From the following data, show that the decomposition of hydrogen peroxide is a reaction of the first order : {:(t,,,0,,,10,,,20),(x,,,46.1,,,29.8,,,19.3):} where t is the time in minutes and x is the volume of standard KMnO_(4) solution in "cm"^(3) required for titrating the same volume of the reaction mixture.

From the following data, show that the decomposition of hydrogen perox

1.	From the following data, show that the decomposition of hydrogen peroxide is a reaction of the first order : {:(t,,,0,,,10,,,20),(x,,,46.1,,,29.8,,,19.3):} where t is the time in minutes and x is the volume of standard KMnO_(4) solution in "cm"^(3) required for titrating the same volume of the reaction mixture.
Answer» Solution :Volume of `"KMnO"_(4)` solution used `prop`amount of `H_(2)O_(2)` present. Hence, ifthe given reaction is of the first order, it must obey the equation : `k=(2.303)/(t)log""(a)/(a-x)=(2.303)/(t)log""(V_(0))/(V_(t))` (Note that the SYMBOL x in the numerical PROBLEM isin FACT `a-x, i.e., V_(t)`) In the present CASE, `V_(0)=46.1" cm"^(3)` The value of k at each instant can be calculated as follows: `{:("t (min)",,,V_(t),,,""k=(2.303)/(t)log""(V_(0))/(V_(t))),(10,,,29.8,,,k=(2.303)/(10min)log""(46.1)/(29.8)=0.0436min^(-1)),(20,,,19.3,,,k=(2.303)/(20min)log""(46.1)/(19.3)=0.0435min^(-1)):}` Thus, the value of k comesout to be nearly constant. Hence, it is a reaction of the first order.