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.