Question

\(A(g) ⇋ 2B(g) + C(g)\)
For the given reaction, if the initial pressure is 450 mm Hg and the pressure at time t is 720 mm Hg at a constant temperature T and constant volume V. The fraction of A(g) decomposed under these conditions is \(x × 10^{–1}\). The value of x is _____ . (nearest integer)

Answer 1

Correct Answer: 3

The reaction is given as: \[ A(g) \rightleftharpoons 2B(g) + C(g) \] At time \( t = 0 \), the pressure of A is 450 mmHg, and at time \( t = t \), the total pressure is 720 mmHg.
Let the extent of decomposition at time \( t \) be \( 2x \), so that the pressures of \( A \), \( B \), and \( C \) at time \( t \) are:
Pressure of A = \( 450 - x \)
Pressure of B = \( 2x \)
Pressure of C = \( x \)
Thus, the total pressure at time \( t \) is: \[ P_t = P_A + P_B + P_C = (450 - x) + 2x + x = 720 \, \text{mmHg} \] Now, solving for \( x \): \[ 720 = 450 - x + 2x + x \] \[ 720 = 450 + 2x \] \[ 270 = 2x \] \[ x = 135 \] The fraction of A decomposed is: \[ \text{Fraction of A decomposed} = \frac{x}{450} = \frac{135}{450} = 0.3 = 3 \times 10^{-1} \] Thus, the value of \( x \) is 3.