Question

For a certain reaction $A\to P$, the half life for different initial concentrations of $A$ is mentioned below.

$A_o$	0.1	0.025
$t_{\frac{1}{2}}$	100	50

Which of the following option(s) is / are incorrect.

• A. The order is $1$
• B. The order is $0.5$
• C. For $\left[A_o\right]=1M,t_{\frac{1}{2}}=100\sqrt{10}\text{sec}$
• D. For $\left[A_o\right]=1M,t_{\frac{1}{2}}=100\text{sec}$

Answer 1

Answer: (A), (D)

For $\left[A_o\right]=1M,t_{\frac{1}{2}}=100\text{sec}$

For a certain reaction,
$A\to P$
Half life $t_{\frac{1}{2}}\propto [A_o{]}^{1-n}$
Where n = order of the reaction
So, $100\propto (0.1{)}^n...(i)$
$50\propto [0.025{]}^{1-n}...(ii)$
On dividing equation (i) by (ii) we get
$2=4^{1-n}$
$n=\frac{1}{2}=0.5$
When initial concentration, $\left[A_o\right]=1M$
Then,
$t_{\frac{1}{2}}\propto [1{]}^{1-\frac{1}{2}}...(iii)$
And
$100\propto (0.1{)}^{\frac{1}{2}}...(iv)$
On dividing equation (iii) by (iv) we get
$\frac{t_{\frac{1}{2}}}{100}=(\frac{1}{0.1}{)}^{\frac{1}{2}}$
$t_{\frac{1}{2}}=100\sqrt{10}\text{sec}$
Hence, incorrect options are (a) and (d).