When moleucles of type A react with molecules of type B in one-step process to give `AB_(2)`, the rate law is

Options

A. `"rate" = K[A]^(1)[B]^(2)`
B. `"rate" = K[A]^(2)[B]^(1)`
C. `"rate" = K[2A][B]`
D. `"rate" = K[A][B]`

Explanation

To determine the rate law for the reaction where a molecule of type A reacts with a molecule of type B to produce \( AB_2 \), we can follow these steps:

### Step 1: Identify the reactants and products
In this reaction, we have:
- Reactants: A and B
- Product: \( AB_2 \)

### Step 2: Write the balanced chemical equation
The balanced equation for the reaction can be written as:
\[ A + 2B \rightarrow AB_2 \]

### Step 3: Determine the stoichiometric coefficients
From the balanced equation, we can see the stoichiometric coefficients:
- For A: 1
- For B: 2

### Step 4: Write the rate law expression
The rate law expression is generally written as:
\[ \text{Rate} = k [A]^m [B]^n \]
where \( k \) is the rate constant, and \( m \) and \( n \) are the stoichiometric coefficients of A and B, respectively.

### Step 5: Substitute the stoichiometric coefficients into the rate law
From our balanced equation:
- \( m = 1 \) (for A)
- \( n = 2 \) (for B)

Thus, the rate law can be expressed as:
\[ \text{Rate} = k [A]^1 [B]^2 \]
or simply:
\[ \text{Rate} = k [A] [B]^2 \]

### Step 6: Conclude the order of the reaction
The overall order of the reaction is the sum of the exponents in the rate law:
\[ \text{Order} = 1 + 2 = 3 \]

### Final Rate Law
Therefore, the rate law for the reaction is:
\[ \text{Rate} = k [A] [B]^2 \]

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