Equilibrium Constants (Kc and Kp) - Chemistry

1. Fundamental Concepts

Definition: Equilibrium constants, $$ K_c $$ and $$ K_p $$, are values that describe the ratio of products to reactants at equilibrium for a chemical reaction.
$$ K_c $$: The equilibrium constant in terms of molar concentrations $$ [A] $$.
$$ K_p $$: The equilibrium constant in terms of partial pressures $$ P_A $$.
Relationship: For a reaction involving gases, $$ K_p = K_c (RT)^{\Delta n} $$, where $$ \Delta n $$ is the change in the number of moles of gas, $$ R $$ is the gas constant, and $$ T $$ is the temperature in Kelvin.

2. Key Concepts

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

Expression for $$ K_p $$: $$K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b}$$

Application: Used to predict the direction of a reaction and the extent to which it will proceed.

3. Examples

Example 1 (Basic)

Problem: For the reaction $$ N_2(g) + 3H_2(g) \leftrightarrow 2NH_3(g) $$, if the equilibrium concentrations are $$ [N_2] = 0.5 \, M $$, $$ [H_2] = 1.5 \, M $$, and $$ [NH_3] = 2.0 \, M $$, calculate $$ K_c $$.

Step-by-Step Solution:

Write the expression for $$ K_c $$:
$$ K_c = \frac{[NH_3]^2}{[N_2][H_2]^3} $$
Substitute the given values:
$$ K_c = \frac{(2.0)^2}{(0.5)(1.5)^3} $$
Simplify the expression:
$$ K_c = \frac{4.0}{(0.5)(3.375)} = \frac{4.0}{1.6875} \approx 2.37 $$

Validation: Substitute the values back into the expression to confirm the calculation.

Example 2 (Intermediate)

Problem: For the reaction $$ 2SO_2(g) + O_2(g) \leftrightarrow 2SO_3(g) $$, if the equilibrium partial pressures are $$ P_{SO_2} = 0.8 \, atm $$, $$ P_{O_2} = 0.4 \, atm $$, and $$ P_{SO_3} = 1.2 \, atm $$, calculate $$ K_p $$.

Step-by-Step Solution:

Write the expression for $$ K_p $$:
$$ K_p = \frac{(P_{SO_3})^2}{(P_{SO_2})^2 (P_{O_2})} $$
Substitute the given values:
$$ K_p = \frac{(1.2)^2}{(0.8)^2 (0.4)} $$
Simplify the expression:
$$ K_p = \frac{1.44}{(0.64)(0.4)} = \frac{1.44}{0.256} \approx 5.625 $$

Validation: Substitute the values back into the expression to confirm the calculation.

4. Problem-Solving Techniques

Identify the Reaction: Write the balanced chemical equation and identify the reactants and products.
Write the Expression: Use the general form of $$ K_c $$ or $$ K_p $$ and substitute the appropriate concentrations or partial pressures.
Substitute Values: Plug in the given equilibrium values and simplify the expression.
Check Units: Ensure that all units are consistent and cancel out appropriately.
Validate Calculation: Substitute the calculated value back into the expression to confirm the result.