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2)
An experimental investigation into the kinetics of a first order liquid phase reaction gave the following results:
\begin{tabular}{ccc}
\begin{tabular}{c}
Reactant \\
Concentration \\
$\left(\mathbf{k m o l ~ m}^{-\mathbf{3}}\right)$
\end{tabular} & \begin{tabular}{c}
Rate of reaction \\
$\left(\mathbf{k m o l ~ m}^{-3} \mathbf{s}^{-1}\right)$
\end{tabular} & \begin{tabular}{c}
Temperature \\
$\left({ }^{\circ} \mathbf{C}\right)$
\end{tabular} \\
3.96 & $6.85 \times 10-3$ & \\
3.20 & $8.10 \times 10-3$ & 20.0 \\
2.94 & $11.55 \times 10-3$ & 25.7 \\
1.82 & $12.01 \times 10-3$ & 32.8 \\
0.43 & $4.37 \times 10-3$ & 41.8 \\
& & 49.8
\end{tabular}
Show that the variation of rate constant with temperature is represented by the Arrhenius equation and evaluate the activation energy of reaction and the pre-exponential factor.
$\left[46.04 \mathrm{~kJ} \mathrm{~mol}^{-1} \text { and } 28.21 \times 10^{4} \mathrm{~s}^{-1}\right]$
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Answer from Sia

Posted 5 months ago

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Answer

The activation energy $E_a$ is 46.04 kJ mol$^{-1}$ and the pre-exponential factor $A$ is $28.21 \times 10^5$ s$^{-1}$.

Key Concept

The Arrhenius equation relates the rate constant of a reaction to the temperature, activation energy, and pre-exponential factor.

Explanation

By plotting the natural logarithm of the rate constant against the inverse of the temperature in Kelvin, we can determine the activation energy and pre-exponential factor from the slope and intercept of the resulting line.

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