Question

The heat change that accompanies the formation of \(1.00 \mathrm{~mol}\) of carbon dioxide from its elements is \(-393.7 \mathrm{~kJ} / \mathrm{mol}\). What heat change accompanies the formation of \(0.650 \mathrm{~mol} \mathrm{CO}_{2}\) ?

Short answer

The heat change accompanying the formation of 0.650 mol CO2 from its elements is -255.9 kJ.

Step-by-step solution

Understand the Problem and What is Given

From the problem, the heat change accompanies the formation of 1.00 mol of CO2 is -393.7 kJ/mol. The heat change is negative because it's an exothermic reaction. Now, it is required to calculate the heat change for the formation of 0.650 mol CO2.

Use the Known Relationship

The heat change for a reaction is directly proportional to the number of moles of substance. So if the heat change for 1 mol of CO2 is -393.7 kJ/mol, then the heat change for n moles of CO2 is n * -393.7 kJ/mol.

Substitute and Solve

Substitute n = 0.650 into the formula obtained in Step 2 to calculate the heat change for formation of 0.650 mol CO2. The answer is \(0.650 * -393.7 = -255.9 \mathrm{~kJ}\).

Key concepts

Exothermic Reaction

An exothermic reaction is a chemical process in which energy is released to the surroundings, usually in the form of heat, light, or sound. In the context of the exercise, the formation of carbon dioxide (\r\(\mathrm{CO}_2\)) from its elements, carbon and oxygen, is an example of such a reaction. The key indicator of an exothermic reaction is a negative value for the heat change, known as the enthalpy change (\r\(\Delta H\)). This negative sign indicates that energy is being given off as the reaction proceeds, which means that the products of the reaction have less energy than the reactants.\r

\rWhy is understanding whether a reaction is exothermic important? Knowing the heat energy involved in chemical reactions helps predict their behavior and stability. For instance, exothermic reactions are often more spontaneous and may occur without external energy input. They play a crucial role in applications like combustion engines, where heat release from fuel burning is harnessed to do work, or in hand warmers, which rely on the exothermic oxidation of iron to generate heat.\r

\rIn solving textbook exercises, identifying an exothermic reaction helps you apply the correct sign to the enthalpy change value, ensuring accuracy in your calculations.

Molar Enthalpy

Molar enthalpy, often denoted by \r\(\Delta H\), is the enthalpy change associated with a chemical reaction per mole of a substance. It's a measure of the heat either absorbed or released during the conversion of one mole of reactants into products under standard conditions. In the provided example, the molar enthalpy is \r\(-393.7 \mathrm{~kJ/mol}\) for the formation of carbon dioxide (\r\(\mathrm{CO}_2\)).\r

\rUnderstanding molar enthalpy is vital when working with chemical reactions because it allows scientists and students to predict the heat change for any given amount of reactant or product, based on stoichiometry. The value of molar enthalpy is constant for a given reaction, as it's characteristic of the specific chemical change. It serves as a foundation for using Hess's law, calculating energy changes in thermochemical cycles, and it's a central concept in calorimetry which involves the measurement of heat transfer. For students, grasping molar enthalpy facilitates the handling of thermochemical equations and enhances comprehension of reaction energetics.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It helps us understand the ratios in which substances react and form products, based on their molecular weights and coefficients from the balanced chemical equation. \r

\rThe concept is crucial for calculating the amounts of reactants needed or products formed. In the exercise, stoichiometry is used to calculate the heat change for 0.650 mol of \r\(\mathrm{CO}_2\). The stoichiometric relationship, coupled with the molar enthalpy, allows us to scale the known heat change of -393.7 kJ for 1 mole to that for 0.650 moles. This is achieved by multiplying the number of moles by the molar enthalpy.\r

\rStudents are often encouraged to pay attention to the stoichiometric coefficients in chemical equations, as they provide the necessary conversion factors. Enhancing one's stoichiometric skills is not only essential for solving chemical problems but also for applications in real-life scenarios such as cooking, where ingredient proportions are based on similar principles, or in industrial processes where the efficiency of raw material usage is crucial.