Question

90% of a first order reaction was completed in 100 min. What is the half life of the reaction ?

• A. 63.3 min
• B. 53.3 min
• C. 43.3 min
• D. 30 min

Answer 1

Answer: (D)

30 min

Here we start the solution by assuming the initial concentration $\left[A_0\right]$ to be 'x'.

According to the given question, the reaction follows first-order kinetics and undergoes 90% completion in 100 minutes which means 90% of the reactant is consumed and only 10% of it is remaining.

Thus the final concentration $\left[A_t\right]$ ( which is 10% of the initial concentration) = '0.1x'

Now we substitute the given values in the integrated rate equation for the first-order reaction and we get the value of k (Rate constant).

$k=\frac{2.303}{timetaken}\times log\frac{\left[A_0\right]}{\left[A_t\right]}$

$\therefore k=\frac{2.303}{100}\times log\frac{1}{0.1}$

$\therefore k=0.02303$

Now, by substituting the value of k we can find the half life time of the given first-order reaction.

$t_{1/2}=\frac{0.693}{k}$ and here $k=0.02303$

$\therefore t_{1/2}=30minutes$

Thus, the correct answer is option(D).