Question

Explain in words the formula that can be used to determine \(\Delta H_{{rm}}^{\circ}\) when using Hess’s law.

Short answer

The formula for Hess's law to determine the enthalpy change for the overall reaction (\(\Delta H_{{rm}}^{\circ}\)) is given by: \[\Delta H_{{rm}}^{\circ} = \sum_{i=1}^n \Delta H_i^{\circ}\] This means that the enthalpy change for the overall reaction is the sum of the enthalpy changes for each individual reaction ( \(\Delta H_1^{\circ}, \Delta H_2^{\circ}, \ldots, \Delta H_n^{\circ}\)) involved in the process, regardless of the path taken. The subscript "rm" signifies the desired reaction, and the superscript "°" indicates that the reactions occur under standard conditions (1 atm pressure and 298.15 K temperature).

Step-by-step solution

Understanding ΔH°rm

ΔH is the change in enthalpy, which in this context refers to the heat absorbed or released by a reaction at standard conditions (1 atm pressure and 298.15 K temperature). The subscript "rm" denotes that we are interested in the enthalpy change of a desired reaction, and the superscript "°" represents that the process is occurring under standard conditions.

Hess's Law

Hess's law states that the total enthalpy change (\(\Delta H_{{rm}}^{\circ}\)) for a chemical reaction is independent of the path taken and only depends on the initial and final states of the system. This means that we can break down a complex reaction into a series of simpler reactions, each with its known enthalpy change, to determine the enthalpy change of the overall reaction.

Formula for Hess's Law

To determine the enthalpy change for the overall reaction (\(\Delta H_{{rm}}^{\circ}\)), we need to add up the enthalpy changes for each of the simpler reactions involved. Suppose we have n reactions with known enthalpy changes \(\Delta H_1^{\circ}, \Delta H_2^{\circ}, \ldots, \Delta H_n^{\circ}\). Then, the formula for Hess's law is: \[\Delta H_{{rm}}^{\circ} = \sum_{i=1}^n \Delta H_i^{\circ}\] This equation means that the enthalpy change for the overall reaction is the sum of the enthalpy changes for each individual reaction involved in the process.

Key concepts

Enthalpy Change

Enthalpy change, denoted as \( \Delta H \), is a fundamental concept in thermochemistry, referring to the heat absorbed or released during a chemical reaction. More formally, it is the difference in the total heat content, or enthalpy, of reactants and products under constant pressure. It's crucial for understanding whether a reaction is endothermic (absorbs heat) or exothermic (releases heat).

Consider the burning of natural gas in a stove: if we could capture and measure all heat released, that heat quantity represents the enthalpy change of the reaction. We then use this value, among others, to calculate the overall enthalpy of a more complex reaction via Hess's Law, providing valuable insight into the nature and feasibility of chemical processes.

Standard Conditions

Standard conditions refer to a set benchmark that scientists and engineers use to report thermodynamic data, such as enthalpy change. For reactions and processes, standard conditions usually mean a pressure of 1 atmosphere (atm) and a temperature of 25 degrees Celsius (298.15 Kelvin).

By convention, the notation for standard conditions is a degree sign (°) placed as a superscript. For instance, \( \Delta H^\circ \) represents the enthalpy change under standard conditions. Standard conditions are not equivalent to 'standard temperature and pressure' (STP), which is used for gas measurements. This distinction is vital because the enthalpy change for a reaction can vary with temperature and pressure.

Chemical Reaction Enthalpy

Chemical reaction enthalpy is the enthalpy change that occurs during a chemical reaction. It reflects how the internal energy of the compounds and the work done by the reaction on the surroundings (or vice versa) contribute to the overall heat content change.

Calculating Reaction Enthalpy

Reaction enthalpy can be calculated directly in a calorimeter or indirectly by using known values through Hess's Law. For instance, when sulfur burns in oxygen to form sulfur dioxide, the enthalpy change is a specific amount that can be measured experimentally. These individual enthalpy changes serve as building blocks to calculate the enthalpy of more complex reactions, emphasizing the essence of tabulated standard enthalpies of formation for many substances.

Thermochemistry

Thermochemistry is the branch of chemistry that deals with the energy and heat associated with chemical reactions and physical transformations. A key goal of thermochemistry is to understand the transfer of energy as heat and work in relation to chemical reactions.

Through thermochemical equations, we can not only note the amount of heat involved in a reaction but also predict which direction a chemical process may naturally proceed. \( \Delta H \) provides insight into the reaction's effects on the surroundings; for example, whether it will cause a surrounding material to heat up or cool down. Thermochemistry sets the foundation for exploring how energy transformation is inherent to the functioning of batteries, engines, ecosystems, and much more.