Question

part b: short answer and calculations (thinking and inquiry and application)

1. draw a graph to represent the concentration of reactant and product gas molecules over time for the equilibrium system below.

in the graph, show the points in time when equilibrium is initially established; when more a is introduced to the system; and when the new position of equilibrium is established. be sure to label your graph appropriately.
briefly justify your predictions.

$$\\ce{a_{(g)} + b_{(g)} \ ightleftharpoons 2ab_{(g)}}$$

Explanation:

Step1: Initial Equilibrium

• Explanation: At the start, the concentration of \( A_{(g)} \) and \( B_{(g)} \) is high, and \( AB_{(g)} \) is 0. As time passes, the forward reaction (\( A + B \to 2AB \)) occurs, so \([A]\) and \([B]\) decrease, and \([AB]\) increases until the rates of forward and reverse reactions are equal (equilibrium is initially established). At this point, the concentrations of \( A \), \( B \), and \( AB \) become constant (horizontal lines on the graph).
• Graph Sketch: Plot time on the x - axis and concentration on the y - axis. Draw two decreasing curves for \([A]\) and \([B]\) starting from a non - zero initial concentration, and an increasing curve for \([AB]\) starting from 0. All three curves become horizontal at the same time (let's say at time \( t_1 \)), indicating the initial equilibrium.

Step2: Introducing More A

• Explanation: When more \( A \) is introduced at time \( t_2 \) (after \( t_1 \)), the concentration of \( A \) suddenly increases (a vertical jump in the \([A]\) curve at \( t_2 \)). According to Le Chatelier's principle, the system will try to counteract this change. The forward reaction (\( A + B \to 2AB \)) will be favored. So, the concentration of \( A \) will start to decrease again (but from a higher initial value at \( t_2 \)), the concentration of \( B \) will decrease more (since more \( A \) is available to react with \( B \)), and the concentration of \( AB \) will increase more.
• Graph Sketch: At \( t_2 \), the \([A]\) curve has a vertical upward shift. Then, the \([A]\) curve decreases, the \([B]\) curve (which was horizontal until \( t_2 \)) starts to decrease again, and the \([AB]\) curve (which was horizontal until \( t_2 \)) starts to increase again.

Step3: New Equilibrium

• Explanation: After the introduction of \( A \), the system will reach a new equilibrium at time \( t_3 \) (after \( t_2 \)). At this point, the rates of the forward and reverse reactions are equal again. The concentration of \( A \) at the new equilibrium (\( t_3 \)) will be higher than the concentration at the initial equilibrium (\( t_1 \)) (because we added more \( A \) initially), the concentration of \( B \) will be lower than at \( t_1 \) (since more \( B \) has reacted), and the concentration of \( AB \) will be higher than at \( t_1 \). All three curves become horizontal again at \( t_3 \).
• Graph Sketch: The \([A]\), \([B]\), and \([AB]\) curves become horizontal at \( t_3 \), with \([A]_{t_3}>[A]_{t_1}\), \([B]_{t_3}<[B]_{t_1}\), and \([AB]_{t_3}>[AB]_{t_1}\).

Step4: Justification

• Explanation: Initially, the system reaches equilibrium when the rates of forward (\( r_f \)) and reverse (\( r_r \)) reactions are equal (\( r_f = r_r \)). When we add more \( A \), the concentration of the reactant \( A \) increases. According to Le Chatelier's principle, the system shifts in the direction that consumes the added \( A \), which is the forward direction (\( A + B

ightleftharpoons2AB \)). This causes the concentrations of \( A \) and \( B \) to decrease (as they are consumed) and the concentration of \( AB \) to increase (as it is produced) until a new equilibrium is established where \( r_f'=r_r' \) (new forward and reverse rates are equal). The new equilibrium concentrations reflect the change: \([A]\) is higher than initial (because we added some), \([B]\) is lower (more reacted), and \([AB]\) is higher (more produced).

Answer:

The graph has time on the x - axis and concentration on the y - axis. Initial equilibrium at \( t_1 \) (horizontal lines for all concentrations), addition of \( A \) at \( t_2 \) (vertical jump in \([A]\)), and new equilibrium at \( t_3 \) (horizontal lines again with \([A]_{t_3}>[A]_{t_1}\), \([B]_{t_3}<[B]_{t_1}\), \([AB]_{t_3}>[AB]_{t_1}\)). Justification is based on Le Chatelier's principle: adding \( A \) shifts equilibrium forward, changing concentrations until a new balance is reached.