In an experiment on the decompoistion 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

`NH_(4)NO_(2) rarr N_(2) +2H_(2)O`
`k = (2.303)/(t)log.(V_(oo))/(V_(oo) - V_(t))`
(a) `k = (2.303)/(1190) log.(9.50)/(9.50-5.0)`
`= (2.303)/(1190) log.(9.50)/(4.5)`
`= (2.303)/(1190) xx 0.32 = 0.0006 s^(-1)`
(b) `k = (2.303)/(2300)log.(9.50)/(9.50-7.30)`
`= (2.303)/(2300) xx 0.635 = 0.0006 s^(-1)`
The value of `k` is constant. Hence, first order reaction.