The isomerization reaction $C{H}_{3}NCC{H}_{3}CN$ obeys the first$-$order rate law, rate $=k[C{H}_{3}NC],$ in the presence of an excess of argon. Measurement at $500.$ K reveals that in $487$ seconds, the concentration of $C{H}_{3}N{C}^2$ has decreased to $73\%$ of its original value. Calculate the rate constant $(k)$ of the reaction at $500.K.$

$s^{-1}$

$($The integrated form for the first$-$order rate law can be written in the general terms $ln[A{]}_t-ln[A{]}_0=-kt,$ where $[A{]}_0$ is the initial concentration of reactant $A,[A{]}_t$ is the concentration of $A$ at time $t,$ and $k$ is the rate constant.$)$

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