Which among the following is a false statement

Options

A. Half life of a third order reaction is inversely proportional to the square of initial concentration of the reactant
B. Molecularity of a reaction may be zero or fractional
C. For a first order reaction `t_(1//2) = (0.693)/(K)`
D. Rate of zero order reaction is independent of initial concentration of reactant

Explanation

To determine which statement is false among the given options regarding chemical kinetics, let's analyze each statement step by step.

### Step 1: Analyze the First Statement
**Statement:** Half-life of a third-order reaction is inversely proportional to the square of the initial concentration of the reactant.

**Analysis:**
- The half-life (\(t_{1/2}\)) of a reaction can be expressed as:
\[ t_{1/2} \propto \frac{1}{[A_0]^{n-1}} \]
where \(n\) is the order of the reaction.
- For a third-order reaction (\(n = 3\)):
\[ t_{1/2} \propto \frac{1}{[A_0]^{3-1}} = \frac{1}{[A_0]^2} \]
- This means that the half-life is indeed inversely proportional to the square of the initial concentration.

**Conclusion:** This statement is **true**.

### Step 2: Analyze the Second Statement
**Statement:** The molecularity of a reaction may be zero or fractional.

**Analysis:**
- Molecularity refers to the number of reactant molecules involved in an elementary reaction step.
- It is defined as an integer (1, 2, 3, etc.) and cannot be zero or fractional.
- Therefore, the statement claiming that molecularity can be zero or fractional is incorrect.

**Conclusion:** This statement is **false**.

### Step 3: Analyze the Third Statement
**Statement:** For a first-order reaction, \(t_{1/2} = \frac{0.693}{k}\).

**Analysis:**
- The half-life for a first-order reaction is given by:
\[ t_{1/2} = \frac{0.693}{k} \]
- This is a well-established formula in chemical kinetics.

**Conclusion:** This statement is **true**.

### Step 4: Analyze the Fourth Statement
**Statement:** The rate of a zero-order reaction is independent of the initial concentration of the reactant.

**Analysis:**
- For a zero-order reaction, the rate law is given by:
\[ R = k[A]^0 = k \]
- This indicates that the rate is constant and does not depend on the concentration of the reactant.

**Conclusion:** This statement is **true**.

### Final Conclusion
After analyzing all statements, the false statement is:
**The molecularity of a reaction may be zero or fractional.**