Question

Indicate whether each statement is true or false. (a) If you measure the rate constant for a reaction al different temperatures, you can calculate the overall enthalpy change for the reaction. (b) Exothermic reactions are faster than endothermic reactions. (c) If you double the temperature for a reaction, you cut the activation energy in half.

Short answer

(a) True - By using the Arrhenius and van 't Hoff equations, we can determine the overall enthalpy change (\(\Delta H\)) for the reaction. (b) False - The rate of a reaction is determined by its activation energy, not whether it is exothermic or endothermic. (c) False - Doubling the temperature affects the rate constant, not the activation energy, which is a characteristic property of the reaction.

Step-by-step solution

a) Enthalpy change calculation from rate constants at different temperatures

The statement is true. By measuring the rate constants for a reaction at different temperatures, we can use the Arrhenius equation to calculate the activation energy and then apply the van 't Hoff equation to determine the overall enthalpy change (\(\Delta H\)) for the reaction.

b) Exothermic vs. Endothermic reaction rates

The statement is false. The rate of a reaction is determined by its activation energy and not by whether the reaction is exothermic or endothermic. Lower activation energy usually results in faster reactions; however, both exothermic and endothermic reactions can have a range of activation energies.

c) Doubling the temperature and its effect on activation energy

The statement is false. Doubling the temperature of a reaction does not necessarily cut the activation energy in half. The relationship between temperature and the rate constant is given by the Arrhenius equation: \(k = Ae^{-\frac{Ea}{RT}}\), where \(k\) is the rate constant, \(A\) is the pre-exponential factor, \(Ea\) is the activation energy, \(R\) is the gas constant, and \(T\) is the temperature in Kelvin. Doubling the temperature will affect the rate constant but not the activation energy itself, as it is a characteristic property of the reaction.

Key concepts

Enthalpy Change

Enthalpy change, symbolized by \(\Delta H\), is a measure of the total energy change in a chemical reaction. When we talk about enthalpy change, we focus on the heat absorbed or released, keeping pressure constant. It is critical in determining whether a process is energy-releasing or energy-absorbing.

When a reaction involves a change in temperature, the rate constants can be measured and analyzed against the Arrhenius and van 't Hoff equations. These help calculate both the activation energy and the overall enthalpy change. The Arrhenius equation is given by: \[ k = Ae^{-\frac{Ea}{RT}}\]Where:

• \(k\) is the rate constant.
• \(A\) is the pre-exponential factor, a constant for each chemical reaction.
• \(Ea\) is the activation energy.
• \(R\) is the gas constant.
• \(T\) is the temperature in Kelvin.

The van 't Hoff equation further aids in identifying \(\Delta H\) from these rate constants, showing the enthalpy change associated with this reaction.

Exothermic Reactions

Exothermic reactions are those that release energy, typically in the form of heat, during the course of the reaction. This release of energy means that the enthalpy change, \(\Delta H\), is negative for exothermic reactions.

One common misconception is that exothermic reactions are inherently faster than endothermic reactions. However, the speed of a chemical reaction is primarily determined by the activation energy, not whether it's exothermic or endothermic. A lower activation energy indicates a potentially faster reaction as it requires less energy for the reactants to form products.

Exothermic reactions can have a wide range of activation energies, meaning some may occur rapidly, while others progress more slowly. Reaction conditions, such as temperature and the presence of catalysts, also play a significant role in the reaction rate.

Activation Energy

Activation energy, denoted as \(Ea\), is the minimum energy that reactant molecules must possess to transform into products. It serves as the energy barrier that needs to be overcome for a reaction to proceed.

The Arrhenius equation, \(k = Ae^{-\frac{Ea}{RT}}\), illustrates how the rate constant \(k\) is influenced by temperature \(T\) and activation energy \(Ea\). Contrary to a common misconception, changing the temperature of a reaction affects the rate constant \(k\), but not the activation energy \(Ea\) itself.

Doubling the temperature will increase the reaction rate, given that the system can achieve higher energy levels more frequently, therefore reducing the time needed for reactant molecules to surpass the activation energy threshold. However, this does not modify \(Ea\) directly; instead, it impacts how frequently the reactants can reach the required energy state to react.