Question

Consider a reaction \(\mathrm{A}_{2}(g)+\mathrm{B}_{2}(g) \rightleftharpoons 2 \mathrm{AB}(g)\), with atoms of A shown in red and atoms of B shown in blue. (a) If \(K_{c}=1\), which system is at equilibrium? (b) What is the sign of \(\Delta G\) for any process in which the contents of a reaction vessel move to equilibrium? (c) Rank the boxes in order of increasing magnitude of \(\Delta G\) for the reaction. [Sections \(19.5\) and \(19.7]\)

Short answer

(a) The system is at equilibrium when the ratio of products to reactants is equal to 1, as Kc = 1 for this reaction. (b) The sign of ΔG is negative when a system moves to equilibrium. (c) The ranking of the boxes in order of increasing magnitude of ΔG would be: low reactant concentration and high product concentration < equal concentration of reactants and products < high reactant concentration and low product concentration.

Step-by-step solution

(a) Determine the system at equilibrium

To find which system is at equilibrium, we need to understand the relationship between Kc and the reaction quotient (Q). When a system is at equilibrium, Q = Kc. Given that Kc = 1 for this reaction, the system where the ratio of products to reactants is equal to 1 is at equilibrium.

(b) Find the sign of ΔG for any process moving to equilibrium

To find the sign of ΔG for a process moving to equilibrium, we need to refer back to the equation: ΔG = RTln(Q/Kc) In cases where the system is not at equilibrium: - If Q > Kc, the reaction proceeds in the reverse direction to achieve equilibrium. In this scenario, ln(Q/Kc) > 0, hence ΔG > 0 (positive). - If Q < Kc, the reaction proceeds in the forward direction to achieve equilibrium. In this case, ln(Q/Kc) < 0, hence ΔG < 0 (negative). Therefore, the sign of ΔG is negative when a system moves to equilibrium.

(c) Rank the boxes in order of increasing magnitude of ΔG for the reaction

Since we do not have any specific information about the boxes, we can only provide a general approach to ranking the boxes concerning the magnitude of ΔG for the reaction. In order to rank the boxes in order of increasing magnitude of ΔG, we can calculate the values of Q for each box: 1. For the box with a high concentration of reactants and a low concentration of products, Q will be smaller than Kc, resulting in a smaller, negative ΔG. 2. For the box with an equal concentration of reactants and product, Q will equal Kc, leading to ΔG equaling zero. 3. For the box with a low concentration of reactants and a high concentration of products, Q will be greater than Kc, resulting in a larger, positive ΔG. Thus, the ranking of the boxes in order of increasing magnitude of ΔG would be: low reactant concentration and high product concentration < equal concentration of reactants and products < high reactant concentration and low product concentration.