The rate law for the single step reaction `2A + B to X` 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)`

Explanation

To determine the rate law for the single step reaction \(2A + B \to X\), we can follow these steps:

### Step 1: Identify the reactants and their stoichiometry
The reaction involves two reactants: \(A\) and \(B\). The stoichiometric coefficients from the balanced equation are:
- For \(A\): 2
- For \(B\): 1

### Step 2: Understand the relationship between stoichiometry and reaction order
For elementary reactions (which this is, since it occurs in a single step), the order of the reaction with respect to each reactant is equal to its stoichiometric coefficient in the balanced equation.

### Step 3: Write the rate law expression
The rate law can be expressed as:
\[ \text{Rate} = k [A]^m [B]^n \]
where:
- \(k\) is the rate constant,
- \(m\) is the order with respect to \(A\),
- \(n\) is the order with respect to \(B\).

### Step 4: Assign the orders based on stoichiometry
From the stoichiometry:
- The order with respect to \(A\) (m) is 2 (since the coefficient of \(A\) is 2).
- The order with respect to \(B\) (n) is 1 (since the coefficient of \(B\) is 1).

### Step 5: Combine the orders to write the complete rate law
Substituting the values of \(m\) and \(n\) into the rate law expression gives:
\[ \text{Rate} = k [A]^2 [B]^1 \]
or simply:
\[ \text{Rate} = k [A]^2 [B] \]

### Step 6: Determine the overall order of the reaction
The overall order of the reaction is the sum of the individual orders:
\[ \text{Overall order} = m + n = 2 + 1 = 3 \]

### Final Answer
Thus, the rate law for the reaction \(2A + B \to X\) is:
\[ \text{Rate} = k [A]^2 [B] \]
and the overall order of the reaction is 3.

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