In an experiment on the decomposition of an aqueous `NH_(4)NO_(2)` at a certain temperature, the volume of nitrogen gas collected at different intervals of time was as follows:
`|{:("Time (s)",1190,2300,oo),("Vol of" N_(2) (mL),5.00,7.30,9.50):}|`
Show how the above data illustrate that the reaction is of first order.
Note: This is an example of direct-estimation of Product, i.e., `N_(2)`.

Explanation

To show that the decomposition of aqueous \( NH_4NO_2 \) is a first-order reaction based on the provided data, we will use the integrated rate law for first-order reactions. The steps are as follows:

### Step 1: Write the balanced decomposition reaction
The decomposition of ammonium nitrite can be represented as:
\[ NH_4NO_2 \rightarrow N_2 + 2 H_2O \]

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