Question

Half life of zero order reaction is 1 hour. If initial concentration of reactant is 2.0 mol \(\text{L}^{-1}\), find the time required to decrease concentration from 0.50 to 0.25 mol \(\text{L}^{-1}\)

• A. \(0.25\) hour
• B. \(0.50\) hour
• C. \(1.00\) hour
• D. \(4.00\) hour

Hint:

For zero order, \(k = [A]_0/(2t_{1/2})\) and \(t = \Delta[A]/k\).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
A zero order reaction has a constant rate, so the concentration falls by the same amount in each equal time. The half life is \(t_{1/2} = \dfrac{[A]_0}{2k}\).

Step 2: Key Formula or Approach
\[ k = \frac{[A]_0}{2\,t_{1/2}} = \frac{2.0}{2\times1} = 1.0\ \text{mol L}^{-1}\text{h}^{-1} \]

Step 3: Detailed Explanation
The concentration falls from 0.50 to 0.25, a drop of 0.25 mol/L.
\[ t = \frac{0.25}{1.0} = 0.25\ \text{h} \]
For a zero order reaction the time does not depend on the starting point of the drop, only on the size of the drop.

Final Answer:
The time needed is 0.25 hour, option (A). \[ \boxed{0.25\ \text{hour (A)}} \]