The activation energy for a reaction at the temperature TK was found to be 2.303 $R T J m o l^{- 1}$ . The ratio of the rate constant to Arrhenius factor is ___

$10^{- 2}$

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$10^{- 1}$

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$2 \times 10^{- 2}$

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$2 \times 10^{- 3}$

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Solution

The correct option is B
$10^{- 1}$

$k = A e^{\frac{- E_{a}}{R T}}$
$E_{a} = 2.303 R T$
$∴ \frac{k}{A} = e^{- (\frac{2.303 R T}{R T})}; \frac{k}{A} = e^{- 2.303}$
$l o g_{e} (\frac{k}{A}) = l o g_{e} e^{- 2.303}$
$l o g_{e} (\frac{k}{A}) = - 2.303$ or $2.303 l o g_{10} (\frac{k}{A}) = - 2.303$
$l o g (\frac{k}{A}) = - 1; l o g (\frac{A}{K}) = 1$
$∴ \frac{A}{k} = a n t i l o g 1 = 10$ or $\frac{k}{A} = \frac{1}{10} = 10^{- 1}$

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The activation energy for a reaction at the temperature TK was found to be 2.303 RTJmol−1. The ratio of the rate constant to Arrhenius factor is ___

The correct option is B 10−1 k=Ae−EaRT Ea=2.303RT ∴kA=e−(2.303RTRT);kA=e−2.303 loge(kA)=loge e−2.303 loge(kA)=−2.303 or 2.303log10(kA)=−2.303 log(kA)=−1;log(AK)=1 ∴Ak=anti log1=10 or kA=110=10−1

The activation energy for a reaction at the temperature TK was found to be 2.303 $R T J m o l^{- 1}$ . The ratio of the rate constant to Arrhenius factor is ___