form the following data for the decompoistion of `N_(2)O_(5)` in carbon tertrachloride solution at `321 K`, show that the reaction is of the first order and calculate the rate constant.

Explanation

If the reaction is of the first order, it must obey the equation.
`k = (2.303)/(t)log.(a)/(a-x) = (2.303)/(t)log.(V_(oo))/(V_(oo)-V_(t))`
Note: It is a case of direct estimation of one of the Product.
In the presents case, we are given that `V_(oo) = 34.75 cm^(3)`. The value of `k` at each can be calculated as follows:

Thus, the value of `k` comes out to be nearly constant, hence it is a reaction of the first order.