The rate law for the reaction `2N_2 O_5 to 4NO_2 + O_2` is

Options

A. `r-k [N_2 O_5]`
B. `r=k [N_2 O_5]^2`
C. `r=k [N_2 O_5]^(0)`
D. `r=k [NO_2]^4 [O_2]`

Explanation

To determine the rate law for the reaction \(2N_2O_5 \rightarrow 4NO_2 + O_2\), we can follow these steps:

### Step 1: Identify the Reaction
The reaction given is:
\[ 2N_2O_5 \rightarrow 4NO_2 + O_2 \]

### Step 2: Determine if the Reaction is Elementary
In this case, we assume that the reaction is elementary. An elementary reaction is one that occurs in a single step and has a rate law that can be directly derived from its stoichiometry.

### Step 3: Write the Rate Law
For an elementary reaction, the rate law can be expressed as:
\[ \text{Rate} = k \cdot [\text{Reactants}]^{\text{stoichiometric coefficient}} \]

Here, the only reactant is \(N_2O_5\), and its stoichiometric coefficient is 2. Therefore, the rate law can be written as:
\[ \text{Rate} = k \cdot [N_2O_5]^2 \]

### Step 4: Determine the Order of the Reaction
The order of the reaction is defined as the sum of the powers of the concentration terms in the rate law. Since the only reactant is \(N_2O_5\) and its exponent is 2, the order of the reaction is:
\[ \text{Order} = 2 \]

### Final Rate Law
Thus, the rate law for the reaction \(2N_2O_5 \rightarrow 4NO_2 + O_2\) is:
\[ \text{Rate} = k \cdot [N_2O_5]^2 \]