The rate law of the reaction `2N_2O_5 rarr4NO_2+O_2` is

Options

A. Rate = `K[NO_2]^(4)[O_2]`
B. Rate `=K[N_2O_5]^2`
C. Rate `=K[N_2O_5]^0`
D. Rate `=K[N_2O_5]`

Answer

To determine the rate law of the reaction \(2N_2O_5 \rightarrow 4NO_2 + O_2\), we need to understand the relationship between the concentration of the reactants and the rate of the reaction. Here’s a step-by-step breakdown of how to derive the rate law:

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

### Step 2: Write the general form of the rate law
The rate law expresses the rate of a reaction in terms of the concentration of its reactants. It can be written as:
\[ \text{Rate} = k [\text{Reactant}]^n \]
where \(k\) is the rate constant, and \(n\) is the order of the reaction with respect to that reactant.

### Step 3: Determine the reactant concentration
In this reaction, the only reactant is \(N_2O_5\). Therefore, we can express the rate law as:
\[ \text{Rate} = k [N_2O_5]^n \]

### Step 4: Determine the order of the reaction
The order of the reaction (denoted by \(n\)) can be determined experimentally. However, for many reactions, especially elementary reactions, the order is often equal to the stoichiometric coefficient of the reactant. In this case, the stoichiometric coefficient of \(N_2O_5\) is 2.

### Step 5: Conclude the order of the reaction
While the stoichiometric coefficient suggests that the order might be 2, the actual order can be different based on experimental data. For the decomposition of \(N_2O_5\), it is known that this reaction is first-order with respect to \(N_2O_5\). Therefore, we set \(n = 1\).

### Final Rate Law
Thus, the rate law for the reaction is:
\[ \text{Rate} = k [N_2O_5]^1 \]
or simply:
\[ \text{Rate} = k [N_2O_5] \]