To calculate the rate of decomposition of `H_(2)O_(2)` in an aqueous solution , a certain volume of the aqueous solution of `H_(2)O_(2)` is pipetted out and titrated against `KMnO_(4)` solution at different interval of time . Intervals The observations are given below :
`{:(Time ("in min"),0,5,10,20),("Volume of "KMnO_(4)("inML"),46.2,37.1,29.8,19.6):}`
Show that the decomposition of `H_(2)O_(2)` in aqueous solution is a first order reaction and calculate its rate constant .