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  •   For a first order reaction, calculate the ratio between the time taken to complete 3/4 th of the reaction and time taken to complete half of the reaction?

For a first order reaction, calculate the ratio between the time taken to complete 3/4 th of the reaction and time taken to complete half of the reaction?

Answers (1)

best_answer

Using the integrated rate law for a first-order reaction, $$
t= \frac {2.303} {k} log \frac {a_0} {a}
$$ 

Here, 

  • a0 = initial concentration
  • a = concentration at time t

For 50 % reaction, $$
t_(\frac {1}{2})= \frac {2.303} {k} log \frac {a_0} {\frac {a_0} {2}}=\frac {2.303} {k} log 2 = \frac {0.693} {k}
$$ 

For 75% reaction, $$
t_(\frac {3}{4})= \frac {2.303} {k} log \frac {a_0} {\frac {a_0} {4}}=\frac {2.303} {k} log 4 = \frac {1.386} {k}
$$ 

The ratio between the time taken to complete 75% of the reaction and the time taken to complete half of the reaction is $$
\frac {t_(\frac {3}{4})}{t_(\frac {1}{2})}=2
$$

Posted by

Saniya Khatri

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