(a) (i) From the following data, show that the decomposition of hydrogen peroxide is a reaction of the first order :
`|{:("t (min)",0,10,20),("V (ml)",46.1,29.1,19.3):}|`
Where t is the time in minutes and V is the volume of standard `KMnO_(4)` solution required for titrating the same volume of the reaction mixture.
(ii) Define molecularity of a reaction.

From the following data, show that the decomposition of hydrogen peroxide is a reaction of the order : {:("t (min)",0,10,20),("V (ml)",46.1,29.8,19.3):} Where t is the time in minutes and V is the volume of standard KMnO_(4) solution required for titrating the same volume of the reaction mixture.

Benzene diazonium chloride in aqueous solution decomposes according to the equation C^(6)H^(5)N^(2)Cl rarr C_(6)H_(5)Cl+N_(2) Starting with an initial concentration of 10 g L^(-1) , the volume of N_(2) gas obtained at 50^(@)C at different intervals of time was found to be as under : {:("t (min)":,6,12,18,24,30,oo),("Vol. of "N_(2) (ml):,19.3,32.6,41.3,46.5,50.4,58.3):} Show that the above reaction follows the first order kinetic. What is the value of the rate constant ?

Consider a tank which initially holds V_(0) liter of brine that contains a lb of salt. Another brine solution, containing b lb of salt per liter is poured into the tank at the rate of eL//"min" . The problem is to find the amount of salt in the tank at any time t. Let Q denote the amount of salt in the tank at any time. The time rate of change of Q, (dQ)/(dt) , equals the rate at which salt enters the tank at the rate at which salt leaves the tank. Salt enters the tank at the rate of be lb/min. To determine the rate at which salt leaves the tank, we first calculate the volume of brine in the tank at any time t, which is the initial volume V_(0) plus the volume of brine added et minus the volume of brine removed ft. Thus, the volume of brine at any time is V_(0)+et-ft The concentration of salt in the tank at any time is Q//(V_(0)+et-ft) , from which it follows that salt leaves the tank at the rate of f(Q/(V_(0)+et-ft)) lb/min. Thus, (dQ)/(dt)=be-f(Q/(V_(0)+et-ft))Q=be A tank initially holds 100 L of a brine solution containing 20 lb of salt. At t=0, fresh water is poured into the tank at the rate of 5 L/min, while the well-stirred mixture leaves the tank at the same rate. Then the amount of salt in the tank after 20 min.

A certain amount of methyl acetate was hydrolysed in the presence of excess of "0.05 M HCl at "25^(@)C . 20 mL of reaction mixture were removed and titrated with NaOH solution, the volume V of alkali required for neutralisation after time ‘t’ were as follows : {:("t(min)",0,20,40,60,oo),("v(mL)",20.2,25.6,29.5,32.8,50.5):} Show that the reaction is the first order reaction.