first-order reaction A → B 25% complete 42 min half-life

first-order reaction A → B 25% complete 42 min half-life

A certain first-order reaction A → B

is 25% complete in 42 min at 25℃.

What is the half-life of the reaction?

A. 21 min

B. 42 min

C. 84 min

D. 20 min

E. 101 min

1차 반응 속도식

ln(C_t / C_0) = –k•t

( 참고 https://ywpop.tistory.com/26 )

25% complete

---> C_0 = 100 이라 두면,

C_t = 75 이므로,

k = –ln(C_t / C_0) / t

= –ln(75 / 100) / 42

= 0.00685 /min

1차 반응의 반감기 식

t_1/2 = ln(2) / k

= 0.693 / k

= 0.693 / 0.00685

= 101.17 min

답: E. 101 min

[키워드] 1차 반응 기준, 1차 반응 반감기 기준