Calculating K

Core Concept

The equilibrium constant quantifies the ratio of the concentrations (or partial pressures) of products to reactants at equilibrium for a given chemical reaction.

There are two forms of equilibrium constants:

Kc: Based on molar concentrations (mol/L).
Kp: Based on partial pressures (atm).

For a generic reaction: aA + bB ⇌ cC + dD

The equilibrium constant is expressed as:

$K_c = \frac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b}$

$K_p = \frac{(P_{\text{C}})^c (P_{\text{D}})^d}{(P_{\text{A}})^a (P_{\text{B}})^b}$

Key Tips

Check Stoichiometry: Ensure coefficients in the balanced equation are correctly applied in the K expression.
Keep Units Consistent: Use concentrations for Kc and partial pressures for Kp.
Temperature Matters: If solving for Kp using Kc, remember to convert temperature to Kelvin.
Don’t Include Solids or Liquids: Pure solids and liquids do not appear in the K expression because their concentrations are constant.

Test Yourself

Assorted Multiple Choice

The reaction $2 SO_2(g) + O_2(g) \rightleftharpoons 2 SO_3(g)$ is allowed to reach equilibrium in a closed vessel. At equilibrium, the concentrations are found to be: $[SO_2] = 0.20 M$, $[O_2] = 0.10 M$, and $[SO_3] = 0.40 M$. What is the value of the equilibrium constant ($K_c$) for this reaction?

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Calculating Equilibrium Constant (K)

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Writing Equilibrium Constant Expressions (Kc and Kp)

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Direct Calculation of K from Equilibrium Values

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Relationship Between Kc and Kp

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Conceptual Interpretation of the Magnitude of K

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Core Concept

The equilibrium constant quantifies the ratio of the concentrations (or partial pressures) of products to reactants at equilibrium for a given chemical reaction.

There are two forms of equilibrium constants:

Kc: Based on molar concentrations (mol/L).
Kp: Based on partial pressures (atm).

For a generic reaction: aA + bB ⇌ cC + dD

The equilibrium constant is expressed as:

$K_c = \frac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b}$

$K_p = \frac{(P_{\text{C}})^c (P_{\text{D}})^d}{(P_{\text{A}})^a (P_{\text{B}})^b}$

$K_c$ vs. $K_p$

Depending on the state of the matter, we calculate $K$ using different units:

$K_c$ (Concentration): Used for aqueous solutions or gases when using molarity ($mol/L$).
$K_p$ (Pressure): Used specifically for gas-phase reactions using partial pressures (usually in $atm$ or $bar$).
$$K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b}$$
The Conversion Formula: You can convert between the two using the Ideal Gas Law derivation:
$$K_p = K_c(RT)^{\Delta n}$$
- $R$ is the gas constant ($0.0821\ L\cdot atm/mol\cdot K$).
- $T$ is the temperature in Kelvin.
- $\Delta n$ is the change in moles of gas ($\text{moles of gaseous product} - \text{moles of gaseous reactant}$).

Calculating $K$ allows us to quantify exactly how far a reaction proceeds toward products before reaching a stable state.

$K_c$ vs. $K_p$

Depending on the state of the matter, we calculate $K$ using different units:

$K_c$ (Concentration): Used for aqueous solutions or gases when using molarity ($mol/L$).
$K_p$ (Pressure): Used specifically for gas-phase reactions using partial pressures (usually in $atm$ or $bar$).
$$K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b}$$
The Conversion Formula: You can convert between the two using the Ideal Gas Law derivation:
$$K_p = K_c(RT)^{\Delta n}$$
- $R$ is the gas constant ($0.0821\ L\cdot atm/mol\cdot K$).
- $T$ is the temperature in Kelvin.
- $\Delta n$ is the change in moles of gas ($\text{moles of gaseous product} - \text{moles of gaseous reactant}$).

The ICE Table Method

In most laboratory or exam scenarios, you aren't given the equilibrium concentrations directly; you are given initial concentrations and told to find $K$. We use an ICE Table to track the changes:

I (Initial): The concentrations of reactants and products before the reaction starts (usually products are $0$).
C (Change): The amount that reacts, represented by "$x$". Use the stoichiometric coefficients (e.g., $-2x$ for a reactant with a coefficient of $2$).
E (Equilibrium): The sum of the Initial and Change rows. These are the values you plug into the $K$ expression.

Manipulating $K$ Values

If you modify the chemical equation, the value of $K$ changes in a predictable mathematical way:

Reversing the Reaction: If you flip the equation, the new $K$ is the reciprocal ($1/K$).
Multiplying Coefficients: If you multiply the entire equation by a factor $n$, the new $K$ is $K^n$.
Adding Reactions: If you add two individual steps to get a net reaction, the net $K$ is the product of the individual constants ($K_1 \times K_2$).

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