Question

Match the column where ‘a’ is the initial concentration of the reactant and ‘P’ is the initial pressure of the reactant.

List 1	List 2
\[{t_{1/2}} = constant\]	First order
\[{t_{1/2}} \propto a\]	Pseudo first order
\[{t_{1/2}} \propto {P^{ - 1}}\]	Zero order
\[{t_{1/2}} \propto {a^{ - 1}}\]	Second order

Answer 1

Hint: We have to know that the Pseudo first order reaction is actually following second order but has some properties like first order reaction thus it is said pseudo order reaction. \[{t_{1/2}} = 0.693/K\]for first order reaction. Half life for a reaction is constant in case of first order.

Complete answer:
In the following question list 1 contains half life and list 2 contains order of the reaction. In the question it is given that ‘a’ is the initial concentration of the reactant and ‘P’ is the initial pressure of reactant. Now let’s start the question.
We know \[{t_{1/2}} = \dfrac{{0.693}}{K}\] for the first order reaction. Thus \[\dfrac{{0.693}}{K}\] this value is constant so we can say that \[{t_{1/2}} = constant\] is for First order reaction. Now look for second one \[{t_{1/2}} \propto a\] it says that half life is directly proportional to initial concentration of reactant so this condition is applicable for zero order reaction, thus \[{t_{1/2}} \propto a\] follows zero order reaction. Now look for the third option which is \[{t_{1/2}} \propto {P^{ - 1}}\] it says that half life is inversely proportional to initial pressure of the reactant. When we look for ideal gas law which says that \[pV = nRT\]or it can be seen like \[pV = aRT\]thus Initial Pressure is directly proportional to initial concentration that is following second order and we left with no option thus it will be Pseudo first order reaction. Now for the last which says \[{t_{1/2}} \propto {a^{ - 1}}\]it says that half life is inversely proportional to the initial concentration this condition is followed by a second order reaction.
Answer-

List 1	List 2
\[{t_{1/2}} = constant\]	First order
\[{t_{1/2}} \propto a\]	Zero order
\[{t_{1/2}} \propto {P^{ - 1}}\]	Pseudo First order
\[{t_{1/2}} \propto {a^{ - 1}}\]	Second order

Note:
We must have to know that in first order reaction the half life is independent of the initial concentration whereas it is dependent directly in case of zero order and for second order reaction it is inversely proportional to the concentration.