Question

Why does a numerically large Keq mean that the products are favored in an equilibrium system?

Short answer

A numerically large Keq means that the products are favored in an equilibrium system because it indicates that the ratio of product concentrations to reactant concentrations at equilibrium is much greater than 1. This implies that the reaction will proceed in the forward direction, favoring the formation of products until equilibrium is reached.

Step-by-step solution

Understand the Equilibrium Constant (Keq)

The equilibrium constant (Keq) is the ratio of the concentrations of products to the concentrations of reactants in an equilibrium reaction. It is a constant value for a given reaction at a specific temperature and is expressed mathematically as: \[ K_\text{eq} = \frac{[\text{Products}]^n}{[\text{Reactants}]^m} \] Here, [Products] and [Reactants] represent the concentrations of the products and reactants at equilibrium, with the exponents 'n' and 'm' representing their respective stoichiometric coefficients according to the balanced equation.

Define a Reaction Quotient (Q)

The reaction quotient (Q) is a measure of the present state of a reaction. It is calculated the same way as Keq, by taking the ratio of products to the reactants raised to their stoichiometric coefficients: \[ Q = \frac{[\text{Products}]^n}{[\text{Reactants}]^m} \] The relationship between Q and Keq will help determine the direction in which a reaction is proceeding.

Compare Q to Keq

Comparing the values of Q and Keq indicates the direction a reaction will proceed to reach equilibrium: - If \( Q < K_\text{eq} \), the reaction proceeds in the forward direction, favoring the formation of products. - If \( Q > K_\text{eq} \), the reaction proceeds in the reverse direction, favoring the formation of reactants. - If \( Q = K_\text{eq} \), the reaction is at equilibrium and concentrations of products and reactants will remain constant.

Explain a Large Keq

A large Keq means that the equilibrium concentrations of the products are much greater than those of the reactants. Mathematically, this is expressed as: \[ K_\text{eq} >> 1 \] In this case, \( Q < K_\text{eq} \), indicating that the reaction will proceed in the forward direction to reach equilibrium, favoring the formation of products. In summary, a numerically large Keq means that products are favored in an equilibrium system because the ratio of products to reactants at equilibrium is much greater than 1. This indicates that the reaction will proceed in the forward direction, favoring the formation of products until equilibrium is achieved.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in a chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction. As a result, the concentrations of reactants and products remain constant over time, though they may not be equal. To visualize this, imagine a busy intersection where cars are moving into and out of the junction at the same rate - the number of cars within the junction remains constant, much like the concentrations at equilibrium.

At equilibrium, no net change is observed, and it's important to note that achieving equilibrium does not mean that the reactants and products are present in equal amounts; it simply means that their rates of formation are equal. This concept is crucial for understanding how reactions behave under certain conditions and predicting the yield of products.

Reaction Quotient

The reaction quotient (\( Q \)) is like a snapshot of a reaction at any point in time, indicating whether a system has reached its equilibrium state. Think of it as taking a photograph of a moving car to determine whether it's parked or still in motion.

\( Q \) is calculated using the same expression as the equilibrium constant (\( K_\text{eq} \) but with the concentrations of reactants and products at any moment, not necessarily at equilibrium. By comparing \( Q \) to \( K_\text{eq} \) we can tell if the reaction is at equilibrium (\( Q = K_\text{eq} \)), or if not, in which direction it will proceed to reach equilibrium. If \( Q \) is less than \( K_\text{eq} \) the reaction moves forward to produce more products, and if \( Q \) is greater, the reaction moves in reverse to produce more reactants.

Stoichiometry

Stoichiometry is the relationship between the quantities of reactants and products in a chemical reaction. It's akin to a recipe that outlines how much of each ingredient is needed and how much product will result.

In the context of the equilibrium constant, stoichiometry defines the exponents in the equilibrium expression, where the stoichiometric coefficients from the balanced chemical equation dictate the powers to which the concentrations of reactants and products are raised. This mathematical embodiment of the balanced equation helps predict the amounts of substances consumed and produced in a reaction, making it a fundamental aspect of chemistry, particularly when calculating the expected yield from a given amount of reactant and understanding how changes in amounts can shift the equilibrium of a reaction.