Ethyl chloride vapor decomposes by the first-order reaction: The activation energy is 249 kJ>mol, and the frequency factor is 1.6 * 1014 s-1. Find the value of the specific rate constant at 710K. What fraction of the ethyl chloride decomposes in 15minutes at this temperature? Find the temperature at which the rate of the reaction would be twice as fast.

The rate constant, often symbolized as \( k \), is a crucial element in chemical kinetics, particularly when dealing with reactions and their rates. This value is indicative of the speed at which a reaction proceeds; the higher the rate constant, the faster the reaction. It is important to know that the rate constant is not only determined by the frequency of molecular collisions but also by how often these collisions lead to a successful reaction. Furthermore, the rate constant is temperature-dependent, changing according to the Arrhenius equation.

In practice, when dealing with a first-order reaction like the decomposition of ethyl chloride, the rate constant allows us to calculate the rate of reaction at any given concentration, since the two are directly proportional. By using the Arrhenius equation, we can calculate the specific rate constant at different temperatures, helping us to predict how the reaction rate will change with varying thermal conditions as seen in the textbook example.

First-order reactions are a fundamental type of chemical reaction where the rate is directly proportional to the concentration of one reactant. These reactions have a simple linear relationship when plotted on a natural logarithm scale versus time, which makes them easy to analyze mathematically.

The decomposition of ethyl chloride, as outlined in our example, follows first-order kinetics meaning the time it takes for half of the reactant to decompose (the half-life) remains constant. This characteristic allows scientists and engineers to determine how long it will take for a certain fraction of the reactant to decompose by using the rate constant \( k \) in a relatively straightforward exponential decay formula. As seen in the solution steps, the fraction of ethyl chloride decomposed after 15 minutes can be calculated, showcasing the practical applications of understanding first-order reaction dynamics.

Activation energy, abbreviated as \( E_a \), is the minimum energy that reacting molecules must possess in order to undergo a chemical reaction. This energy barrier explains why some reactions that are thermodynamically favorable still occur slowly; the molecules involved simply do not have enough kinetic energy to overcome this barrier under normal conditions.

In the case of ethyl chloride decomposition, the activation energy helps dictate the rate at which the reaction proceeds. The Arrhenius equation encompasses activation energy as a key factor, helping us to calculate how the rate constant, and thereby the reaction rate, changes with temperature. Understanding \( E_a \) also gives insight into the reaction's sensitivity to temperature changes. A higher \( E_a \) generally means a greater effect of temperature on the reaction rate, as a small increase in temperature can result in a significantly higher rate, an aspect which is often critical in industrial and chemical processes.

The frequency factor, designated as \( A \) in the Arrhenius equation, represents the frequency of collisions and the likelihood that those collisions have the correct orientation to lead to a reaction. Essentially, it is a measure of how many times molecules collide in the correct orientation per unit time. In other words, while activation energy gauges the energy aspect of a reaction, the frequency factor focuses on the steric and probabilistic aspects.

When calculating the rate constant for the ethyl chloride reaction, the frequency factor is an essential part of the equation, providing a base rate from which the effects of thermal energy are assessed. It is not temperature-dependent but intrinsic to the specific reaction under consideration. In our example, the high value of the frequency factor suggests that collisions with appropriate orientations for reaction are relatively frequent, but the high activation energy demands that only a fraction of these collisions lead to a successful reaction. This interplay between frequency and activation energy is a crucial concept for students to grasp when analyzing reaction kinetics.