The value of Kc for the reaction 2A ? B + C is 2 × 10–3. At a given time, the composition of reaction mixture is [A] = [B] = [C] = 3 × 10–4 M. In which direction the reaction will proceed?

To determine the direction in which the reaction will proceed, we need to compare the reaction quotient (Q) with the equilibrium constant (Kc). The reaction in question is:

Understanding the Reaction

The balanced equation is:

2A ⇌ B + C

Given that Kc for this reaction is 2 × 10^-3, we can use this value to analyze the current state of the reaction mixture.

Calculating the Reaction Quotient (Q)

The reaction quotient (Q) is calculated using the same expression as Kc, but with the current concentrations of the reactants and products. For our reaction, the expression for Q is:

Q = [B][C] / [A]²

Substituting the given concentrations into this expression:

• [A] = 3 × 10^-4 M
• [B] = 3 × 10^-4 M
• [C] = 3 × 10^-4 M

Now, we can calculate Q:

Q = (3 × 10^-4)(3 × 10^-4) / (3 × 10^-4)²

Q = (9 × 10^-8) / (9 × 10^-8)

Q = 1

Comparing Q and Kc

Now that we have Q = 1 and Kc = 2 × 10^-3, we can analyze the situation:

• If Q < Kc, the reaction will proceed to the right (toward products).
• If Q > Kc, the reaction will proceed to the left (toward reactants).
• If Q = Kc, the system is at equilibrium.

In this case, since Q (1) is greater than Kc (2 × 10^-3), the reaction will shift to the left to form more reactants (A).

Conclusion

To summarize, the reaction will proceed in the direction that favors the formation of reactants because the current reaction quotient exceeds the equilibrium constant. This shift will continue until equilibrium is re-established, where Q will equal Kc.