3. At 300 K, a vessel containing 0.55 M of azomethane (C2H6N2) takes 2.0 h for 70% of the compound to decompose. What is the rate constant of this first order process?
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The decomposition of azomethane, $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{~N}_{2},$ to nitrogen and ethane gases is a first-order reaction, $$ \left(\mathrm{CH}_{3}\right)_{2} \mathrm{~N}_{2}(g) \rightarrow \mathrm{N}_{2}(g)+\mathrm{C}_{2} \mathrm{H}_{6}(g) $$ At a certain temperature, a 29 -mg sample of azomethane is reduced to $12 \mathrm{mg}$ in $1.4 \mathrm{~s}$. (a) What is the rate constant $k$ for the decomposition at that temperature? (b) What is the half-life of the decomposition? (c) How long will it take to decompose $78 \%$ of the azomethane?
Azomethane, $\mathrm{CH}_{3} \mathrm{~N}_{2} \mathrm{CH}_{5}(g)$, decomposes according to the equation $$ \mathrm{CH}_{3} \mathrm{~N}_{2} \mathrm{CH}_{3}(g) \rightarrow \mathrm{CH}_{3} \mathrm{CH}_{3}(g)+\mathrm{N}_{2}(g) $$ Given that the decomposition is a first-order process with $k=4.0 \times 10^{-4} \mathrm{~s}^{-1}$ at $300^{\circ} \mathrm{C}$, calculate the fraction of azomethane that remains after $1.0$ hour.
Gaseous azomethane, $\mathrm{CH}_{3} \mathrm{N}=\mathrm{NCH}_{3},$ decomposes in a first-order reaction when heated: $$\mathrm{CH}_{3} \mathrm{N}=\mathrm{NCH}_{3}(\mathrm{g}) \rightarrow \mathrm{N}_{2}(\mathrm{g})+\mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{g})$$ The rate constant for this reaction at $600 \mathrm{K}$ is 0.0216 $\min ^{-1} .$ If the initial quantity of azomethane in the flask is $2.00 \mathrm{g},$ how much remains after $0.0500 \mathrm{h} ?$ What quantity of $\mathbf{N}_{2}$ is formed in this time?
David C.
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