1. Tardigrade
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  4. The thermal decomposition of a molecule shows first order kinetics. The molecule decomposes 50% in 120 min. How much time it will take to decompose 90%?

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Q. The thermal decomposition of a molecule shows first order kinetics. The molecule decomposes 50% in 120 min. How much time it will take to decompose 90%?

JamiaJamia 2012

Solution:

For first order reaction, $ t=\frac{2.303}{k}\log \frac{a}{a-x} $ For 1st case, $ a=100,\text{ }x=50\text{ }and\text{ }t=120\text{ }min $ $ k=\frac{2.303}{120}\log \frac{100}{100-50} $ $ =\frac{2.303}{120}\log 2 $ $ =\frac{2.303}{120}\times 0.3010 $ $ k=0.005775{{\min }^{-1}} $ For the Und case $ t=\frac{2.303}{0.005775}\log \frac{100}{100-90} $ $ =\frac{2.303}{0.005775}\log 10 $ $ =398.78-398.8\text{ }min $