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Wize High School Grade 12 Chemistry Textbook > Equilibrium

The Equilibrium Constant (K)

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Equilibrium Constant (K)

To define the extent to which equilibrium favors one side of the reaction over the other, we can use the Equilibrium Constant.

Given the model reaction:
aA+bB⇌cC+dD\large{aA +bB \rightleftharpoons cC + dD}
A & B are reactants and C & D are products.
a,b,c,d are their stoichiometric coefficients


The Equilibrium Expression (in terms of concentration) can be written as:


Kc=[ Products][Reactants]=[C]c[D]d[A]a[B]b\large\boxed{K_c=\frac{\left[\ Products\right]}{\left[Reactan ts\right]}=\frac{\left[C\right]^c\left[D\right]^d}{\left[A\right]^a\left[B\right]^b}}


The equilibrium constant (K) is a ratio used to describe the relative concentrations of products and reactants at equilibrium!
You may also see it called the Law of Mass Action.


Examples:
Keq (at equilibrium), Ka (for acids), Kb (for bases), Kw (for water), Ksp (solubility product constant)

Wize Concept
K can have different subscripts, but all K's follow the same rules!

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Example: What is the K expression for the reaction below?

N2(g) + 3H2(g) ⇌ 2NH3(g)


Wize Tip
Since coefficients become exponents in the K expression, we need to make sure that our equation is balanced!


K= [NH3]2[N2][H2]3\frac{\left[NH_3\right]^2}{\left[N_2\right]\left[H_2\right]^3}

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Additional Notes About K:

1) Above we wrote Kc. The c stands for concentration because we are considering the concentrations of the species in mol/L.

2) If instead we were considering gases and their pressures in atm, then we would write Kp!

Example: What is the Kp expression for the following reaction?

2SO2(g) + O2(g) ⇌ 2SO3(g)



Kp=(PSO3)2(PSO2)2(PO2)Kp=\frac{\left(PSO_3^{ }\right)^2}{\left(PSO_2\right)^2\left(PO_2\right)}


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3) If any species in the reaction are solids (s) or liquids (l), their concentrations do not affect equilibrium and therefore they do not appear in the equilibrium expression!

Example: What is the equilibrium expression for the following reaction?

PbCl2(s) ⇌ Pb2+ (aq) + 2Cl- (aq)

K= [Pb2+][Cl-]2


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4) We will see that changes in volume, pressure, temperature, and concentration can shift the equilibrium (according to Le Chatelier's Principle)

But the only factor that will change K is temperature!



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The Magnitude of the Equilibrium Constant, K

K tells us which side of the reaction (products or reactants) are favored and to what extent.

Example:
If we had the K value 1.8x1010 would products or reactants be favored at equilibrium?
Products!

Since there is an exponent of 10, then (products/reactants)
products
are favored to a (small/great)
great
extent!




Example:
If K was 1.2x10-8 then are products or reactants favored at equilibrium? And to a great or small extent?

Reactants
are favored to a
great
extent!

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Example: Are products or reactants favored at equilibrium according to the following reaction and concentration time graph?

2SO2(g) + O2(g) ⇌ 2SO3(g)

Photo by OpenStax / CC BY

Products are favored at equilibrium since at equilibrium (when the concentrations start to get flat in the graph), there is a higher concentration of SO3 (a product) than the reactants.

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Summary of What K Tells Us

Kc=[ Products][Reactants]\large{K_c=\frac{\left[\ Products\right]}{\left[Reactan ts\right]}}

Keq > 1

  • At equilibrium, products/reactants are favored:
    products
  • This is because products/reactants are more stable:
    products
  • As a result, at equilibrium there will be more reactants, more products, or equal amounts of products and reactants:
    more products

Keq = 1

  • At equilibrium, products/reactants are favored:
    neither
  • This is because products/reactants are more stable:
    equally stable
  • As a result, at equilibrium there will be more reactants, more products, or equal amounts of products and reactants:
    equal amounts

Keq < 1

  • At equilibrium, products/reactants are favoured:
    reactants
  • This is because products/reactants are more stable:
    reactants
  • As a result, at equilibrium there will be more reactants, more products, or equal amounts of products and reactants:
    more reactants

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Which of the following expression is the correct equilibrium-constant expression for the reaction below?

HF(aq) + H2O(l) ⇌ H3O+(aq) + F-(aq)

1.
Kc=[HF][H2O][H3O+][F−]K_c=\frac{[HF][H_2O]}{[H_3O^+][F^-]}
2.
Kc=1[HF]K_c=\frac{1}{[HF]}
3.
Kc=[H3O+][F−][HF][H2O]K_c=\frac{[H_3O^+][F^-]}{[HF][H_2O]}
4.
Kc=[H3O+][F−][HF]K_c=\frac{[H_3O^+][F^-]}{[HF]}
5.
Kc=[F−][HF]K_c=\frac{[F^-]}{[HF]}




For the process: N2 (g) + 3 H2 (g) ⇌ 2 NH3 (g)
Determine the value of Kc when an equilibrium mixture contains 0.0420 mol N2, 0.516 mol H2, and 0.0357 mol NH3 in a 1.00 liter container at 400oC.

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Earlier we learned about how only one factor changes K (the equilibrium constant) and that factor is temperature.

Given the reaction:
H2(g) + I2(g) ⇌ 2HI(g) + heat

At 448oC K=50.5. Would you predict the K value to be higher or lower at 348oC?
Extra Practice
Equilibrium constant
For the following equilibria determine whether K>1K > 1, K<1K < 1 or K≈1K \approx 1. Enter your answers as "Greater", "Less", "1" respectively.
A)
B)
Equilibrium: Reaction quotient
If the reaction A⇌BA⇌B has an equilibrium constant of K = 10–4, which one of the following statements is always true?
Equilibrium and Le Chatelier's Principle
At time = t0, 0.40 mol of Br2 (ℓ) and 0.40 mol of Cℓ2 (g) are placed in an empty, rigid 10.00 L flask and allowed to reach equilibrium.
After reaching equilibrium at time = t2, the flask is found to contain 0.20 mol of BrCℓ (g). The temperature is held constant throughout the reaction.
Equilibrium Constant
Balance each reaction and write its equilibrium constant expression
NO(g)+O2(g)↔N2O3(g)NO_{(g)}+O_{2(g)} \leftrightarrow N_2O_{3(g)}
SF6(g)+SO3(g)↔SO2F2(g)SF_{6(g)}+SO_{3(g)}\leftrightarrow SO_2F_{2(g)}
Le Chatelier's Principle: Equilibrium constant
Consider the following reaction:
PCℓ5(g)⇌PCℓ3(g)+Cℓ2(g)PCℓ_5 (g) ⇌ PCℓ_3 (g) + Cℓ_2 (g)
The measured equilibrium constant is 5.0x10–4 at 373 K and 0.20 at 473 K. Which of the following statements about the reaction must be true?
Equilibrium: Constant
At 25 ˚C, KP = 5.2 × 10–2 for the following decomposition reaction:
NH4HS(s)⇌NH3(g)+H2S(g)NH_4HS (s) ⇌ NH_3 (g) + H_2S (g)
(a) Calculate the equilibrium partial pressures of ammonia (NH3) and hydrogen sulfide (H2S) if a sample of solid NH4HS is placed in a closed vessel initially containing 11 atm of NH3 gas. Note that the vessel still contains some solid NH4HS at equilibrium. State and justify any assumptions you might make during your calculation.
Equilibrium plots: Equilibrium constant
You mix three unknown compounds in a container: a solid (A), and two gases (E and X). You do not know the chemical formula of any of the compounds, but you are able to track the progress of the reaction by measuring changes in the concentrations of both gases, as shown in the graph below.
Which of these reactions and equilibrium constants could be represented by the data shown in this graph?