A) 1.1 times that of half-life
B) 2.2 times that of half-life
C) 3.3 times that of half-life
D) 4.4 times that of half-life
Correct Answer: C
Solution :
Half-life period of first order reaction is \[{{t}_{1/2}}=\frac{2.303\times 0.3010}{k}\] ??(i) Time for completion of 90% of a first order reaction is \[{{t}_{90}}=\frac{2.303}{k}\log \frac{100}{10}\] \[\therefore \] \[{{t}_{90}}=\frac{2.303}{k}\] .,,,(ii) On dividing Eq. (i) by (ii), we get \[\frac{{{t}_{1/2}}}{{{t}_{90}}}=\frac{2.303\times 0.3010}{k}\times \frac{k}{2.303}\] \[\Rightarrow \] \[\frac{{{t}_{1/2}}}{{{t}_{90}}}=\frac{0.3010}{1}\] \[\Rightarrow \] \[{{t}_{90}}=\frac{1}{0.3010}\times {{t}_{1/2}}\] \[\therefore \] \[{{t}_{90}}=3.322\times {{t}_{1/2}}\]
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