Question

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

Short answer

(a) False - Measuring the rate constant at different temperatures doesn't provide information about the overall enthalpy change for the reaction. (b) False - Reaction speed is primarily determined by the activation energy, not by whether the reaction is exothermic or endothermic. (c) False - Doubling the temperature doesn't directly cut the activation energy in half, though it can increase the rate of reaction by making it easier for molecules to overcome the activation energy barrier.

Step-by-step solution

Statement (a)

If you measure the rate constant for a reaction at different temperatures, you can calculate the overall enthalpy change for the reaction. False. The rate constant is related to the activation energy and temperature of the reaction by the Arrhenius equation, but it does not directly provide information about the overall enthalpy change for the reaction. The enthalpy change, which represents the overall energy change in a reaction, is determined experimentally or through computation with chemical equations and thermodynamics.

Statement (b)

Exothermic reactions are faster than endothermic reactions. False. The speed of a reaction is not determined solely by whether it is exothermic or endothermic. Reaction speed is primarily determined by the activation energy, not the overall energy change in the reaction. It is possible for an exothermic reaction to have a high activation energy and be slower than an endothermic reaction.

Statement (c)

If you double the temperature for a reaction, you cut the activation energy in half. False. The relationship between the temperature and the activation energy is described by the Arrhenius equation: \(k = Ae^{\frac{-E_{a}}{RT}}\), where k is the rate constant, A is the pre-exponential factor, E_a is the activation energy, R is the gas constant, and T is the temperature in Kelvin. Doubling the temperature does not directly cut the activation energy in half. Instead, increasing the temperature can increase the rate of reaction by making it easier for molecules to overcome the activation energy barrier, but it does not directly affect the value of the activation energy.

Key concepts

Rate Constant

The rate constant, often symbolized by the letter \( k \), is a crucial component when discussing chemical reaction rates. It serves as a proportionality factor in the rate equation, which relates the rate of a reaction to the concentrations of the reactants. Unlike concentration, the rate constant is independent of the reactant concentrations but is highly influenced by temperature.

At higher temperatures, the rate constant usually increases, signifying that the reaction proceeds faster. This change is explained by the Arrhenius equation, which links the rate constant with temperature and activation energy. It's worth noting that the rate constant doesn't provide direct information about the reaction's enthalpy change but offers insights into how quickly a reaction can proceed under given conditions.

Activation Energy

Activation energy is the minimum amount of energy required for a chemical reaction to occur. It acts as an energy barrier that reactants must overcome to be transformed into products. This concept is crucial in determining the speed of a reaction. A high activation energy indicates that the reactants need a lot of energy to reach the transition state, usually resulting in a slower reaction.

Conversely, reactions with low activation energy proceed quickly since the energy hurdle is easier to surpass. Activation energy is usually measured in kilojoules per mole (kJ/mol) and is an essential factor in the Arrhenius equation, affecting the rate constant. However, it does not decrease with an increase in temperature; instead, higher temperatures provide reactants with more energy, making it easier for them to overcome the activation energy barrier.

Arrhenius Equation

The Arrhenius equation is a fundamental formula in chemical kinetics that shows how the rate constant \( k \) of a chemical reaction depends on temperature and activation energy. It is expressed as: \[ k = Ae^{-\frac{E_a}{RT}} \]
where \( A \) represents the pre-exponential factor, \( E_a \) is the activation energy, \( R \) is the universal gas constant, and \( T \) is the temperature in Kelvin.

This equation highlights that an increase in temperature leads to an exponential increase in the rate constant, thereby speeding up the reaction. The Arrhenius equation is valuable for understanding how chemical reactions behave under various conditions and is instrumental for calculating the activation energy if experimental rate constants are known.

Enthalpy Change

Enthalpy change, denoted as \( \Delta H \), is the total heat change that occurs during a chemical reaction at constant pressure. It is an important thermodynamic quantity that indicates whether a reaction is exothermic or endothermic.

An exothermic reaction releases heat, thus the enthalpy change is negative, while an endothermic reaction absorbs heat, leading to a positive enthalpy change. The enthalpy change is distinct from the reaction rate and is not directly measured by the rate constant. Instead, it is typically determined experimentally or calculated using thermodynamic data and related equations.

Exothermic and Endothermic Reactions

Exothermic reactions are chemical processes that release energy, usually in the form of heat, resulting in a net loss of energy from the system to the surroundings. These reactions often have negative enthalpy changes, indicating an energy release. On the other hand, endothermic reactions absorb energy from their surroundings, yielding a net gain in energy captured within the products, and are characterized by positive enthalpy changes.

Although exothermic reactions might intuitively seem faster due to the release of energy, the speed of a reaction is more significantly influenced by its activation energy rather than its enthalpy change. For instance, some exothermic reactions can have high activation energies and thus proceed slower than certain endothermic reactions with lower activation energies. Understanding the differences between these reaction types is essential for predicting the heat exchange involved and the potential energy changes in a reaction system.