Question

The decomposition of dinitrogen pentoxide (\[N{a_2}{O_5}\]) follows first order rate law . Calculate the rate constant from the given data :
\[t = 800\sec \] \[[N{a_2}{O_5}] = 1.45mol{L^{ - 1}} = [{A_1}]\]
\[t = 1600\sec \] \[[N{a_2}{O_5}] = 0.88mol{L^{ - 1}} = [{A_2}]\]

Answer 1

Hint: As we know that dinitrogen pentoxide also known as nitrogen pentoxide. Boiling point of dinitrogen pentoxide is \[47^\circ C\]. Its chemical formula is \[N{a_2}{O_5}\]. It comes out as colourless crystals which melts at \[41^\circ C\]. It show by chemical reaction:
\[2{N_2}{O_5} \to 4N{O_2} + {O_2}\]
In this reaction , \[2\]moles of \[{N_2}{O_5}\] gives \[4\]moles of \[N{O_2}\] .
\[1\]mole of \[{N_2}{O_5}\] gives \[2\]moles of \[N{O_2}\] . This balanced chemical reaction. The rate of law produces the rate equation for elementary reaction. We can derive the rate equation from first principles used in collision theory.

Complete answer: or Complete step by step answer:
For chemical reaction in the rate of law is an equation that the reaction rate with the concentration or partial pressures of the reactants . For normal reaction are
\[aA + bB \to C\]
Its meaning that is elementary reaction the rate of law is given by :
\[r = k{[A]^x}{[B]^y}\]
Dinitrogen pentoxide is binary nitrogen oxides . It is an unsteady and potentially dangerous oxidizer . It is utilized as a reagent when melted in chloroform for nitration . It adopts two structures depending on the situations . According to the question , decompositions of dinitrogen pentoxide follow order rate of law . So , from first order rate of law equation :
\[k = \dfrac{{2.303}}{{({t_2} - {t_1})}}\log \dfrac{{[{A_{1`}}]}}{{[{A_2}]}}\]
\[k = \dfrac{{2.303}}{{(1600 - 800)}}\log \dfrac{{1.45}}{{0.88}}\]
\[ = \dfrac{{2.303}}{{800}} \times 0.2169\]
Value of \[{t_1}\] and \[{t_2}\] given in question . Thus ,
\[k = 6.24 \times {10^{ - 4}}{s^{ - 1}}\]

Note:
Dinitrogen pentoxide is used in chloroform reagents. \[{N_2}{O_5}\] is a highly toxic nitrogen dioxide gas. Decomposition of dinitrogen pentoxide is a hard oxidizer that forms explosive combinations with ammonium salts.