First slide

First order reactions

Question

For the first order reaction, X $\to$ Y the time taken for 90% completion of the reaction is 666 minutes. Time taken for 75% completion of the reaction will be ------ minutes

Moderate

A

600
B

400
C

540
D

450

Solution

$\frac{t_{90 %}}{t_{50 %}} = \frac{\frac{2.303}{K} \log \frac{100}{100 - 90}}{\frac{2.303}{K} \log \frac{100}{100 - 50}}; \frac{t_{90 %}}{t_{50 %}} = \frac{1}{\log 2} t_{90 %} = 3.33 t_{50 %}; t_{50 %} = \frac{666}{3.33} = 200 minutes; Conclusion : t_{99.9 %} = 10 t_{50 %}; t_{75 %} = 2 t_{50 %}; t_{87.5 %} = 3 t_{50 %}; t_{93.75 %} = 4 t_{50 %}; t_{96.875 %} = 5 t_{50 %};$

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