Problem 42 - Chemistry: The Central Science

Question

(a) If \(Q_{c}>K_{c}\), how must the reaction proceed to reach equilibrium? (b) 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) If \(Q_c > K_c\), the reaction must proceed in the reverse direction to create more reactants and reach equilibrium. (b) At the start of the reaction, when only reactants are present and no products have been formed, the value of \(Q_c\) is 0.

Step 1: (a) Understanding the relationship between \(Q_c\) and \(K_c\)

When a reaction is at equilibrium, the concentrations of the reactants and products will stay constant, and the reaction quotient, \(Q_c\), will be equal to the equilibrium constant, \(K_c\). If the reaction is not at equilibrium, the reaction will proceed in a certain direction to reach equilibrium. There are three possible cases: 1. If \(Q_c < K_c\), the reaction has more reactants than products, and it will proceed in the forward direction to create more products and reach equilibrium. 2. If \(Q_c = K_c\), the reaction is at equilibrium, and the concentrations of the reactants and products will stay constant. 3. If \(Q_c > K_c\), the reaction has more products than reactants, and it will proceed in the reverse direction to create more reactants and reach equilibrium. In the given exercise, we are told that \(Q_c\) is greater than \(K_c\), i.e., \(Q_c > K_c\). Therefore, the reaction must proceed in the reverse direction to create more reactants and reach equilibrium.

Step 2: (b) Calculating the value of \(Q_c\) at the start of the reaction

At the start of a reaction, only reactants are present and no products have been formed. Let's denote reactants as 'A' and 'B', and products as 'C' and 'D'. The balanced chemical equation for the reaction can be written as: \(aA + bB \rightleftharpoons cC + dD\) The reaction quotient, \(Q_c\), is calculated as: \(Q_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}\) At the beginning of the reaction, since no products have been formed, the concentrations of 'C' and 'D' are both 0. Therefore, we have: \(Q_c = \frac{0^c \times 0^d}{[A]^a[B]^b} = 0\) Thus, the value of \(Q_c\) at the start of the reaction, when only reactants are present and no products have been formed, is 0.