A certain organic compound A decomposes by two parallel first order mechanism
If $k_{1} : k_{2} = 1 : 9$ and $k_{1} = 1.3 \times 1 0^{- 5} s^{- 1}$ , calculate the concentration ratio of C to A, if an experiment is started with only A and allowed to run for one hour.
( $ln 1.6 = 0.468$ , $ln 1.52 = 0.4212$ )

Question

A certain organic compound A decomposes by two parallel first order mechanism

If $k_{1} : k_{2} = 1 : 9$ and $k_{1} = 1.3 \times 1 0^{- 5} s^{- 1}$ , calculate the concentration ratio of C to A, if an experiment is started with only A and allowed to run for one hour.

( $ln 1.6 = 0.468$ , $ln 1.52 = 0.4212$ )

TestHub · Accepted Answer

For a parallel first-order reaction: [ A ] [ C ] ​ = k 1 ​ k 2 ​ ​ ( 1 − e − k t ) Given: k 1 ​ : k 2 ​ = 1 : 9 , k 1 ​ = 1.3 × 1 0 − 5 s − 1 k 2 ​ = 9 ( 1.3 × 1 0 − 5 ) = 1.17 × 1 0 − 4 s − 1 k = k 1 ​ + k 2 ​ = 1.3 × 1 0 − 4 s − 1 , t = 3600 s [ A ] [ C ] ​ = 10 9 ​ ( 1 − e − 0.468 ) = 10 9 ​ ( 1 − 0.626 ) [ A ] [ C ] ​ ≈ 0.54

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