The following results were obtained in the decomposition of `N_2 O_5` in `C Cl_4` at 315 K:

where x denotes the volume of oxygen evolved in seconds. Show that reaction is of first order and also calculate the rate constant.

Explanation

From the data given, we see that (i) Reading given at time indicates a. Thus, a = 34.75
(ii)x= 11.4, 15.53, 18.90 at t= 1200, 1800 and 2400 seconds respectively. If the reaction is of first order, it will obey the equation
` k=( 2.303 )/(t) log "" (a)/(a-x)`
since ` V_(oo ) prop a and V_t prop x , K = ( 2.303 )/(t) log "" (V_(oo) ) /( V_(oo) -V_(t))`
thus we have

As the values of k are nearly constant, the reaction is of first order. The average value of rate constant is 0.0003272.