Question

If the initial concentrations of reactants and products are substituted into the equilibrium constant expression, and the value obtained is greater than 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

The system is not in a state of equilibrium. The reaction will shift left (towards the reactants) to reach equilibrium.

Step-by-step solution

Understand Le Chatelier's Principle and Equilibrium Constant

Le Chatelier's principle states that a chemical system at equilibrium will attempt to counteract any change in conditions to re-establish equilibrium. In this question, change in conditions is referring to the concentration of reactants and products. The equilibrium constant (K) is a reflection of this condition.

Compare Values

If the value obtained by substituting the initial concentrations of reactants and products into the equilibrium constant (K) expression is greater than K, it means that the concentration of products is higher than expected at equilibrium.

Determine the Direction

Based on Le Chatelier's Principle, to re-establish equilibrium, the reaction will shift in the direction that decreases the concentration of products and increases the concentration of reactants. Hence, the reaction will shift to the left (towards the reactants).

Key concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemistry that describes how a system at equilibrium reacts to external changes. When a dynamic equilibrium is disturbed by changing the conditions, such as concentration, temperature, or pressure, the system responds in a way that counteracts the disturbance and tries to restore a new state of equilibrium. Imagine a see-saw that is perfectly balanced, and someone suddenly adds weight to one side. The see-saw will tilt, and the system will adjust itself to either decrease the added weight's impact or redistribute the weight more evenly.
In the context of chemical equilibrium, if you change the concentration of reactants or products, the system will adjust to minimize that change. This is why, in the exercise, when the concentration of products is initially higher than at equilibrium, the system will shift the reaction toward the side that increases reactants and decreases products. This adaptable behavior is the cornerstone of Le Chatelier's Principle.

Equilibrium Constant

The Equilibrium Constant, often represented by the symbol \( K \), is a numeric expression that provides insight into the ratio of the concentrations of products to reactants at equilibrium for a given reaction. Mathematically, for a general reaction \( aA + bB \rightleftharpoons cC + dD \), the equilibrium constant is defined as:

• \( K = \frac{[C]^c [D]^d}{[A]^a [B]^b} \)

Here, \([A]\), \([B]\), \([C]\), and \([D]\) are the molar concentrations of the reactants and products, and \( a, b, c, \) and \( d \) are their respective stoichiometric coefficients.
The value of \( K \) gives us valuable information regarding the position of equilibrium. A large \( K \) (much greater than 1) suggests that products are favored at equilibrium, while a small \( K \) (much less than 1) indicates that reactants are favored. Therefore, comparing the calculated expression value using initial concentrations with \( K \) helps to determine how the system is away from equilibrium and guides in predicting the reaction's behavior according to Le Chatelier's principle.

Reaction Shift

The concept of Reaction Shift is essential for understanding how a chemical system approaches equilibrium from a non-equilibrium state. When the expression for the reaction quotient \( Q \), calculated using initial concentrations, differs from the equilibrium constant \( K \), it indicates that the system is not in equilibrium.
If \( Q > K \), as with the given problem, it means there are more products than expected at equilibrium, so the reaction will need to "shift" to balance itself.

• If \( Q > K \), the system shifts to the left, favoring the reverse reaction and producing more reactants.
• If \( Q < K \), the system shifts to the right, favoring the forward reaction and producing more products.
• If \( Q = K \), the system is at equilibrium, and no shift occurs.

The direction of the shift is a result of the system's innate response to satisfy the equilibrium condition as predicted by Le Chatelier's Principle. Understanding this shift helps chemists control reactions for desired outcomes, making it a pivotal aspect of industrial chemistry processes.