A gaseous compound 'A' reacts by three independent first order processes (as shown in figure) with rate constant 2 × 1 0 − 3 , 3 × 1 0 − 3 and 1.93 × 1 0 − 3 sec − 1 for products B, C and D,

Question

A gaseous compound 'A' reacts by three independent first order processes (as shown in figure) with rate constant $2 \times 1 0^{- 3}, 3 \times 1 0^{- 3}$ and $1.93 \times 1 0^{- 3} sec^{- 1}$ for products B, C and D, respectively. It initially pure 'A' was taken in a closed container with $P = 2 atm$ , find the partial pressure of 'B' (in atm) after 100 sec from start of experiment.

TestHub · Accepted Answer

Total Rate Constant ( k t o t a l ​ ): For parallel first-order reactions, k t o t a l ​ = k 1 ​ + k 2 ​ + k 3 ​ = ( 2 + 3 + 1.93 ) × 1 0 − 3 = 6.93 × 1 0 − 3 s − 1 . Decomposed Pressure of A ( Δ P A ​ ): At t = 100 s , Δ P A ​ = P 0 ​ ( 1 − e − k t o t a l ​ t ) = 2 ( 1 − e − 0.693 ) a t m . Simplification: Since e − 0.693 = 0.5 , the total reacted pressure of A is Δ P A ​ = 2 × ( 1 − 0.5 ) = 1 a t m . Partial Pressure of B ( P B ​ ): P B ​ = k t o t a l ​ k 1 ​ ​ × Δ P A ​ = 6.93 × 1 0 − 3 2 × 1 0 − 3 ​ × 1 a t m ≈ 0.29atm (or 0.28 a t m ).

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