Problem 27 - General Chemistry

Question

Hypothetical elements \(\mathrm{A}_{2}\) and \(\mathrm{B}_{2}\) react according to the following equation, forming the compound \(\mathrm{AB}\). $$ \mathrm{A}_{2}(a q)+\mathrm{B}_{2}(a q) \longrightarrow 2 \mathrm{AB}(a q) ; \Delta H^{\circ}=+271 \mathrm{~kJ} / \mathrm{mol} $$ If solutions \(\mathrm{A}_{2}(a q)\) and \(\mathrm{B}_{2}(a q)\), starting at the same temperature, are mixed in a coffee-cup calorimeter, the reaction that occurs is a. exothermic, and the temperature of the resulting solution rises. b. endothermic, and the temperature of the resulting solution rises. c. endothermic, and the temperature of the resulting solution falls. d. exothermic, and the temperature of the resulting solution falls. e. exothermic or endothermic, depending on the original and final temperatures.

Step-by-Step Solution

Answer

The reaction is endothermic, and the temperature of the solution falls (option c).

Step 1: Understand the Reaction and Heat Change

The given chemical reaction is \( \mathrm{A}_{2}(a q)+\mathrm{B}_{2}(a q) \longrightarrow 2 \mathrm{AB}(a q) \). The given \( \Delta H^{\circ} = +271 \, \mathrm{kJ/mol} \) indicates that the standard enthalpy change of the reaction is positive. A positive \( \Delta H \) means that the reaction is endothermic, meaning it absorbs heat from the surroundings.

Step 2: Assess Reaction Type from Enthalpy Change

An endothermic reaction absorbs energy from its surroundings, which means it requires an input of heat to proceed. In this scenario, the absorption of heat by the reaction will result in a decrease in the temperature of the surroundings, which in this case is the solution in the calorimeter.

Step 3: Identify Correct Option Based on Reaction Type

Given that the reaction is endothermic, we expect the temperature of the solution to decrease because the reaction absorbs heat from the solution. Therefore, option c, 'endothermic, and the temperature of the resulting solution falls,' is the correct choice.

Key Concepts

enthalpy change

Enthalpy change, often denoted as \( \Delta H \), refers to the amount of heat absorbed or released during a chemical reaction at constant pressure. Specifically, in a chemical reaction, it represents the difference in enthalpy between the products and reactants. When \( \Delta H \) is positive, like in the given exercise \( (\Delta H^{\circ} = +271 \, \mathrm{kJ/mol}) \), the reaction is called endothermic. This means that the reaction requires an input of energy (heat) from the surroundings to proceed. The absorbed heat increases the enthalpy of the system. Understanding enthalpy change helps determine whether a reaction will absorb or release energy. In endothermic reactions, the enthalpy of the reactants is less than that of the products because energy is absorbed from the surroundings. For students working on textbook solutions, recognizing a positive \( \Delta H \) as an indication of an endothermic process is crucial for understanding how the temperature and heat flow may change in a chemical reaction.

coffee-cup calorimeter

A coffee-cup calorimeter is a simple device used to measure the heat change or enthalpy change during chemical reactions occurring in a solution. It's composed of an insulated cup, often a Styrofoam cup, with a lid and a thermometer that measures temperature changes. This device operates at constant pressure, making it ideal for observing reactions like the ones given in the exercise. When substances react in a coffee-cup calorimeter, any change in temperature recorded is directly related to the heat absorbed or released during the reaction. Key features of a coffee-cup calorimeter include:

• It provides an approximation of enthalpy changes at constant pressure.
• It's simple, cost-effective, and easy to use.
• It's especially suitable for reactions occurring in aqueous solutions.

By using a coffee-cup calorimeter, students can deduce the endothermic or exothermic nature of reactions by observing how the temperature changes during the process.

temperature change

Temperature change in a chemical reaction is a direct consequence of the heat flow between the system and its surroundings. When a reaction takes place, it can either absorb heat from or release heat to its surroundings, leading to temperature changes.For endothermic reactions, like the one in the exercise, energy is absorbed from the surrounding solution, leading to a decrease in temperature. This means that as reactants \( \mathrm{A}_2 \) and \( \mathrm{B}_2 \) form \( \mathrm{AB} \), the surrounding solution's temperature will drop because heat is being pulled into the reaction to help it proceed. The temperature change allows us to:

• Determine the direction of heat flow.
• Understand the energy requirements of the reaction.
• Predict the feasibility of the reaction occurring under specific conditions.

In educational settings, noticing how the temperature varies during a reaction is vital, as it clues students into the type of reaction and its heat dynamics.

heat absorption

Heat absorption is a critical concept, especially in understanding endothermic reactions. In such reactions, heat is absorbed from the surroundings, which provides the necessary energy for the reaction to occur. This process can be illustrated clearly in a system like the coffee-cup calorimeter, where the reaction mixture takes in heat, causing a decrease in the temperature of the surrounding solution. The absorbed heat supplies the potential energy needed for breaking bonds in reactants and forming new bonds in products. In practical terms, the implications of heat absorption in a classroom setup include:

• Recognizing the relationship between heat absorption and temperature change.
• Understanding the energy requirements of different types of reactions.
• Gaining insights into calorimetry as a method for measuring energy changes.

Heat absorption in endothermic reactions highlights the dynamic interplay of energy within chemical processes, emphasizing the necessity of energy input for the reaction to proceed.