
Volume is decreased:
What affect does that have? ______
How will the equilibrium shift? ______
Why will the equilibrium shift? ______
Explain why pressure and volume can only affect Kp and not Kc. ______
What change would affect Kc? ______
If 2A(g) + 3B(g) ⇌ C(g) + 2D(g)
[A] is increased:
What affect does that have? ______
How will the equilibrium shift? ______
Why will the equilibrium shift? ______
If 2A(g) + 3B(g) ⇌ C(g) + 2D(g)
[A] is decreased:
What affect does that have? ______
How will the equilibrium shift? ______
Why will the equilibrium shift? ______
If 2A(g) + 3B(g) ⇌ C(g) + 2D(g)
[D] is increased:
What affect does that have? ______
How will the equilibrium shift? ______
Why will the equilibrium shift? ______
If 2A(g) + 3B(g) ⇌ C(g) + 2D(g)
[D] is decreased:
What affect does that have? ______
How will the equilibrium shift? ______
Why will the equilibrium shift? ______
Why would catalysts not change the equilibrium? ______
______
Why would the addition of inert gases not change the equilibrium? ______
______
What affect does changing temperature have on equilibrium? ______
What can we do with LeChatelier’s principle? ______
If 2A(g) + 3B(g) ⇌ C(g) + 2D(g) + Heat
Temperature is increased:
What affect does that have? ______
How will the equilibrium shift? ______
Why will the equilibrium shift? ______
If 2A(g) + 3B(g) ⇌ C(g) + 2D(g) + Heat
Temperature is decreased:
What affect does that have? ______
How will the equilibrium shift? ______
Why will the equilibrium shift? ______
If 2A(g) + 3B(g) + Heat ⇌ C(g) + 2D(g)
Temperature is increased:
What affect does that have? ______
How will the equilibrium shift? ______
Why will the equilibrium shift? ______
If 2A(g) + 3B(g) + Heat ⇌ C(g) + 2D(g)
Temperature is decreased:
What affect does that have? ______
How will the equilibrium shift? ______
Why will the equilibrium shift? ______
If 2A(g) + 3B(g) ⇌ C(g) + 2D(g)
∆H = + 76 kJ/mol
Temperature is decreased:
What affect does that have? ______
How will the equilibrium shift? ______
Why will the equilibrium shift? ______
If 2A(g) + 3B(g) ⇌ C(g) + 2D(g)
∆H = - 76 kJ/mol
Temperature is increased:
What affect does that have? ______
How will the equilibrium shift? ______
Why will the equilibrium shift? ______
Practice:
in a 1 L vessel, H2 + I2 ⇌ 2HI
at equilibrium [HI] = 0.490 M, [H2] = 0.080 M and [I2] = 0.060 M
then 0.300 more moles of HI is added, what will be the new equilibrium concentrations?
First, find the Kc
______
______
______
Next, find the new [] with the addition and find Q (we are sure we are not at equilibrium!)
______
______
______
Then, we set us a RICE Table with the new initial [] and the change that Q vs Kc told us would happen, finally solve for x
______
______
______
______
______
______
There are other things we can do with K:
1) Remember ΔG0rxn? ΔG0rxn is the energy change as ALL reactants react to produce ONLY products. In an equilibrium we still have some reactants left over, so this can be accounted for…
ΔG0rxn = -RTlnK (can be Kc or Kp or Q)
Why would ΔG0rxn be less if there are still some reactants left over? ______
Another form, on the equation pages:
∆G = ∆G° + RTlnQ
Why Q, not K? ______
Notice! For both of these equations R is used in Joules but G is typically measured in kiloJoules. Be careful that the units match!
2) The Nernst equation should actually look like this:
Ecell = E°cell - / RT / lnQnF
Why Q, and not K?
______
R would be in volt coulombs mol-1 k-1!
3) As mentioned earlier, K varies with Temperature, but thanks to van’t Hoff’s equation we can calculate the K at a new temperature if ΔH0 is known.
ln ( / KT2 / ) = / ΔH0 / ( / 1 / - / 1 / )KT1 / R / T1 / T2