Home › ISC Class 12 › Chemistry › Chemical Kinetics › For a first order reaction, show that the time r…
For a first order reaction, show that the time required for 99.9% completion is how many times the half-life t1/2?
A5 times
B10 times
C100 times
D3 times
Answer & Solution
Correct answer: B. 10 times
1. At 99.9% completion, $[R] = [R]_0 - 0.999[R]_0 = 0.001[R]_0$.
2. $t = \dfrac{2.303}{k}\log\dfrac{[R]_0}{0.001[R]_0} = \dfrac{2.303}{k}\log 10^3 = \dfrac{6.909}{k}$.
3. Half-life $t_{1/2} = \dfrac{0.693}{k}$.
4. $\dfrac{t}{t_{1/2}} = \dfrac{6.909}{0.693} = 10$.
5. Distractor A would correspond to 99% type fractions; this is exactly ten times.
_Source: NCERT Class 12 Chemistry Ch 3 "Chemical Kinetics", p.16_
Related questions
It is observed that for many reactions the rate constant nearly doubles for a rise in tempThe half-life for the radioactive decay of carbon-14 is 5730 years and decay is first ordeIn a pseudo first order reaction, [A]/mol L^-1 reads 0.31 at t = 30 s and 0.17 at t = 60 sIn collision theory, what is meant by the collision frequency (Z)?According to collision theory, in the modified rate expression Rate = P Z_AB e^(-Ea/RT), wHow does a catalyst increase the rate of a chemical reaction?The first order rate constant for decomposition of ethyl iodide is 1.60 x 10^-5 s^-1 at 60The rate constants of a reaction at 500 K and 700 K are 0.02 s^-1 and 0.07 s^-1 respective