Question

For the first order reaction, $t_{99}$% $=x\times t_{90}$%, the value of $x$ will be:

• A. 10
• B. 6
• C. 3
• D. 2

Answer 1

The correct option is D 2

For $t_{90\%}$ ,$a_t=\frac{10a_0}{100}=\frac{a_0}{10}$

$t_{90\%}=\frac{1}{k}In\frac{a-0}{a_0/10}=\frac{In10}{k}$....(1)

For $t_{99\%}$, $a_t=\frac{1}{100}a-0$

$t_{99\%}=\frac{1}{K}In\frac{a_0}{a_0/100}=\frac{2In10}{k}$....(2)

From (1) and (2),

$t_{99\%}=2\times t_{90\%}=>x=2$