In a reaction at equilibrium moles of the reactant A decompose to give 1 mole of each of B and C. It has been found that the fraction of A decomposed at equilibrium is independent of the initial concentration of A. Calculate x.

Explanation

To solve the problem, we need to analyze the decomposition of reactant A into products B and C. Let's denote the initial moles of A as \( x \) and the degree of dissociation of A as \( \alpha \). The reaction can be represented as follows:

### Step 1: Write the balanced chemical equation
The reaction can be represented as:
\[ A \rightleftharpoons B + C \]

### Step 2: Define the initial concentrations
Let the initial concentration of A be \( [A]_0 = x \). At the start of the reaction, the concentrations of B and C are zero:
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