Question

For the reaction \( \mathrm{A \rightleftharpoons B} \), the number of moles of A and B at equilibrium in a \(1\,\text{L}\) vessel are \(0.50\) and \(0.375\), respectively. If \(0.10\) mol of A is added further, determine the number of moles of A and B at the new equilibrium.

• A. \(0.557,\ 0.557\)
• B. \(0.418,\ 0.557\)
• C. \(0.33,\ 0.56\)
• D. \(0.6,\ 0.2\)

Hint:

After adding a reactant at equilibrium, always recalculate using the {same equilibrium constant}. ICE tables make such problems quick and systematic.

Answer 1

The Correct Option is A

To solve this problem, we will first calculate the equilibrium constant K_c for the reaction \( \mathrm{A \rightleftharpoons B} \) at the initial equilibrium and then use it to find the number of moles of A and B at the new equilibrium after adding more A.

1. At the initial equilibrium, the moles of A and B are given as \(0.50\) and \(0.375\), respectively, in a \(1 \, \text{L}\) vessel. Thus, the initial concentrations are:

   [A] = 0.50 \, \text{mol/L} [B] = 0.375 \, \text{mol/L}

   The equilibrium constant K_c for the reaction is given by the expression:

   K_c = \frac{[B]}{[A]}

   Substituting the values, we get:

   K_c = \frac{0.375}{0.50} = 0.75

2. Now, let's determine the new equilibrium after adding \(0.10\) mol of A. The total moles of A are now:

   0.50 + 0.10 = 0.60 \, \text{mol}

   At this point, assume \(x\) moles of A convert to B to reach new equilibrium. Thus, at the new equilibrium:

   [A] = 0.60 - x [B] = 0.375 + x

   Using the equilibrium constant:

   K_c = \frac{[B]}{[A]} = \frac{0.375 + x}{0.60 - x} = 0.75

   Solving for \(x\):

   0.75 (0.60 - x) = 0.375 + x 0.45 - 0.75x = 0.375 + x 0.45 - 0.375 = x + 0.75x 0.075 = 1.75x x = \frac{0.075}{1.75} \approx 0.043

3. Substituting the value of \(x\) back, the concentrations at equilibrium are:

   [A] = 0.60 - 0.043 \approx 0.557 \, \text{mol/L} [B] = 0.375 + 0.043 = 0.418 \, \text{mol/L}

   Thus, the number of moles of A and B at the new equilibrium are approximately \(0.557\) mol each.

Therefore, the correct answer is:

\(0.557, 0.557\)