The rate for the single -step reaction `2A+B to 2C` is given by

Options

A. rate =`k[A]*[B]`
B. rate =`k[A]^(2) *[B]`
C. rate =k`[2A] *[B]`
D. rate `=k[A]^(2)*[B]^(0)`

Answer

To derive the rate law expression for the reaction \(2A + B \rightarrow 2C\), we follow these steps:

### Step-by-Step Solution:

1. **Identify the Reaction**: The given reaction is \(2A + B \rightarrow 2C\). This is a single-step reaction.

2. **Understand the Stoichiometry**: In a single-step reaction, the rate of the reaction can be expressed in terms of the stoichiometric coefficients of the reactants. The stoichiometric coefficients indicate the order of the reaction with respect to each reactant.

3. **Write the Rate Law Expression**:
- The rate law is generally expressed as:
\[ \text{Rate} = k \cdot [A]^m \cdot [B]^n \]
- Here, \(k\) is the rate constant, \([A]\) and \([B]\) are the concentrations of the reactants, and \(m\) and \(n\) are the orders of the reaction with respect to \(A\) and \(B\), respectively.

4. **Assign Orders Based on Stoichiometry**:
- For reactant \(A\), the stoichiometric coefficient is 2, so the order with respect to \(A\) is 2.
- For reactant \(B\), the stoichiometric coefficient is 1, so the order with respect to \(B\) is 1.

5. **Final Rate Law Expression**:
- Substituting the values of \(m\) and \(n\) into the rate law expression, we get:
\[ \text{Rate} = k \cdot [A]^2 \cdot [B]^1 \]
- This can also be written as:
\[ \text{Rate} = k \cdot [A]^2 \cdot [B] \]

### Summary:
The rate law expression for the reaction \(2A + B \rightarrow 2C\) is:
\[ \text{Rate} = k \cdot [A]^2 \cdot [B] \]