For the elementary reaction, `A+2B rarr C`, the rate law will be equal to :-

Options

A. `R=k[A]^(2)[B]^(1)`
B. `R=k[A][B]`
C. `R=k[A]^(1)[B]^(0)`
D. `R=k[A][B]^(2)`

Answer

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

### Step 1: Identify the reaction components
The reaction involves:
- Reactant A
- Reactant B (with a stoichiometric coefficient of 2)
- Product C

### Step 2: Write the general form of the rate law
For an elementary reaction, the rate law can be expressed as:
\[ \text{Rate} = k [A]^m [B]^n \]
where \( k \) is the rate constant, and \( m \) and \( n \) are the stoichiometric coefficients of the reactants in the balanced equation.

### Step 3: Assign the stoichiometric coefficients
From the reaction \( A + 2B \rightarrow C \):
- The stoichiometric coefficient for A is 1.
- The stoichiometric coefficient for B is 2.

### Step 4: Write the rate law using the coefficients
Substituting the stoichiometric coefficients into the rate law gives us:
\[ \text{Rate} = k [A]^1 [B]^2 \]
This simplifies to:
\[ \text{Rate} = k [A] [B]^2 \]

### Step 5: Determine the overall order of the reaction
The overall order of the reaction is the sum of the powers of the concentration terms in the rate law:
\[ \text{Overall order} = 1 + 2 = 3 \]

### Conclusion
The rate law for the reaction \( A + 2B \rightarrow C \) is:
\[ \text{Rate} = k [A] [B]^2 \]
And the overall order of the reaction is 3.

---