Question

A first order reaction was 90% completed in 10 hours when will be the 99.9% of the reaction completed

Answer 1

Answer:

30

Explanation:

t99.9% = t90% x 3= 10x t50%

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Answer 2

The time after which 99.9% reactions gets completed is 30 hours

Explanation:

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant

a - x = amount left after decay process  

a) for completion of 90 % of the reaction:

$10=\frac{2.303}{k}\log\frac{100}{100-90}$

$k=0.2303hours^{-1}$

b) for completion of 99.9 % of the reaction:

$t=\frac{2.303}{0.2303}\times \log\frac{100}{100-99.9}$

$t_{99.9}=30hours$

The time after which 99.9% reactions gets completed is 30 hours

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