Question

For a first order reaction, the time required for completion of $90 \%$ reaction is ' $x$ ' times the half life of the reaction. The value of ' $x$ ' is
(Given: $\ln 10=2.303$ and $\log 2=0.3010$ )

• A. $1.12$
• B. $2.43$
• C. $3.32$
• D. $33.31$

Answer 1

Answer: (C)

Given $t _{0.90}= t _{0.90}= xt _{1 / 2}$
First order rate constant
$K =\frac{\ln 2}{ t _{1 / 2}}=\frac{1}{ xt _{1 / 2}} \ln \frac{ A _{0}}{ A _{0}- A _{0} \times \frac{90}{100}}$
$\frac{\ln 2}{ t _{1 / 2}}=\frac{\ln 10}{ xt _{1 / 2}}$
$x=\frac{\ln 10}{\ln 2}=\frac{2.303}{2.303 \times 0.3010}=3.32$