7.5.A.1 Equilibrium Reactions: Large K vs Small K:

1. Equilibrium Constant (K):

The equilibrium constant (K) is the ratio of product concentrations to reactant concentrations at equilibrium.

– Large K (K >> 1): Forecasts the reaction favors products, with a high concentration of products at equilibrium.
– Small K (K << 1): Forecasts the reaction favors reactants, with a high concentration of reactants at equilibrium.
– K ≈ 1: Forecasts equal concentrations of reactants and products at equilibrium.

In brief:
– K > 1: They are in excess.
– K < 1: They are in excess.
– K ≈ 1: They are equal in amount.

2. Le Chatelier’s Principle:

Le Chatelier’s Principle states that an equilibrium system will adjust to an alteration in conditions.

– Concentration: Releasing reactants/products shifts equilibrium to the other side; taking away reactants/products shifts it to the same side.
– Temperature: Increases equilibrium in the direction of the endothermic process; decreases equilibrium in the direction of the exothermic process.
– Pressure (gases): Applying pressure shifts equilibrium to the side with fewer molecules of gas; removing pressure shifts it to the side with more molecules of gas.

3. Thermodynamics and K:

The relationship between **Gibbs free energy (ΔG)** and the **equilibrium constant (K)** can be described using the following equation:

ΔG∘=−RTlnK

Where:
– ΔG° is the standard Gibbs free energy change.
– R is the universal gas constant (8.314 J/mol·K).
– T is the temperature in Kelvin units.
– K is the equilibrium constant.

### Key Points:
– ΔG° < 0 (spontaneous reaction): K > 1 (products favored at equilibrium).
– ΔG° > 0 (non-spontaneous reaction): K < 1 (reactants are favored at equilibrium).
– ΔG° = 0 (equilibrium): K = 1 (reactants and products in equal concentrations).

In summary, a negative ΔG° has a large K (products favored), and a positive ΔG° has a small K (reactants favored).

4. Characteristics of Large vs Small K:

Reactions with large K and small K have distinct equilibrium positions:

– Large K (K >> 1):
– Favors products at equilibrium.
– The concentration of products is significantly higher than the concentration of reactants.
– The reaction proceeds mostly to completion.

– Small K (K << 1):
– Favors reactants at equilibrium.
– The concentration of reactants is much higher than the concentration of products.
– The reaction scarcely goes to the products.

In summary:
– K > 1: Products dominate.
– K < 1: Reactants dominate.

5. Factors Affecting K:

The equilibrium constant (K) is a function of two variables:

i. Temperature:
– Exothermic reactions (heat released): Rising temperature decreases K (shifts the equilibrium towards reactants).
–Endothermic reactions (heat absorbed): Rising temperature increases K (shifts the equilibrium towards products).

ii. Nature of Reactants/Products:
– The chemical nature of the reactants and products determines the position of equilibrium and hence K. For example, reactions involving more stable compounds will favor product formation, which determines a higher K.

Finally, temperature determines the value of K depending on whether the reaction is endothermic or exothermic, while the nature of reactants/products determines how K is calculated.