Consider the following in respect of zero order reaction.
I. `t_(1//2)` is directly proportional to the initial concentration
II. Time taken for the completion of the reaction is twice its `t_(1//2)`
III Concentration of the reactant decreases linearly with time
Which of the statements given above are correct ?

Options

A. I & II only
B. I & III only
C. II & III only
D. I, II & III

Answer

To solve the question regarding the statements about zero-order reactions, let's analyze each statement step by step.

### Step 1: Understanding Zero-Order Reactions
In a zero-order reaction, the rate of reaction is constant and does not depend on the concentration of the reactants. The rate law for a zero-order reaction can be expressed as:
\[ \text{Rate} = k \]
where \( k \) is the rate constant.

### Step 2: Analyzing Statement I
**Statement I:** \( t_{1/2} \) is directly proportional to the initial concentration.

The half-life (\( t_{1/2} \)) for a zero-order reaction is given by the formula:
\[ t_{1/2} = \frac{[A]_0}{2k} \]
where \( [A]_0 \) is the initial concentration of the reactant. From this equation, we can see that \( t_{1/2} \) is directly proportional to the initial concentration \( [A]_0 \).

**Conclusion:** Statement I is correct.

### Step 3: Analyzing Statement II
**Statement II:** Time taken for the completion of the reaction is twice its \( t_{1/2} \).

For a zero-order reaction, the total time (\( t \)) taken for the reaction to go to completion can be derived from the equation:
\[ [A] = [A]_0 - kt \]
When the reaction is complete, \( [A] = 0 \):
\[ 0 = [A]_0 - kt \]
This gives:
\[ kt = [A]_0 \]
Now, substituting \( t_{1/2} \) into the equation:
\[ k \cdot (2 \cdot t_{1/2}) = [A]_0 \]
Thus, the time taken for the completion of the reaction is indeed twice the half-life:
\[ t = 2t_{1/2} \]

**Conclusion:** Statement II is correct.

### Step 4: Analyzing Statement III
**Statement III:** Concentration of the reactant decreases linearly with time.

For a zero-order reaction, the concentration of the reactant decreases linearly over time, as shown by the equation:
\[ [A] = [A]_0 - kt \]
This indicates that as time increases, the concentration decreases at a constant rate, which is characteristic of linear behavior.

**Conclusion:** Statement III is correct.

### Final Conclusion
All three statements regarding zero-order reactions are correct:
- Statement I: Correct
- Statement II: Correct
- Statement III: Correct

Thus, the answer is that all statements are correct.

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