The first-order rate constant for the conversion of cyclobutane to ethylene at 1000°C is 87 s?¹. C?H? (g) ? 2 C?H? (g) cyclobutane ethylene a) Calculate the half-life for this reaction at 1000°C. b) If there is initially 2.00 g cyclobutane, how long would it take to consume 1.50 g of it?
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The first-order rate constant for the conversion of (a) What cyclobutane to ethylene at $1000 .{ }^{\circ} \mathrm{C}$ is $87 \mathrm{~s}^{-1}$. is the half-life of this reaction at $1000 .{ }^{\circ} \mathrm{C} ?(\mathrm{~b})$ If you started with $4.00 \mathrm{~g}$ of cyclobutane, how long would it take to consume $2.50 \mathrm{~g}$ of it? (Hint: Write the ratio of concentrations, $[\mathrm{A}]_{0} /[\mathrm{A}],$ in terms of mass, molecular weight, and volume.) (c) How much of an initial $1.00-\mathrm{g}$ sample of cyclobutane would remain after $1.00 \mathrm{~s}$ ?
Consider the first-order decomposition of cyclobutane at $438^{\circ} \mathrm{C}$ at constant volume: $\mathrm{C}_{4} \mathrm{H}_{8}(g) \rightarrow 2 \mathrm{C}_{2} \mathrm{H}_{4}(g)$. a. Express the rate of the reaction in terms of the change in total pressure as a function of time. b. The rate constant for the reaction is $2.48 \times 10^{-4} \mathrm{s}^{-1} .$ What is the half-life? c. After initiation of the reaction, how long will it take for the initial pressure of $\mathrm{C}_{4} \mathrm{H}_{8}$ to drop to $90 \%$ of its initial value?
Cyclobutane decomposes to form ethane according to: \[ \mathrm{C}_{4} \mathrm{H}_{8}(\mathrm{g}) \rightarrow 2 \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g}) \] A quantity of cyclobutane was sealed in a container and exerted a pressure of $53.30 \mathrm{kPa}$ at $700 \mathrm{K}$. The pressure changed during the reaction as follows. At the end of the reaction, the pressure was $106.60 \mathrm{kPa}$ $$\begin{array}{ll} \hline \text { Time/s } & \text { Total pressure/kPa } \\ \hline 0 & 53.30 \\ 2000 & 64.53 \\ 4000 & 73.59 \\ 6000 & 80.53 \\ 8000 & 85.99 \\ 10000 & 90.39 \end{array}$$ Assuming the gases behave ideally, show graphically that the reaction is first order with respect to cyclobutane. Calculate the rate constant and the half life for the reaction. (Section $9.4)$
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