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

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.