In the Arrhenius equation for a first order reaction- the values of -A- and -E a- are 4 - 1013 sec-1 and 98-6 kJ mol-1 respectively- At what temperature will its half life period be 10 minutes- -R - 8-314 J K-1 mol-1-

The half life period t_1/2 is 10 minutes. The rate constant #160; k = 0.693 t_1/2 k = 0.69310 min × 60 s/min k = 1.155 × 10^ 3 /s Th ...

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Standard XII

Chemistry

Elementary and Complex Reactions

In the Arrhen...

Question

In the Arrhenius equation for a first order reaction, the values of 'A' and 'E $_{a}$ ' are $4 \times 10^{13} s e c^{- 1}$ and $98.6 k J m o l^{- 1}$ respectively. At what temperature will its half life period be 10 minutes?
$[R = 8.314 J K^{- 1} m o l^{- 1}]$

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Solution

The half life period $t_{1 / 2}$ is 10 minutes. The rate constant $k = \frac{0.693}{t_{1 / 2}}$
$k = \frac{0.693}{10 m i n \times 60 s / m i n}$
$k = 1.155 \times 10^{- 3} / s$
The Arrhenius equation is
$l n k = l n A - \frac{E_{a}}{R T}$
Here, k is the rate constant, A is the frequency factor, $E_{a}$ is the energy of activation, R is the ideal gas constant and T is absolute temperature.
$l n 1.155 \times 10^{- 3} / s = l n 4 \times 10^{13} s e c^{- 1} - \frac{98600 J / m o l}{8.314 J K^{- 1} m o l^{- 1} \times T}$
$\frac{98600 J / m o l}{8.314 J K^{- 1} m o l^{- 1} \times T} = 38.08$
$T = 311.4 K$
Hence, at a temperature of 311.4 K, half life period will be 10 minutes.

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In the Arrhenius equation for a first order reaction, the values of 'A' and 'Ea' are 4×1013sec−1 and 98.6kJmol−1 respectively. At what temperature will its half life period be 10 minutes?[R=8.314JK−1mol−1]

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