Ethylene is produced by C_4H_8 (text{Cyclobut | vedclass

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(B) The reaction is $C_4H_8 \rightarrow 2C_2H_4$. Let the initial moles of $C_4H_8$ be $a$. At time $t$,let $x$ moles of $C_4H_8$ react. Remaining mol

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$30$

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(B) The reaction is $C_4H_8 ightarrow 2C_2H_4$. Let the initial moles of $C_4H_8$ be $a$. At time $t$,let $x$ moles of $C_4H_8$ react. Remaining moles of $C_4H_8 = a - x$. Moles of $C_2H_4$ formed = $2x$. Given that the molar ratio $\frac{[C_2H_4]}{[C_4H_8]} = 1$,so $\frac{2x}{a - x} = 1$. $2x = a - x$ $\Rightarrow 3x = a$ $\Rightarrow x = \frac{a}{3}$. Remaining concentration of $C_4H_8$ at time $t$ is $[A]_t = a - \frac{a}{3} = \frac{2a}{3}$. Using the first-order rate equation $t = \frac{2.303}{k} \log \frac{[A]_0}{[A]_t}$: $t = \frac{2.303}{2.3 	imes 10^{-4}} \log \frac{a}{2a/3} = 10013 	imes \log(1.5)$. $t = 10013 	imes 0.1761 \approx 1763.3 	ext{ s}$. Converting to minutes: $t = \frac{1763.3}{60} \approx 29.39 	ext{ min} \approx 30 	ext{ min}$.

Ethylene is produced by $C_4H_8 (\text{Cyclobutane}) \xrightarrow{\text{Heat}} 2C_2H_4$. The rate constant is $2.3 \times 10^{-4} \text{ s}^{-1}$. In what time will the molar ratio of ethylene to cyclobutane in the reaction mixture attain the value $1$? ...... $\text{min}$

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