For a reaction of order n, the integrated form of the rate equation is: (n - 1)K·t = (C)^1-n - (C0)^1-n, where C0 and C are the values of the reactant concentration at the start and after time 't'. Wh

Question

For a reaction of order n, the integrated form of the rate equation is: (n - 1)K·t = (C)^1-n - (C0)^1-n, where C0 and C are the values of the reactant concentration at the start and after time 't'. What is the relationship between t_3/4 and t_1/2, where t_3/4 is the time required for C to become C0/4.

Prashant Kotian · Accepted Answer

Correct answer: A. For t_1/2, C = C0/2 => (n-1)K t_1/2 = C0^(1-n) (2^(n-1) - 1). For t_3/4, C = C0/4 => (n-1)K t_3/4 = C0^(1-n) (4^(n-1) - 1). Dividing the two gives t_3/4 / t_1/2 = (4^(n-1) - 1) / (2^(n-1) - 1) = 2^(n-1) + 1. Therefore, correct answer is A.

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