Problem 61 - Chemistry: An Atoms-Focused Approach

Question

The hypothetical equilibrium \(\mathrm{X}+\mathrm{Y} \rightleftharpoons \mathrm{Z}\) has \(K_{e}=1.00\) at \(350 \mathrm{K}\). If the initial molar concentrations of \(\mathrm{X}, \mathrm{Y},\) and Z in a solution are all \(0.2 M\), in which direction will the reaction shift to reach equilibrium? a. To the left, making more \(X\) and \(Y\) b. To the right, making more \(Z\) c. The system is at cquilibrium and the concentrations will not change.

Step-by-Step Solution

Answer

Answer: To the left, making more X and Y.

Step 1: Understanding the Equilibrium Constant

The equilibrium constant (Ke) for the reaction is given as 1.00. This tells us that at equilibrium, the ratio of the concentration of Z to the product of the concentrations of X and Y is equal to 1. In equation form, this will be: Ke = [Z] / ([X]*[Y]) This formula will help us determine which direction the reaction will shift to achieve equilibrium.

Step 2: Calculating the Initial Reaction Quotient Q

Before we can determine the direction of the shift, we need to calculate the Reaction Quotient (Q). This will tell us the state of the system before it reaches equilibrium. The reaction quotient is calculated just like the equilibrium constant, but using initial concentrations before equilibrium is achieved. Given that the initial concentrations of X, Y, and Z are all 0.2M, we can substitute these values into the equation to find the initial Q: Q = [0.2] / ([0.2]*[0.2]) = 5 Because Q > Ke, we know the reaction will shift in the direction that reduces the reaction quotient to achieve equilibrium.

Step 3: Determining the Direction of the Shift

To reduce the reaction quotient, Q, and bring it closer to the equilibrium constant, Ke, the reaction will proceed in the direction that decreases the concentration of the product (Z), while increasing the concentration of the reactants (X and Y). So, the reaction will shift to the left, making more X and Y to reach equilibrium. Therefore, option a. "To the left, making more X and Y" is the correct answer.

Key Concepts

Equilibrium Constant (Ke)

In chemistry, the equilibrium constant, represented as \(K_e\), is an essential value that determines the ratio of concentrations of products to reactants at equilibrium. Understanding \(K_e\) helps us predict the extent to which a reaction will proceed under given conditions.
For a general reaction like \(\text{X} + \text{Y} \rightleftharpoons \text{Z}\), the equilibrium constant is determined by the equation:

• \(K_e = \frac{[ ext{Z}]}{[ ext{X}] \cdot [\text{Y}]}\)

This equation implies that at equilibrium, there is a specific proportion of product ([Z]) compared to the reactants ([X] and [Y]).
The \(K_e\) value of 1.00 at 350 K means that, at this temperature, the concentrations of reactants and products are balanced such that their ratio is exactly 1. This does not imply equal concentrations of Z, X, and Y, but rather that the system is balanced in a way described by the equilibrium constant. In other scenarios, \(K_e\) can tell us which side of the reaction is favored: a large \(K_e\) indicates more products compared to reactants, while a small \(K_e\) favors the reactants.

Reaction Quotient (Q)

The reaction quotient, \(Q\), is a dynamic measurement used to understand a chemical system before it reaches equilibrium. It is calculated using the same formula as the equilibrium constant, but with initial concentrations before equilibrium is achieved. For our hypothetical reaction \(\text{X} + \text{Y} \rightleftharpoons \text{Z}\), the equation is:

• \(Q = \frac{[ ext{Z}]}{[ ext{X}] \cdot [\text{Y}]}\)

In the exercise example, all initial concentrations are 0.2 M. Substituting these values gives us \(Q = \frac{0.2}{0.2 \times 0.2} = 5\).
The relationship between \(Q\) and \(K_e\) determines the direction in which the reaction will proceed:

• If \(Q < K_e\), the reaction will move forward, producing more products.
• If \(Q > K_e\), it will reverse, forming more reactants.
• If \(Q = K_e\), the system is at equilibrium.

Since in our case, \(Q > K_e\), the system will shift towards the reactants (to the left) to achieve equilibrium.

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept used to predict how a change in conditions can shift the equilibrium of a reaction. It states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium will shift to counteract the change.
In the case of our exercise, knowing that the reaction starts with \(Q = 5\) while \(K_e = 1\), Le Chatelier's Principle helps us understand why the reaction shifts to the left. To lower \(Q\) and match \(K_e\), less product \(Z\) is favored, so the reaction moves towards producing more reactants \(X\) and \(Y\).
This principle applies not only to changes in concentration, but also to changes in temperature, pressure, or volume of the system, affecting gases in particular:

• Increasing pressure by reducing volume shifts the reaction towards the side with fewer gas moles.
• Changes in temperature favor the reaction that absorbs or releases heat, depending on whether the change involves adding or removing heat.

Understanding Le Chatelier's Principle provides a comprehensive way to predict and control the outcome of reactions under various conditions, ensuring that equilibrium is maintained or restored.