42.0 min first-order reaction to drop from 0.45 M to 0.32 M

42.0 min first-order reaction to drop from 0.45 M to 0.32 M

It takes 42.0 min for the concentration of a reactant in a first-order reaction to drop from 0.45 M to 0.32 M at 25℃. How long will it take for the reaction to be 90% complete?

A. 13.0 min

B. 86.0 min

C. 137 min

D. 222 min

E. 284 min

1차 반응 속도식

ln(C_t / C_0) = –k•t

( 참고 https://ywpop.tistory.com/26 )

k = –ln(C_t / C_0) / t

= –ln(0.32 / 0.45) / 42.0

= 0.0081173 /min

90% complete

---> C_0 = 100 이면,

C_t = 10 이므로,

t = –ln(C_t / C_0) / k

= –ln(10 / 100) / 0.0081173

= 283.6639 min

답: E. 284 min

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