Decomposition of A 2 ( g ) and B 3 ( g ) follows first-order kinetics as follows. Here, K 1 and K 2 are the rate constants with respect to disappearance of A 2 and B 3 , respectively. One mole, ea

Question

Decomposition of A 2 ​ ( g ) and B 3 ​ ( g ) follows first-order kinetics as follows. Here, K 1 and K 2 are the rate constants with respect to disappearance of A 2 and B 3 , respectively. One mole, each of A 2 (g) and B 3 (g), is taken in a 100 L evacuated flask and at some temperature at which they start decomposing at the same rate. The incorrect information regarding the reactions is

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Question Explanation:

Find incorrect information regarding the reactions.

Concept :

This question is based on first order reaction.

Solution:

$K_{1} = K_{2} \Rightarrow - \frac{14000}{RT} + 5 = - \frac{20000}{RT} + 10$

$\Rightarrow T = \frac{1200}{8.314} K$

Now, $\frac{P _{A_{2}}}{P _{B_{3}}} = \frac{1 \times e ^{- K_{1} t}}{1 \times e ^{- K_{2} t}} = \frac{1}{1}$

Now, initial pressure

$P_{0} = \frac{( 1 + 1 ) \times 0.0821 \times \frac{1200}{8.314}}{100} = 0.237 atm$

As number of moles will increase on reaction, the total pressure can never be less than 0.2 atm Now, $\frac{P _{A}}{P _{B}} = \frac{2 K _{1}}{3 K _{2}} = \frac{2}{3}$

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