Question

Which of the following is the correct relation for half life period of a zero order reaction?

• A. It is directly proportional to initial concentration of reactants
• B. It is inversely proportional concentrations of reactants
• C. It is directly proportional to the concentration of product.
• D. It is inversely proportional to the square of initial concentration of reactants

Hint:

Use the integrated rate equation of a zero order reaction to find how the half life depends on the initial concentration.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
For a zero order reaction the rate does not depend on concentration, so the reactant is used up at a constant rate.

Step 2: Integrated equation
\([A]_t=[A]_0-kt\)

Step 3: Half life
At \(t=t_{1/2}\), \([A]_t=\dfrac{[A]_0}{2}\). So \(\dfrac{[A]_0}{2}=kt_{1/2}\), which gives \(t_{1/2}=\dfrac{[A]_0}{2k}\).

Step 4: Compare the options
Since \(t_{1/2}\propto[A]_0\), the half life is directly proportional to the initial concentration of the reactant.

Final Answer:
The half life is directly proportional to the initial concentration of the reactant. \[ \boxed{\text{(A) }\text{It is directly proportional to initial concentration of reactants}} \]