Conisder the following elementary reaction,
`2A + B + C rarr` Products. All reactants are present in the gaseous state and reactant `C` is taken in excess.
What is the rate expresison of the reaction?

Options

A. Rate `= k[A]^(2)[B][C]`
B. Rate `= k[A]^(2)[B]`
C. Rate `= k([A]^(2)[B])/([C])`
D. Rate `= k[C]^(0)`

Explanation

To derive the rate expression for the given elementary reaction \(2A + B + C \rightarrow \text{Products}\), follow these steps:

### Step 1: Identify the reaction and its components
The reaction involves three reactants: \(A\), \(B\), and \(C\). The stoichiometric coefficients are important as they indicate the relationship between the reactants and the rate of the reaction.

### Step 2: Consider the excess reactant
Since reactant \(C\) is taken in excess, its concentration will not change significantly during the reaction. Therefore, it can be considered constant for the purpose of writing the rate expression.

### Step 3: Write the general form of the rate expression
For an elementary reaction, the rate can be expressed in terms of the concentrations of the reactants raised to the power of their respective stoichiometric coefficients. The general form is:
\[ \text{Rate} = k [A]^m [B]^n [C]^p \]
where \(k\) is the rate constant, and \(m\), \(n\), and \(p\) are the coefficients of \(A\), \(B\), and \(C\) respectively.

### Step 4: Substitute the coefficients
From the reaction \(2A + B + C\):
- The coefficient of \(A\) is \(2\) (so \(m = 2\)),
- The coefficient of \(B\) is \(1\) (so \(n = 1\)),
- The coefficient of \(C\) is \(1\) but since \(C\) is in excess, we do not include it in the rate expression.

Thus, the rate expression simplifies to:
\[ \text{Rate} = k [A]^2 [B]^1 \]

### Step 5: Finalize the rate expression
We can write the final rate expression as:
\[ \text{Rate} = k [A]^2 [B] \]