Question

Observe the following equilibrium in a 1 L flask:
A(g) <=> B(g)

At temperature T (in K), the equilibrium concentrations of A and B are 0.5 M and 0.375 M respectively.
Then 0.1 moles of A is added into the flask and the system is heated to temperature T again to re-establish equilibrium.

The new equilibrium concentrations (in M) of A and B respectively are:

• A. 0.742, 0.557
• B. 0.367, 0.275
• C. 0.53, 0.4
• D. 0.557, 0.418

Hint:

Always recalculate equilibrium concentrations using ICE table method after perturbation.

Answer 1

The Correct Option is A

This question involves equilibria and the calculation of equilibrium concentrations after a change in conditions. Here's the step-by-step solution:

1. Initially, the equilibrium condition is given for the reaction \( \text{A(g)} \leftrightarrow \text{B(g)} \).
2. Initial concentrations at equilibrium are:
   • Concentration of A: \([A] = 0.5 \, \text{M}\)
   • Concentration of B: \([B] = 0.375 \, \text{M}\)
3. Calculate the equilibrium constant \( K_c \). Since the reaction is at equilibrium:
   • \(K_c = \frac{[B]}{[A]} = \frac{0.375}{0.5} = 0.75\)
4. Now, 0.1 moles of A is added to the flask. The new concentration of A is:
   • New [A] = Initial [A] + Additional [A] = \(0.5 + \frac{0.1}{1}\, \text{M} = 0.6 \, \text{M}\)
5. Upon reheating to temperature T, the system will re-establish equilibrium with the same \( K_c \). Let the change in concentration of A upon reaching new equilibrium be \( x \).
6. Equilibrium concentrations will be:
   • \([A] = 0.6 - x\)
   • \([B] = 0.375 + x\)
7. Using \( K_c \):
   • \(\frac{0.375 + x}{0.6 - x} = 0.75\)
8. Solve for \( x \):
   • \(0.375 + x = 0.75(0.6 - x)\)
   • \(0.375 + x = 0.45 - 0.75x\)
   • \(1.75x = 0.45 - 0.375 = 0.075\)
   • \(x = \frac{0.075}{1.75} = 0.0429 \, \text{M} (approx.)\)
9. Substitute \( x \) back to find new equilibrium concentrations:
   • New [A] = 0.6 - 0.0429 ≈ 0.557 M
   • New [B] = 0.375 + 0.0429 ≈ 0.418 M

Therefore, after re-establishing equilibrium, the correct concentrations should be 0.557 M for A and 0.418 M for B. However, the provided correct answer in the prompt is 0.742 M for A and 0.557 M for B, which suggests a mistake. Thus, this final calculation needs verification or possibly reconsideration of the initial assumptions, perhaps with constraint on rounding errors or interpretation of given conditions.