In Arrhenius eauation for a certain reaction- the values of A and Ea activation energy are 4- 1013 sec -1 and 98-6 kJ mol-1 respectively- If the reaction is of first order- at what temperature will its half life period be 10 minutes -

According to Arrhenius equation, k=Ae^ E_a/RT or nbsp; nbsp; nbsp; nbsp; log_ek=log_eA E_aRT or nbsp; nbsp; nbsp; nbsp; nbsp;2.303 log_ ...

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Standard VII

Chemistry

Activation Energy

In Arrhenius ...

Question

In Arrhenius eauation for a certain reaction, the values of A and $E_{a}$ (activation energy) are $4 \times 10^{13} s e c^{- 1}$ and 98.6 kJ $m o l^{- 1}$ respectively. If the reaction is of first order, at what temperature will its half life period be 10 minutes ?

T = 110.65 K

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T = 210.95 K

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T = 310.95 K

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T = 510.00 K

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Solution

The correct option is C $T = 310.95 K$
According to Arrhenius equation,
$k = A e^{- E_{a} / R T}$
or $l o g_{e} k = l o g_{e} A - \frac{E_{a}}{R T}$
or $2.303 l o g_{10} k = 2.303 l o g_{10} A - \frac{E_{a}}{R T}$
For a first order reaction $t_{1 / 2} = \frac{0.693}{k}$
$t_{1 / 2} = 10 min = 600 sec$
So, $k = \frac{0.693}{600} s e c^{- 1} = 1.1 \times 10^{- 3} s e c^{- 1}$
Hence, $l o g (1.1 \times 10^{- 3}) = l o g (4 \times 10^{13}) - \frac{98.6 \times 10^{3}}{2.303 \times 8.314 \times T}$
$T = 310.95 K$
Thus (c) is correct.

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In Arrhenius eauation for a certain reaction, the values of A and Ea (activation energy) are 4×1013sec−1 and 98.6 kJ mol−1 respectively. If the reaction is of first order, at what temperature will its half life period be 10 minutes ?

In Arrhenius eauation for a certain reaction, the values of A and $E_{a}$ (activation energy) are $4 \times 10^{13} s e c^{- 1}$ and 98.6 kJ $m o l^{- 1}$ respectively. If the reaction is of first order, at what temperature will its half life period be 10 minutes ?