Problem 44 - Chemistry The Central Science

Question

(a) How is a reaction quotient used to determine whether a system is at equilibrium? (b) If \(Q_{c}>K_{c}\), how must the reaction proceed to reach equilibrium? (c) At the start of a certain reaction, only reactants are present; no products have been formed. What is the value of \(Q_{c}\) at this point in the reaction?

Step-by-Step Solution

Answer

(a) To determine if a system is at equilibrium, compare the reaction quotient, \(Q_{c}\), to the equilibrium constant, \(K_{c}\): If \(Q_{c} = K_{c}\), the system is at equilibrium; if \(Q_{c} < K_{c}\), the forward reaction occurs; and if \(Q_{c} > K_{c}\), the reverse reaction occurs to reach equilibrium. (b) If \(Q_{c} > K_{c}\), the reaction proceeds in the reverse direction to reach equilibrium. (c) At the start of a reaction when only reactants are present and no products have been formed, the value of \(Q_{c}\) is 0.

Step 1: (a) Understanding the Reaction Quotient and Equilibrium

The reaction quotient, \(Q_{c}\), is used to determine the current state of a system relative to the equilibrium state. The equilibrium constant, \(K_{c}\), is a number that characterizes the equilibrium state of a reaction. At equilibrium, the forward and reverse reaction rates are equal, and the concentrations of reactants and products no longer change. To determine whether a system is at equilibrium, compare the reaction quotient (\(Q_{c}\)) to the equilibrium constant (\(K_{c}\)): - If \(Q_{c} = K_{c}\), the system is at equilibrium. - If \(Q_{c} < K_{c}\), the system is not at equilibrium, and the forward reaction will occur to reach equilibrium. - If \(Q_{c} > K_{c}\), the system is not at equilibrium, and the reverse reaction will occur to reach equilibrium.

Step 2: (b) Reaction with \(Q_{c} > K_{c}\)

If the reaction quotient \(Q_{c}\) is greater than the equilibrium constant \(K_{c}\) (\(Q_{c} > K_{c}\)), the system is not at equilibrium. In this case, the concentrations of products are higher than what they should be at equilibrium, and the system will shift toward the reactants to reach equilibrium. This means that the reverse reaction will occur until the system reaches equilibrium.

Step 3: (c) Reaction Quotient at the Start of the Reaction

At the beginning of a reaction, only reactants are present, and no products have been formed. Therefore, the concentration of the products is zero. The reaction quotient is defined as the ratio of the concentrations of products to the concentrations of reactants, each raised to the power of their stoichiometric coefficients. For example, consider the general reaction: \[aA + bB \rightleftharpoons cC + dD\] The reaction quotient, \(Q_{c}\), is given by: \[Q_{c} = \frac{[C]^c[D]^d}{[A]^a[B]^b}\] At the beginning of the reaction, \([C] = 0\) and \([D] = 0\). Therefore, regardless of the values of \([A]\) and \([B]\), the reaction quotient will be zero: \[Q_{c} = 0\] So, at the start of a reaction when only reactants are present and no products have been formed, the value of the reaction quotient, \(Q_{c}\), is 0.

Key Concepts

Chemical Equilibrium

When studying chemical reactions, it is essential to understand the concept of chemical equilibrium. Equilibrium occurs in a closed system when the rate of the forward reaction equals the rate of the reverse reaction. This balance means that the concentrations of the reactants and products remain constant over time, even though both reactions are still occurring.

In a sense, equilibrium is like a tug of war where both teams are equally strong; no one wins, but the effort continues. Equilibrium does not imply that the reactants and products are in equal concentrations, but rather that their ratios do not change. To comprehend this concept, visualize a container of water with a small hole; the amount of water entering and leaving the container is the same, thus the amount of water in the container stays constant – this is analogous to chemical equilibrium.

Equilibrium Constant

The equilibrium constant, denoted by (K_c), is a fundamental aspect of the equilibrium state of a chemical reaction. It is a numerical value that represents the ratio of the concentrations of the products to the reactants at equilibrium, each raised to the power of their stoichiometric coefficients.

For a general reaction, where (aA + bB \rightleftharpoons cC + dD), the equilibrium constant is given by the expression:
\[K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}\]
Knowing the value of (K_c) is crucial for predicting how the reaction mix will look at equilibrium. If (K_c) is a large number, it suggests that, at equilibrium, the products are favored. Conversely, a small (K_c) value indicates that the reactants are favored.

A key point to remember is that (K_c) is constant for a given temperature. Thus, it serves as a benchmark for determining the direction of the reaction to reach equilibrium, which brings us to the reaction quotient (Q_c), used to gauge the system's current state compared to equilibrium.

Reaction Direction

To predict the reaction direction towards equilibrium, the reaction quotient (Q_c) comes into play. It is a snapshot of the reaction at any given moment and is calculated in the same way as the equilibrium constant, but using the current concentrations of reactants and products.
\[Q_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}\]
The comparison between (Q_c) and (K_c) dictates the direction in which the reaction will proceed to achieve equilibrium:

• If (Q_c < K_c), the system will move forward, converting reactants into products.
• If (Q_c > K_c), the reaction will go in reverse, forming more reactants from the products.
• If (Q_c = K_c), the reaction is at equilibrium and no net change will occur.

This understanding allows chemists to manipulate conditions to shift the equilibrium in the desired direction, crucial for optimizing product yields in industrial processes. For example, if the goal is to produce more product, conditions can be adjusted so that (Q_c) is less than (K_c), driving the reaction forward.