The rate equation for the reaction `2A+B to C` is found to be : rate = k[A] [B] The correct statement in relation to this reaction is that the

Options

A. unit of k must be `s^(-1)`
B. `t_(1//2)` is a constant
C. rate of formation of C is twice the rate of disappearance of A
D. value of k is independent of the initial concentration of A and B.

Explanation

To solve the question regarding the reaction \(2A + B \rightarrow C\) with the rate equation given as \(\text{rate} = k[A][B]\), we need to analyze the implications of this rate law step by step.

### Step 1: Identify the Order of the Reaction
The rate equation is given as \(\text{rate} = k[A][B]\). This indicates that the reaction is first order with respect to \(A\) and first order with respect to \(B\). Therefore, the overall order of the reaction is:
\[ \text{Order} = 1 + 1 = 2 \]

**Hint:** The overall order of a reaction can be determined by summing the powers of the concentration terms in the rate equation.

### Step 2: Understand the Implications of the Rate Law
The rate of the reaction depends on the concentrations of both \(A\) and \(B\). This means that if the concentration of either \(A\) or \(B\) changes, the rate of the reaction will change accordingly.

**Hint:** The rate law shows how the rate of a reaction is affected by the concentration of reactants.

### Step 3: Analyze the Half-Life of the Reaction
For a second-order reaction, the half-life (\(t_{1/2}\)) is not constant and depends on the initial concentration of the reactants. The half-life for a second-order reaction can be expressed as:
\[ t_{1/2} = \frac{1}{k[A]_0} \]
where \([A]_0\) is the initial concentration of \(A\). This shows that as the concentration of \(A\) decreases, the half-life increases.

**Hint:** The half-life of a reaction can provide insights into how the reaction rate changes over time, especially for different orders of reactions.

### Step 4: Relate the Rates of Reactants and Products
From the stoichiometry of the reaction \(2A + B \rightarrow C\), we can write the relationships between the rates of disappearance and formation:
\[ \text{Rate of disappearance of } A = -\frac{1}{2} \frac{d[A]}{dt} \]
\[ \text{Rate of formation of } C = \frac{d[C]}{dt} \]
According to stoichiometry, the rate of formation of \(C\) is twice the rate of disappearance of \(A\):
\[ \frac{d[C]}{dt} = -\frac{1}{2} \frac{d[A]}{dt} \Rightarrow \text{Rate of formation of } C = 2 \times \text{Rate of disappearance of } A \]

**Hint:** Stoichiometry of the reaction can be used to relate the rates of reactants and products.

### Step 5: Evaluate the Statement Regarding the Rate Constant \(k\)
The rate constant \(k\) is specific to the reaction at a given temperature and is independent of the initial concentrations of the reactants. However, it is affected by temperature and the nature of the reaction.

**Hint:** The rate constant \(k\) is a characteristic of the reaction and can change with temperature but not with concentration.

### Conclusion
Based on the analysis, the correct statement in relation to the reaction \(2A + B \rightarrow C\) is:
- The rate of formation of \(C\) is twice the rate of disappearance of \(A\).