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Standard VII

Chemistry

Arrhenius Equation

It has been f...

Question

It has been found that for a chemical reaction with rise in temperature by $9 K$ the rate constant gets doubled. Assuming a reaction to be occurring at $300 K,$ the value of activation energy is found to be _______ $k J m o l^{- 1} .$ [nearest integer]
(Given $l n 10 = 2.3, R = 8.3 J K^{- 1} m o l^{- 1}, log 2 = 0.30)$

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Solution

$T_{1} = 300 K$
$T_{2} = 309 K$
Since the rate constant doubles with every 9K rise in temperature:
$K_{2} = 2 K_{1}$
Activation energy, $E_{a} = ?$
$log \frac{K_{2}}{K_{1}} = \frac{E_{a}}{2.3 R} [\frac{T_{2} - T_{1}}{T_{2} . T_{1}}]$
$log 2 = \frac{E_{a}}{2.3 \times 8.3} [\frac{9}{309 \times 300}]$
$E_{a} = \frac{0.3 \times 309 \times 300 \times 2.3 \times 8.3}{9}$
$= 58988.1 J / m o l$
$= 59 k J / m o l$

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It has been found that for a chemical reaction with rise in temperature by 9 K the rate constant gets doubled. Assuming a reaction to be occurring at 300 K, the value of activation energy is found to be _______kJ mol−1. [nearest integer] (Given ln10=2.3,R=8.3 J K–1 mol–1,log 2=0.30)

T1=300 K T2=309 K Since the rate constant doubles with every 9K rise in temperature: K2=2K1 Activation energy, Ea=? logK2K1=Ea2.3R[T2−T1T2.T1] log2=Ea2.3×8.3[9309×300] Ea=0.3×309×300×2.3×8.39 =58988.1 J/mol =59 kJ/mol