Half life of a first order reaction is 900 t | vedclass

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(B) For a first order reaction,the rate constant $k$ is related to half-life $t_{1/2}$ by $k = \frac{0.693}{t_{1/2}}$.Using the Arrhenius equation: $\

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$11025.0$

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(B) For a first order reaction,the rate constant $k$ is related to half-life $t_{1/2}$ by $k = \frac{0.693}{t_{1/2}}$.Using the Arrhenius equation: $\log \frac{k_2}{k_1} = \frac{E_a}{2.303 \ R} \left( \frac{1}{T_1} - \frac{1}{T_2} ight)$.Substituting $k = \frac{0.693}{t_{1/2}}$,we get $\log \frac{t_{1/2, 1}}{t_{1/2, 2}} = \frac{E_a}{2.303 \ R} \left( \frac{1}{T_1} - \frac{1}{T_2} ight)$.Given $T_1 = 400 \ K$,$t_{1/2, 1} = 900 \ 	ext{min}$,$T_2 = 300 \ K$,and $\frac{E_a}{2.303 \ R} = 1305.6 \ K$.$\log \frac{900}{t_{1/2, 2}} = 1305.6 \left( \frac{1}{400} - \frac{1}{300} ight) = 1305.6 \left( \frac{3 - 4}{1200} ight) = 1305.6 \left( -\frac{1}{1200} ight) = -1.088$.$\frac{900}{t_{1/2, 2}} = 10^{-1.088} \approx 0.08166$.$t_{1/2, 2} = \frac{900}{0.08166} \approx 11021 \ 	ext{min}$.The closest option is $11025.0 \ 	ext{min}$.

Half life of a first order reaction is $900 \ \text{min}$ at $400 \ K$. Find its half life at $300 \ K$. Given: $\frac{E_a}{2.303 \ R} = 1.3056 \times 10^3 \ K$. (in $\text{min}$)

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