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First Order Reaction

A gaseous com...

Question

A gaseous compound A reacts by three independent first-order processes (as shown in the figure) with rate constant $2 \times 10^{3}, 3 \times 10^{3} a n d 1.93 \times 10^{3} s e c^{1}$ for products B, C and D respectively. If initially pure A was taken in a closed container with $P = 8 a t m,$ then the partial pressure of B (in atm) after 100 sec from the start of experiment:

A

0.288

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B

0.577

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C

1.154

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D

n o n e o f t h e s e

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Solution

The correct option is B $1.154$
Overall rate constant $= k = k_{1} + k_{2} + k_{3} = 6.93 * 10^{3} t_{1 / 2} = \frac{0.693}{6.93 * 10^{- 3}} = 100 s e c;$
After half-life, $P_{B} + P_{C} + P_{D} = 4 a t m \frac{P_{B}}{P_{B} + P_{C} + P_{D}} = \frac{k_{1}}{k_{1} + k_{2} + k_{3}} = \frac{200}{693} P_{B} = 4 * \frac{200}{693} = 1.154 a t m$

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Similar questions

Q. A gaseous compound

A

reacts by three independent first order processes (as shown in figure) with rate constant

2 \times 10^{- 3}, 3 \times 10^{- 3}

1.93 \times 10^{- 3}

s e c^{- 1}

B, C

D

respectively. If initially pure

A

was taken in a closed container with

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dissociate by two parallel first order paths at certain temperature

A (g) k_{1} ({m i n}^{- 1}) - ----- \to 2 B (g)

k_{1} = 6.93 \times 10^{- 3} m i n^{- 1}

A (g) k_{2} ({m i n}^{- 1}) - ----- \to C (g)

k_{2} = 6.93 \times 10^{- 3} m i n^{- 1}

The reaction started with

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