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Given that for a reaction of order n the integrated form of the rate equation is k = 1 t ( n - 1 ) 1 C n - 1 - 1 C 0 n - 1 where C 0 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 1 4 C 0

Options

  1. At 3 4 = t 1 2 2 n - 1 + 1
  2. Bt 3 4 = t 1 2 2 n - 1 - 1
  3. Ct 3 4 = t 1 2 2 n + 1 - 1
  4. Dt 3 4 = t 1 2 [ 2 n + 1 + 1 ]

Correct answer

A. t 3 4 = t 1 2 2 n - 1 + 1

Step-by-step solution

t 1 / 2 = 1 k n − 1 2 n − 1 C 0 n − 1 − 1 C 0 n − 1 = 1 k n − 1 2 n − 1 − 1 C 0 n − 1 → 1 t 3 / 4 = 1 k n − 1 2 2 n − 2 − 1 C 0 n − 1 → 2 t 3 / 4 t 1 / 2 = 2 n - 1 + 1 ⇒ t 3 / 4 = t 1 2 2 n - 1 + 1

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