R2.3.3 Magnitude of K and temperature dependence

Equilibrium Constants and Their Applications

The Equilibrium Constant ( $K$ )

As discussed in the previous section, the equilibrium constant $K$ is a quantitative measure of the position of equilibrium for a chemical reaction. It is expressed as:

$K = \frac{[Products]^{stoichiometric coefficients}}{[Reactants]^{stoichiometric coefficients}}$

Note

The magnitude of $K$ provides valuable information about the extent of a reaction at equilibrium.

When $K << 1$ : Reactants are Favored
- A very small $K$ value (e.g., $K = 10^{- 5}$ ) indicates that the equilibrium position is heavily skewed toward the reactants.
- Only a small proportion of reactants has been converted into products.

Example

Dissociation of Water

In the reaction $H_{2} O ⇋ H^{+} + {OH}^{-}$ , $K \approx 10^{- 14}$ at 25°C.
This small value shows that water largely remains undissociated.

When $K \approx 1$ : Comparable Amounts of Reactants and Products
- When $K$ is close to 1 (e.g., $K = 0.8$ ), there are significant amounts of both reactants and products at equilibrium.
- Neither direction of the reaction is strongly favored.
When $K >> 1$ : Products are Favored
- A large $K$ value (e.g., $K = 10^{5}$ ) means the equilibrium position is strongly shifted toward the products.
- Most reactants are converted into products.

Example

Combustion of Methane

For the reaction ${CH}_{4} + 2 O_{2} ⇋ {CO}_{2} + 2 H_{2} O$ , $K$ is very large, indicating that nearly all methane and oxygen are converted into carbon dioxide and water.

Tip

If $K$ is close to 1, small changes in external conditions (e.g., temperature or pressure) can significantly shift the equilibrium position.

Examples of reactions and their equilibrium constants.

Relationship Between Forward and Reverse ( $K$ )

Reversible reactions can proceed in both forward and reverse directions.
The equilibrium constant for the reverse reaction is the reciprocal of the forward reaction:

$K_{reverse} = \frac{1}{K_{forward}}$

This relationship arises because reversing the reaction inverts the roles of products and reactants, thereby inverting the ratio.

Example

Calculating $K_{reverse}$

For the reaction $2 {NH}_{3} (g) ⇌ N_{2} (g) + 3 H 2 (g)$ , if $K forward = 0.59$ , then:

$K_{reverse} = \frac{1}{0.59} \approx 1.7$

Common Mistake

Students often forget to adjust $K$ when the stoichiometric coefficients of a reaction are changed. For example, doubling all coefficients requires squaring $K$ , while halving them requires taking the square root of $K$ .

Manipulating $K$ for different reactions

	Effect on $K_{c}$
Reversing the reaction	$\frac{1}{K_{c}}$
Doubling the reaction coefficients	${K_{c}}^{2}$
Halving the reaction coefficients	$\sqrt{K_{c}}$
Adding together two reactions	$K_{c} (1) \times K_{c} (2)$

Reflection

Self review

What does a $K$ value of 0.01 indicate about the position of equilibrium?
How does increasing temperature affect $K$ for an endothermic reaction?
If $K_{forward} = 4.0$ , what is $K_{reverse}$ ?

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Question 1

If the equilibrium constant for a reaction is $K = 10^5$ , what can be inferred about the position of equilibrium?

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What does a very small $K$ value (e.g., $K = 10^{-5}$ ) indicate?

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Note

Equilibrium Constants and Their Applications

An equilibrium constant is a mathematical expression that describes the ratio of concentrations of products to reactants at equilibrium for a reversible chemical reaction. It provides valuable information about the position of equilibrium and whether a reaction favors products or reactants under specific conditions.

Equilibrium constants are only valid at a specific temperature
They are independent of the starting concentrations of reactants or products
Different types of equilibrium constants exist for different types of reactions (e.g., $K_c$ for concentration, $K_p$ for pressure)

Analogy

Think of an equilibrium constant as a "balance point" for a seesaw. It tells you which side (products or reactants) is heavier at equilibrium, but doesn't change based on how you load the seesaw.

Definition

Equilibrium Constant

A numerical value that represents the ratio of concentrations of products to reactants at equilibrium, raised to the power of their stoichiometric coefficients.

Example

For the reaction $\text{N}_2(g) + 3\text{H}_2(g) \leftrightharpoons 2\text{NH}_3(g)$ , the equilibrium constant expression is: $K_c = \frac{[\text{NH}_3]^2}{[\text{N}_2][\text{H}_2]^3}$

Common Mistake

Students often forget to include the stoichiometric coefficients as exponents when writing equilibrium constant expressions.

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R2.3.3 Magnitude of K and temperature dependence

Equilibrium Constants and Their Applications

The Equilibrium Constant (K)

Dissociation of Water

Combustion of Methane

Relationship Between Forward and Reverse (K)

Calculating Kreverse

Manipulating K for different reactions

Reflection

You've read 2/2 free chapters this week.

Equilibrium Constants and Their Applications

The Equilibrium Constant ( $K$ )

Relationship Between Forward and Reverse ( $K$ )

Calculating $K_{reverse}$

Manipulating $K$ for different reactions