The rate constant (k) for a reaction was measured as a...

The rate constant $(k)$ for a reaction was measured as a function of temperature. A plot of In $k$ versus $1 / T$ (in $\mathrm{K}$ ) is linear and has a slope of -7445 K. Calculate the activation energy for the reaction.

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Key Concepts

Arrhenius Equation

This fundamental equation describes the temperature dependence of reaction rates, relating the rate constant (k) to temperature (T) and activation energy (Ea) through the expression k = A exp(-Ea/(RT)). It is a cornerstone in chemical kinetics that explains how reactants overcome an energy barrier to form products.

Activation Energy

Activation energy is the minimum energy required for a reaction to proceed. It represents the energy barrier that must be overcome for reactants to transform into products. In the context of the Arrhenius equation, it is directly related to the sensitivity of the rate constant to temperature changes.

Linearization of the Arrhenius Equation

By taking the natural logarithm of the Arrhenius equation, ln k = ln A - Ea/(RT), the relationship between ln k and 1/T becomes linear. This allows one to determine the activation energy from the slope of the linear plot, where the slope is equal to -Ea/R. This method is widely used to extract kinetic parameters from experimental data.

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