Question

For a certain reaction A $\to$ products, the $t_{1/2}$ as a function of [A]${}_0$ is given as below:
$\left[A{]}_0\right(M):$ 0.1 0.025
$t_{1/2}(min.):$ 100 50
Which of the following is/are true?

• A. The order is $\frac{1}{2}$
• B. $t_{t/2}$ would be $100\sqrt{10}$ min for $[A{]}_0=1M$
• C. The order is 1
• D. $t_{1/2}$ would be 100 min for $[A{]}_0=1M$

Answer 1

Answer: (A), (B)

The correct options are
A The order is $\frac{1}{2}$
B $t_{t/2}$ would be $100\sqrt{10}$ min for $[A{]}_0=1M$

$100\alpha (0.1{)}^{1-n}$
$50\alpha (0.025{)}^{1-n}$
Divide $2=4^{1-n}$
$2=2^{2-2n}$ $\Rightarrow 2-2n=1$
$n=\frac{1}{2}$
$100\alpha (0.1{)}^{1/2}$
$t^{1/2}\alpha (1{)}^{1/2}$
$Divide\frac{t_{1/2}}{100}={\left(\frac{1}{0.1}\right)}^{1/2}$
$t_{1/2}=100\sqrt{10}min.$