For the reaction , the backward reaction rate constant is higher than the forward reaction rate constant by a factor of 2500, at 1000 K. [Given: ] for the reaction at 1000 K is: [2025]

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Solution

Q.
For the reaction $A_{(g)} ⇌ 2 B_{(g)}$ , the backward reaction rate constant is higher than the forward reaction rate constant by a factor of 2500, at 1000 K.

[Given: $R = 0.0831$ $L$ $atm$ ${mol}^{- 1}$ $K^{- 1}$ ]

$K_{p}$ for the reaction at 1000 K is: [2025]

1 0.033

2 0.021

3 83.1

4 $2.077 \times 10^{5}$

Ans.
(1)

For reaction, $A_{(g)} ⇌ 2 B_{(g)}$

R = 0.0831 L atm ${mol}^{- 1}$ $K^{- 1}$ , T = 1000 K

$K_{c} = \frac{k_{f}}{k_{b}} = \frac{k_{f}}{2500 k_{f}} = \frac{1}{2500}$

As $K_{p} = K_{c} {(R T)}^{Δ n_{g}}$

$K_{p} = \frac{1}{2500} {(0.0831 \times 1000)}^{1} = 0.033$ $[As, Δ n_{g} = 2 - 1 = 1]$

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