The rate of a first-order reaction is 0.048 m o l L − 1 s − 1 at 10 minutes and 0.03 m o l L − 1 s − 1 at 20 minutes after initiation. Find the time in seconds when 75% of the reactant is consumed.

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r 1 ​ = k C 1 ​ , and r 2 ​ = k C 2 ​ . r 2 ​ r 1 ​ ​ = C 2 ​ C 1 ​ ​ = 0.03 0.048 ​ k = t 2.303 ​ lo g ( C 2 ​ C 1 ​ ​ ) k = 10 2.303 ​ lo g ( 0.03 0.048 ​ ) = 0.047 min − 1 t = k 2.303 ​ lo g ( 25 100 ​ ) = 29.5 min = 1770 sec

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