Question

For a first order reaction, the time required for $99.9\%$ of the reaction to take place in nearly:

• A. $10$ times that required for half the reaction
• B. $100$ times that required for two-third of the reaction
• C. $10$ times that required for one-fourth of the reaction
• D. $20$ times that required for half of the reaction.

Answer 1

Answer: (A)

$10$ times that required for half the reaction

Using the integral rate law we know

$t_{1/2}=\frac{ln\left(2\right)}{k}$ ( from $ln\left(\frac{A_o}{A}\right)=kt)$

and,

$t_{99.9\%}=\frac{ln\left(100\right)}{k}$

$=\frac{10ln2}{k}$

$t_{99.9\%}=10t_{1/2}$