First slide

First order reactions

Question

For the first order reaction, X $\to$ Y the time taken for 99.9% completion of the reaction is 500 minutes. Time taken for 50% completion of the reaction will be ------ minutes

Moderate

A

100
B

50
C

150
D

200

Solution

$\frac{t_{99.9 %}}{t_{50 %}} = \frac{\frac{2.303}{K} \log \frac{100}{100 - 99.9}}{\frac{2.303}{K} \log \frac{100}{100 - 50}}; \frac{t_{99.9 %}}{t_{50 %}} = \frac{3 \log 10}{0.3010}; \frac{t_{99.9 %}}{t_{50 %}} = 10; t_{99.9 %} = 10 t_{50 %}; similarly \frac{t_{75 %}}{t_{50 %}} = \frac{\frac{2.303}{K} \log \frac{100}{100 - 75}}{\frac{2.303}{K} \log \frac{100}{100 - 50}}; \frac{t_{75 %}}{t_{50 %}} = \frac{2 \log 2}{\log 2} t_{75 %} = 2 t_{50 %}; Conclusion : t_{99.9 %} = 10 t_{50 %}; t_{75 %} = 2 t_{50 %}; t_{87.5 %} = 3 t_{50 %}; t_{93.75 %} = 4 t_{50 %}; t_{96.875 %} = 5 t_{50 %};$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App