Question

If the initial concentrations of reactants and products are substituted into the equilibrium constant expression, and the value obtained is equal to the equilibrium constant, is the system in a state of equilibrium? If not, in which direction will the reaction shift to reach equilibrium? Explain.

Short answer

If the value obtained from substituting initial concentrations into the equilibrium constant expression equals to the equilibrium constant, then the system is indeed in equilibrium. If not, based on Le Chatelier's Principle, if calculated value is greater than K, the reaction shifts to the left, and if less, to the right.

Step-by-step solution

Understanding the Equilibrium Principle

Chemical equilibrium is a state in a chemical reaction where the concentrations of both reactants and products remain constant over time. The equilibrium constant (K) represents the ratio of the concentrations of products over reactants when the reaction is at equilibrium, each raised to their respective stoichiometric coefficients. The concept of chemical equilibrium is based on the Law of Mass Action.

Applying the Law of Mass Action

According to the Law of Mass Action, if the system has the concentrations of reactants and products that, when substituted into the equilibrium law expression gives value equal to K, then the system is considered to be in equilibrium. This means that the rate of forward reaction matches the rate of the backward reaction, and concentrations of both reactants and products remain unaltered.

Determining Reaction Shift

If the system is not in equilibrium (meaning the value calculated from the ratio of initial concentrations does not equal to K), it will shift to re-establish equilibrium. This is according to Le Chatelier's Principle. If the value calculated happens to be greater than K (denoted as Q > K), it indicates a surplus of products, and the reaction shifts to the left to consume them and produce more reactants. If Q < K, it indicates a deficit of products, and the reaction shifts to the right to produce more products.

Key concepts

Equilibrium Constant

Chemical reactions often reach a point where they appear to stop changing, even though they continue to take place. This state is known as chemical equilibrium. At equilibrium, the rate at which reactants are converted into products is equal to the rate at which products are converted back into reactants.
The equilibrium constant, represented by the symbol "K", is a number that expresses the relationship between the concentrations of reactants and products at equilibrium. It is calculated using the formula: \[ K = \frac{{[products]}}{{[reactants]}} \]Each concentration is raised to a power equal to its coefficient in the balanced chemical equation.

• If the equilibrium constant is a large number, this means that, at equilibrium, the concentration of products is much greater than the concentration of reactants.
• If K is a small number, it indicates that there are more reactants than products at equilibrium.

This value remains constant as long as the temperature does not change.

Law of Mass Action

The Law of Mass Action is a principle that guides how the equilibrium constant is calculated. It states that, at a given temperature, the rate of a chemical reaction is directly proportional to the product of the concentrations of the reactants, each raised to the power of its stoichiometric coefficient.
This principle allows us to write the equilibrium expression that relates the concentrations of products and reactants in a balanced recipe of a chemical reaction.

• When you plug in the concentrations of the substances at any given moment, the computed value (Q) helps determine the state of the reaction in relation to equilibrium.
• If Q equals K, the system is in equilibrium; no net change occurs in concentrations. The forward and backward reactions are perfectly balanced.

Understanding this principle is key to knowing how shifts in concentration affect a reaction's equilibrium state.

Le Chatelier's Principle

Le Chatelier's Principle offers valuable insight into how a system at equilibrium responds to changes. It states that if a dynamic equilibrium is disturbed by changing the conditions, the system adjusts itself to partially counteract the change and thereby establish a new equilibrium.

• If additional reactants are added to a system, it will shift to the right, producing more products to re-establish equilibrium.
• Conversely, if products are removed, the reaction shifts to the left, converting more reactants into products.

Additionally, if the value calculated from initial concentrations, known as Q, is different from K, the system will adjust to restore equilibrium.

• If Q > K, there is an excess of products, and the reaction will shift left, favoring the formation of reactants.
• If Q < K, more products will form as the reaction shifts to the right.

These shifts ensure that systems naturally balance themselves when external changes occur.