The conversion of cyclopropane, an anesthetic, to propylene...

The conversion of cyclopropane, an anesthetic, to propylene (see Problem 14.61) has a rate constant $k=1.3 \times$ $10^{-6} \mathrm{~s}^{-1}$ at $673 \mathrm{~K}$ and $k=1.1 \times 10^{-5} \mathrm{~s}^{-1}$ at $703 \mathrm{~K}$ (a) What is the activation energy in $\mathrm{kJ} / \mathrm{mol}$ ? (b) Use the data given at $703 \mathrm{~K}$ to calculate the frequency factor, $A$, for this reaction? (c) What is the rate constant for the reaction at $350^{\circ} \mathrm{C}$ ?

The conversion of cyclopropane, an anesthetic, to propylene (see Problem 14.61) has a rate constant $k=1.3 \times$ $10^{-6} \mathrm{~s}^{-1}$ at $673 \mathrm{~K}$ and $k=1.1 \times 10^{-5} \mathrm{~s}^{-1}$ at $703 \mathrm{~K}$
(a) What is the activation energy in $\mathrm{kJ} / \mathrm{mol}$ ?
(b) Use the data given at $703 \mathrm{~K}$ to calculate the frequency factor, $A$, for this reaction?
(c) What is the rate constant for the reaction at $350^{\circ} \mathrm{C}$ ?

Key Concepts

Arrhenius Equation

The Arrhenius equation, k = A exp(–Ea/RT), is a fundamental formula in chemical kinetics that relates the rate constant (k) of a reaction to its activation energy (Ea), the frequency factor (A), and the absolute temperature (T). This relationship helps us understand how changes in temperature affect the reaction rate and allows for the determination of kinetic parameters by analyzing rate constants at different temperatures.

Activation Energy

Activation energy is the minimum energy required to initiate a chemical reaction. It is a crucial concept in kinetics because it indicates the sensitivity of a reaction's rate to temperature changes. A higher activation energy corresponds to a greater sensitivity of the reaction rate to temperature, which can be quantitatively determined using the Arrhenius equation.

Frequency Factor (Pre-exponential Factor)

The frequency factor, A, represents the number of times reactant molecules approach the activation barrier per unit time, essentially reflecting the frequency of effective collisions in a reaction. It is an important parameter in the Arrhenius equation, providing insight into the reaction mechanism and the inherent likelihood of reactant collisions leading to a reaction.

Rate Constant

The rate constant, k, is a proportionality constant in the rate law that quantifies the speed of a chemical reaction under given conditions. Its value changes with temperature and is influenced by the activation energy and the frequency of successful molecular collisions as described by the Arrhenius equation.

Temperature Conversion

Temperature conversion, particularly between scales such as Celsius and Kelvin, is essential in kinetic calculations because the Arrhenius equation requires the absolute temperature in Kelvin. Correct temperature conversion ensures accurate computation of kinetic parameters like the rate constant and activation energy.

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