The following data were reported for the decompoistion of `N_(2)O_(5)` in `C Cl_(4)` at `303 K`:
`|{:("Time (min)",120,160,200,240,oo),("Vol of" O_(2) (mL),37.70,45.85,52.67,58.34,84.35):}|`
Show that the reaction is the first order and calculate the rate constant.
Note: This is an example of direct-estimation of Product, i.e., `O_(2)`.

Explanation

`2N_(2)O_(5) rarr 4NO_(2) + O_(2)`
`k = (2.303)/(t) log.(V_(oo))/(V_(oo) - V_(t))`
(a) `k = (2.303)/(120) log.(84.35)/(84.35-37.70)`
`= (2.303)/(120) log.(84.35)/(46.65)`
`= (2.303)/(120) xx 0.2572 = 0.0049 min^(-1)`
(b) `k = (2.303)/(160) log.(84.35)/(84.35-45.85) = 0.0049 min^(-1)`
( c) `k = (2.303)/(200) log.(84.35)/(84.35-52.67) = 0.0049 min^(-1)`
(d) `k = (2.303)/(240)log.(84.35)/(84.35 - 58.34) = 0.0049 min^(-1)`
The value of `k` is constant. Hence, first order reaction.