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 \( A + 2B \rightarrow C \) with the rate law given as \( -\frac{d[C]}{dt} = k[A]^2 \), we need to analyze the provided statements to identify the false one.

### Step-by-Step Solution:

1. **Understanding the Rate Law**:
The rate law is given as \( -\frac{d[C]}{dt} = k[A]^2 \). This indicates that the rate of the reaction depends only on the concentration of \( A \) and is proportional to the square of its concentration. The concentrations of \( B \) and \( C \) do not appear in this rate law, indicating that they do not affect the rate of the reaction.

**Hint**: Focus on which species affect the rate based on the rate law.

2. **Analyzing Statement 1**:
Statement 1 claims that doubling the concentrations of \( B \) and \( C \) will not affect the rate of reaction. Since the rate law only depends on \( [A] \), this statement is true.

**Hint**: Check if the rate law includes \( B \) or \( C \).

3. **Analyzing Statement 2**:
Statement 2 states that reducing the concentration of \( A \) to half will reduce the rate to one-fourth. If \( [A] \) is halved, the new rate becomes:
\[ \text{New Rate} = k\left(\frac{[A]}{2}\right)^2 = k\frac{[A]^2}{4} \]
This confirms that the rate becomes one-fourth, making this statement true.

**Hint**: Calculate the new rate using the given rate law when \( [A] \) is halved.

4. **Analyzing Statement 3**:
Statement 3 claims that the half-life period of the reaction depends on the concentration of \( B \). The half-life for a reaction of this order (second order in \( A \)) is given by:
\[ t_{1/2} = \frac{1}{k[A]_0} \]
This shows that the half-life depends only on the initial concentration of \( A \) and not on \( B \). Therefore, this statement is false.

**Hint**: Determine how the half-life is derived from the rate law.

5. **Analyzing Statement 4**:
Statement 4 states that the half-life period of the reaction is inversely proportional to the first power of the concentration of \( A \). Since we derived that \( t_{1/2} \) is inversely proportional to \( [A]_0 \), this statement is true.

**Hint**: Confirm the relationship between half-life and concentration from the derived formula.

### Conclusion:
The false statement regarding the reaction is **Statement 3**, which incorrectly claims that the half-life period depends on the concentration of \( B \).