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Learning goals and key skills: Explain what is meant by chemical equilibrium and how it relates to reaction rates Write the equilibrium-constant expression for any reaction Convert Kc to Kp and vice versa Relate the magnitude of an equilibrium constant to the relative amounts of reactants and products present in an equilibrium mixture. Manipulate the equilibrium constant to reflect changes in the chemical equation Write the equilibrium-constant expression for a heterogeneous reaction Calculate an equilibrium constant from concentration measurements Predict the direction of a reaction given the equilibrium constant and the concentrations of reactants and products Calculate equilibrium concentrations given the equilibrium constant and all but one equilibrium concentration Calculate equilibrium concentrations given the equilibrium constant and the starting concentrations Use Le Chatelier’s principle to predict how changing the concentrations, volume, or temperature of a system at equilibrium affects the equilibrium position.
Chapter 15
Chemical Equilibrium
The Concept of Equilibrium
Chemical equilibrium occurs when a reaction and its reverse reaction proceed at the same rate.
Concept of Equilibrium
- As a system approaches equilibrium, both the forward and reverse reactions are occurring.
- At equilibrium, the forward and reverse reactions are proceeding at the same rate.
- Once equilibrium is achieved, the amount of each reactant and product remains constant.
The same equilibrium is reached whether we
start with only reactants (N 2 and H 2 ) or with
only product (NH 3 ).
Equilibrium is reached from either direction.
Equilibrium Constant
- Therefore, at equilibrium
Ratef = Rater
kf [N 2 O 4 ] = kr [NO 2 ]^2
- Rewriting this, it becomes
kf
kr
[NO 2 ]
[N 2 O 4 ]
Keq =
kf
kr
[NO 2 ]
[N 2 O 4 ]
= = a constant
Example
N 2 (g) + 3 H 2 (g) ⇌ 2 NH 3 (g) Write the equilibrium constant expression of the following reaction:
Relationship Between Kc and Kp
Plugging this into the expression for Kp
for each substance, the relationship
between Kc and Kp becomes
where
Kp = Kc (RT)
n n = (moles of gaseous product) - (moles of gaseous reactant)
From the Ideal Gas Law we know that:
PV = nRT and P = (n/V)RT = [A]RT
What Does the Value of K Mean?
- If K>>1, the reaction is product-favored; product predominates at equilibrium.
- If K<<1, the reaction is reactant-favored; reactant predominates at equilibrium. *When 10-3^ < K < 10^3 , the reaction is considered to contain a significant amount of both reactants and products at equilibrium.
2 NOBr ⇌ 2 NO + Br 2 K 1 = 0.
Br 2 + Cl 2 ⇌ 2 BrCl K 2 = 7.
2 NOBr + Cl 2 ⇌ 2 NO + 2 BrCl
K 3 = K 1 × K 2 = 0.014 × 7.2 = 0.
The equilibrium constant for a net reaction
made up of two or more steps is the
product of the equilibrium constants for the
individual steps.
Multiple equilibria and K
Example
Consider the following reactions at 1200 K. CO(g) + 3 H 2 (g) ⇌ CH 4 (g) + H 2 O(g) Kc,1 = 3. CH 4 (g) + 2 H 2 S(g) ⇌ CS 2 (g) + 4 H 2 (g) Kc,2 = 3.3x10^4 Use the above reactions to determine the equilibrium constant (Kc) for the following reaction at 1200 K. CO(g) + 2 H 2 S(g) ⇌ H 2 O(g) + CS 2 (g) + H 2 (g)
Homogeneous vs Heterogeneous
Homogeneous equilibria occur when all reactants and products are in the same phase. Heterogeneous equilibria occur when reactant or product in the equilibrium is in a different phase.
- The value used for the concentration of a pure substance is always 1. Therefore, the concentrations of solids and liquids do not appear in the equilibrium expression.
Kc = [Pb2+][Cl-]^2
PbCl 2 (s) ⇌ Pb2+(aq) + 2 Cl-(aq) As long as some CaCO 3 or CaO remain in the system, the amount of CO 2 above the solid will remain the same. Kc = [CO 2 ] and Kp = PCO 2
What Do We Know?
[H 2 ], M [I 2 ], M [HI], M
Initially 1.000 x 10-3^ 2.000 x 10-3^0 Change Equilibrium 1.87 x 10-
[HI] Increases by 1.87 x 10-3^ M
[H 2 ], M [I 2 ], M [HI], M
Initially 1.000 x 10-3^ 2.000 x 10-3^0 Change +1.87 x 10- Equilibrium 1.87 x 10-
Stoichiometry tells us [H 2 ] and [I 2 ]
decrease by half as much.
[H 2 ], M [I 2 ], M [HI], M
Initially 1.000 x 10-3^ 2.000 x 10-3^0 Change -9.35 x 10-4^ -9.35 x 10-4^ +1.87 x 10- Equilibrium 1.87 x 10-
Calculate the equilibrium concentrations
of all three compounds…
[H 2 ], M [I 2 ], M [HI], M
Initially 1.000 x 10-3^ 2.000 x 10-3^0 Change -9.35 x 10-4^ -9.35 x 10-4^ +1.87 x 10- Equilibrium 6.5 x 10-5^ 1.065 x 10-3^ 1.87 x 10- Kc = [HI]^2 [H 2 ] [I 2 ]
(1.87 x 10-3)^2 (6.5 x 10-5)(1.065 x 10-3)
If Q < K
- There’s too much reactant
- Need to increase the amount of products and decrease the amount of reactants If Q > K
- There’s too much product
- Need to decrease the amount of products and increase the amount of reactants Comparing K and Q Example A 50.0 L reaction vessel contains 1.00 mol N 2 , 3. mol H 2 , and 0.500 mol NH 3. Will more ammonia (NH 3 ) be formed or will NH 3 dissociate when the reaction mixture approaches equilibrium at 400 °C? N 2 (g) + 3H 2 (g) ⇌ 2NH 3 (g) Kc = 0.500 at 400 °C.
Example In the steam-reforming reaction, methane reacts with water vapor to form carbon monoxide and hydrogen gas. At 900 K, Kc = 2.4 × 10-4. If 0.012 mol of methane, 0.0080 mol of water vapor, 0.016 mol of carbon monoxide and 0.0060 mol of hydrogen gas are placed in a 2.0-L steel reactor and heated to 900 K, which way will the reaction proceed: to the right (products) or left (reactants)? Problem: Finding equilibrium concentrations from initial concentrations and the equilibrium constant. Example A reaction mixture at 2000 °C initially contains [N 2 ] = 0.200 M and [O 2 ] = 0.200 M. Find the equilibrium concentrations of the reactants and products at this temperature.
- Represent the change in concentration of one of the reactants (or products) with the variable ‘x’.
- Define the changes in concentration of the other reactants and/or products in terms of x.
- Tip: Usually convenient to let x represent the change in concentration of the reactant (or product) with the smallest stoichiometric coefficient. N 2 (g) + O 2 (g) ⇌ 2NO(g) Kc = 0.10 at 2000 °C
N2 (g) + 3 H2 (g) ⇌ 2 NH3 (g) Kp = 0.0214 at 540 K
Example: Le Châtelier’s Principle
At equilibrium PH2 = 2.319 atm PNH3 = 0.454 atm PN2 = 0.773 atm What happens upon addition of 1 atm of H 2?
The Haber Process
This apparatus helps push the equilibrium to the right by removing the ammonia (NH 3 ) from the system as a liquid.
Change in Volume or Pressure
If gases are involved in an equilibrium, a
change in pressure or volume will affect K:
- Higher volume or lower pressure favors the side of the equation with more moles of gas (and vice-versa).
The Effect of Changes in Temperature
Co(H 2 O) 6 2+^ (aq) + 4 Cl-^ (aq) ⇌ CoCl 4 2-^ (aq) + 6 H 2 O (l)
Example: Le Châtelier’s Principle
N 2 O 4 (g) 2 NO 2 (g) is endothermic.
What occurs with increasing temperature?
Catalysts
Catalysts increase the rate of both the forward and reverse reactions. When one uses a catalyst, equilibrium is achieved faster, but the equilibrium composition remains unaltered.
