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Factors Affecting Alpha

A homogeneous...

Question

A homogeneous ideal gaseous reaction $A B_{2 (g)} ⇌ A_{(g)} + 2 B_{(g)}$ is carried out in a $25 L$ flask at $27^{o} C$ . The initial amount of $A B_{2}$ was $1 m o l$ and the equilibrium pressure was $1.9 a t m$ . The value of $K_{P}$ is $x \times 10^{- 2}$ . The value of $x$ is ______. $[R = 0.08206 d m^{3} a t m K^{- 1} m o l^{- 1}]$

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Solution

$A B_{2 (g)} ⇌ A_{(g)} + 2 B_{(g)}$
Initial mole $100$
At eq. $1 - x x 2 x$
At equilibrium,
$n_{T} = \frac{P V}{R T} n_{T} = \frac{1.9 \times 25}{0.08206 \times 300} = 1.93 Total number of moles at equilibrium: n_{T} = 1 - x + x + 2 x = 1 + 2 x 1 + 2 x = 1.93 ∴ x = 0.465$

$K_{P} = \frac{P_{A} P_{B}^{2}}{P_{A B_{2}}} P_{A} = X_{A} P_{t o t a l} K_{P} = \frac{(\frac{0.465}{1.93} \times 1.9) {(\frac{0.93}{1.93} \times 1.9)}^{2}}{(\frac{0.535}{1.93} \times 1.9)} ∴ K_{P} = 73 \times 10^{- 2} a t m^{2}$

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