Reaction `A+2B+C to` Product, follows the rate law `-(d[C])/(dt)=k[A]^2` False statement regarding the above reaction is :

Options

A. On doubling the concentration of B and C the rate of the reaction remains unaffected
B. Reducing the concentration of A to half, the rate becomes one-fourth
C. Half life period of the reaction depends upon the concentration of B
D. Half life period of the reaction is inversely proportional to the first power concentration of A

Answer

To solve the question regarding the reaction \( A + 2B + C \to \text{Products} \) and its rate law \( -\frac{d[C]}{dt} = k[A]^2 \), we need to analyze the implications of the given rate law and identify the false statement among the options provided.

### Step-by-Step Solution:

1. **Understanding the Rate Law**:
The rate law given is \( -\frac{d[C]}{dt} = k[A]^2 \). This indicates that the rate of the reaction depends on the concentration of \( A \) raised to the power of 2, while the concentrations of \( B \) and \( C \) do not appear in the rate law. This suggests that \( A \) is the only reactant that affects the rate of the reaction.

**Hint**: Focus on how the rate law relates to the concentrations of reactants.

2. **Analyzing the Half-Life**:
For a reaction where the rate depends on \( [A]^2 \), the half-life \( t_{1/2} \) can be derived from the integrated rate law. The half-life for a second-order reaction (in terms of \( A \)) is given by:
\[ t_{1/2} = \frac{1}{k[A]_0} \]
This shows that the half-life is inversely proportional to the initial concentration of \( A \) and does not depend on the concentration of \( B \).

**Hint**: Recall the relationship between half-life and concentration for different orders of reactions.

3. **Evaluating Statements**:
- **Statement A**: "On doubling the concentration of \( B \) and \( C \), the rate becomes one-fourth." This is false because the rate does not depend on \( B \) or \( C \) at all.
- **Statement B**: "The half-life period of the reaction depends on the concentration of \( B \)." This is false since the half-life only depends on \( [A] \).
- **Statement C**: "Reducing the concentration of \( A \) to half makes the rate one-fourth." This is true because if \( [A] \) is halved, \( [A]^2 \) becomes one-fourth.
- **Statement D**: "The half-life period is inversely proportional to the first power of the concentration of \( A \)." This is true since the half-life is inversely proportional to \( [A]_0 \).

4. **Identifying the False Statement**:
The false statement is **Statement B**, which claims that the half-life depends on the concentration of \( B \). Since the rate law does not include \( B \), this statement is incorrect.

**Hint**: Compare the implications of the rate law with each statement to identify inconsistencies.

### Conclusion:
The false statement regarding the reaction is that the half-life period of the reaction depends on the concentration of \( B \). The correct option is **B**.