Home / AP Chemistry 7.6 Properties of the Equilibrium Constant Study Notes

AP Chemistry 7.6 Properties of the Equilibrium Constant Study Notes

AP Chemistry 7.6 Properties of the Equilibrium Constant Study Notes - New Syllabus Effective fall 2024

AP Chemistry 7.6 Properties of the Equilibrium Constant Study Notes- New syllabus

AP Chemistry 7.6 Properties of the Equilibrium Constant Study Notes – AP Chemistry –  per latest AP Chemistry Syllabus.

LEARNING OBJECTIVE

Represent a multistep process with an overall equilibrium expression, using the constituent K expressions for each individual reaction.

Key Concepts: 

  • Calculating the Equilibrium Constant
  • Magnitude of the Equilibrium Constant
  • Manipulating the Equilibrium Constant

AP Chemistry-Concise Summary Notes- All Topics

AP Chemistry Exam Questions MCQs and FRQs

7.6.A.1 Reversing a Reaction: Inversion of K:

1. Equilibrium Constant (K) Definition:

The equilibrium constant (K) is the ratio of the product concentration to the reactant concentration at equilibrium:

For a reaction

aA + bB \rightleftharpoons cC + dD

:

K=[C]c[D]d[A]a[B]b

– K > 1: favors products.
– K < 1: favors reactants.
– K ≈ 1: Both are available in equal amounts.

In brief, K indicates the degree of a reaction at equilibrium.

2. Effect of Reversing a Reaction:

When a reaction is reversed, the equilibrium constant (K) changes to the inverse of its original value.

For a reaction:

 

aA+bB⇌cC+dDwithK=[C]c[D]d[A]a[B]baA + bB \rightleftharpoons cC + dD \quad \text{with} \quad K = \frac{[C]^c [D]^d}{[A]^a [B]^b}

 

If the reaction is reversed:

 

cC+dD⇌aA+bBcC + dD \rightleftharpoons aA + bB

 

The equilibrium constant for the reversed reaction becomes:

 

Kreverse=1KK_{\text{reverse}} = \frac{1}{K}

 

3. Example of Reaction Reversal:

Example 1: Haber Process

Forward:

 

N2(g)+3H2(g)⇌2NH3(g)K=[NH3]2[N2][H2]3N_2 (g) + 3H_2 (g) \rightleftharpoons 2NH_3 (g) \quad K = \frac{[NH_3]^2}{[N_2][H_2]^3}

 

Reversed:

 

2NH3(g)⇌N2(g)+3H2(g)Kreverse=1K2NH_3 (g) \rightleftharpoons N_2 (g) + 3H_2 (g) \quad K_{\text{reverse}} = \frac{1}{K}

 

Example 2: Dissociation of Hydrogen Iodide

Forward:

 

2HI(g)⇌H2(g)+I2(g)K=[H2][I2][HI]22HI (g) \rightleftharpoons H_2 (g) + I_2 (g) \quad K = \frac{[H_2][I_2]}{[HI]^2}

 

Reversed:

 

H2(g)+I2(g)⇌2HI(g)Kreverse=1KH_2 (g) + I_2 (g) \rightleftharpoons 2HI (g) \quad K_{\text{reverse}} = \frac{1}{K}

 

Summary: Reversing a reaction makes K equal to 1/K.

 

7.6.A.2 Stoichiometric Coefficients and K: K Raised to the Power of c:

1. Equilibrium Constant (K) Definition:

The equilibrium constant (K) depends on the stoichiometric coefficients in a balanced chemical equation. For a reaction:

The expression of the equilibrium constant is:

K=[C]c[D]d[A]a[B]b

The exponents of the concentrations (or the partial pressures of gases) are equal to the stoichiometric coefficients of the reactants and products in the balanced equation:

– a, b are coefficients of reactants A and B.
– c, d are coefficients of products C and D.

### Key Points:
– The stoichiometric coefficients specify the exponents to which the concentrations of the reactants and products are raised in the equation for K.
– Doubling the coefficients (for example, 2A+2B→2C+2D results in K’ = K^2.
– Halving the coefficients (e.g.,) provides K’ = (sqrt{K}).

Briefly, the stoichiometric coefficient control the form of the equilibrium constant expression.

2. Effect of Multiplying Coefficients by c:

When the stoichiometric coefficients of a reaction are multiplied by a factor c, the equilibrium constant (K) changes in a specific way.

General Reaction:

aA+bB⇌cC+dDaA + bB \rightleftharpoons cC + dD

The equilibrium constant is:

K=[C]c[D]d[A]a[B]bK = \frac{[C]^c [D]^d}{[A]^a [B]^b}

Effect of Scaling Coefficients by c:

If we multiply all coefficients by a factor c (e.g.,

aA+bB→cC+dDaA + bB \rightarrow cC + dD

becomes

caA+cbB→ccC+cdDcaA + cbB \rightarrow ccC + cdD

), the new equilibrium constant K’ is:

K′=KcK’ = K^c

Example:

For the reaction:

N2(g)+3H2(g)⇌2NH3(g)N_2 (g) + 3H_2 (g) \rightleftharpoons 2NH_3 (g)

The equilibrium constant is:

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

If we multiply the coefficients by 2:

2N2(g)+6H2(g)⇌4NH3(g)2N_2 (g) + 6H_2 (g) \rightleftharpoons 4NH_3 (g)

The new equilibrium constant is:

K′=K2=([NH3]2[N2][H2]3)2=[NH3]4[N2]2[H2]6K’ = K^2 = \left( \frac{[NH_3]^2}{[N_2][H_2]^3} \right)^2 = \frac{[NH_3]^4}{[N_2]^2 [H_2]^6}

Summary:

When you multiply the stoichiometric coefficients by c, the equilibrium constant K is raised to the power of c: K’ = K^c.

7.6.A.3 Adding Reactions: K as the Product of Individual Ks: 

1. Equilibrium Constant (K):

The equilibrium constant (K) defines how a reaction reaches equilibrium and indicates whether products or reactants are favored. Its value is influenced by the nature of the reaction and temperature, but it remains constant once equilibrium is established under specific conditions.

2. Addition of Reactions:

When two or more reactions are added together, the overall equilibrium constant (K) for the combined reaction is the product of the individual equilibrium constants.

General Rule:

If you have two reactions:

  1. Reaction 1:

    A⇌BA \rightleftharpoons B with K1K_1

  2. Reaction 2:

    C⇌Dwith K2K_2

When these reactions are added (i.e., combined):

A+C⇌B+DA + C \rightleftharpoons B + D

The equilibrium constant for the combined reaction, K total, is:

Ktotal=K1×K2K_{\text{total}} = K_1 \times K_2

Example:

  • Reaction 1:

    N2(g)+3H2(g)⇌2NH3(g) with K1K_1

  • Reaction 2:

    2NH3(g)⇌N2(g)+3H2(g) with K2K_2

Adding these reactions:

(N2+3H2⇌2NH3)+(2NH3⇌N2+3H2)(N_2 + 3H_2 \rightleftharpoons 2NH_3) + (2NH_3 \rightleftharpoons N_2 + 3H_2)

The overall reaction:

N2+3H2⇌N2+3H2N_2 + 3H_2 \rightleftharpoons N_2 + 3H_2

The equilibrium constant for this combined reaction would be:

Ktotal=K1×K2K_{\text{total}} = K_1 \times K_2

Summary:

When reactions are added together, the overall equilibrium constant Ktotal is the product of the individual equilibrium constantsK1, K2,…

 
 

7.6.A.4 K and Q: Identical Mathematical Forms and Algebraic Manipulations:

1. K and Q Comparison:

K (Equilibrium Constant) and Q (Reaction Quotient) have the same mathematical expression:

K or Q=[C]c[D]d[A]a[B]b\text{K or Q} = \frac{[C]^c [D]^d}{[A]^a [B]^b}

– K when the reaction is in equilibrium.

– Q when the reaction is at any time.

Comparison:
– Q < K: Reaction goes forward (towards the products).
– Q > K: Reaction goes backwards (towards reactants).
– Q = K: The system is at equilibrium.

2. Algebraic Manipulations:

The algebraic conditions for K (equilibrium constant) and Q (reaction quotient) are the same:

i. Multiplying reactions:

or .

ii. Reversing a reaction:
or Qreverse=1/Q

. Scaling reaction coefficients by c:

Kscaled=KcK_{\text{scaled}} = K^c

or

Qscaled=QcQ_{\text{scaled}} = Q^c

Thus, the very same conventions can be used for both K and Q to combine, reverse, or scale reactions.

 

OLD Content

Properties of the Equilibrium Constant

  • The equilibrium constant of the reverse reaction is the reciprocal of the K value of the forward reaction
    • Ex: Forward reaction: →

       (flip it) Reverse Reaction: →

  • When the equation for a reaction is multiplied by n,
    • Ex:  →

        mult. by factor of 2:  →

  • When multiple reactions (elementary steps) are added together, the K of the overall reaction is the product (multiply) of the K’s from the reactions that were added
Scroll to Top