Question

If enthalpy of an overall reaction \(X \rightarrow Y\) along one route is \(\Delta_{r} H\) and \(\Delta_{r} H_{1}, \Delta_{1} H_{2}, \Delta_{r} H_{3} \ldots\) representing enthalpies of reactions leading to same product \(y\) then \(\Delta_{r} H\) is (a) \(\Delta_{r} H=\Delta_{r} H_{1}+\Delta_{r} H_{2}+\Delta_{r} H_{3} \ldots\) (b) \(\Delta_{r} H=\Delta_{r} H_{1} \times \Delta_{r} H_{2} \times \Delta_{r} H_{3} \ldots\) (c) \(\Delta_{r} H=\Delta_{r} H_{1}+\Delta_{r} H_{2}-\Delta_{r} H_{3} \ldots\) (d) \(\Delta_{r} H=\frac{\Delta_{r} H_{1} \times \Delta_{r} H_{2} \times \Delta_{r} H_{3}}{2} \cdots\)

Short answer

\(\Delta_{r} H=\Delta_{r} H_{1}+\Delta_{r} H_{2}+\Delta_{r} H_{3} \ldots\)

Step-by-step solution

Analysis of the Problem

This problem is based on Hess's law, which states that the total enthalpy change for a chemical reaction is the same, regardless of the route by which the chemical reaction takes place, provided the initial and final conditions are the same. The question asks for the correct expression that relates the overall enthalpy change \(\Delta_{r} H\) for a reaction \(X \rightarrow Y\) with the sum of enthalpy changes of individual steps leading to the same product Y.

Evaluate Each Option

Option (a) is a sum of individual enthalpy changes and reflects the additive nature of enthalpy according to Hess's law.Option (b) suggests a multiplication of individual enthalpy changes, which is not consistent with Hess's law. Enthalpy is an extensive property and is not multiplied when reactions are combined.Option (c) presents a mixture of addition and subtraction which generally doesn't correspond to Hess's law unless specifically stated which steps are endothermic or exothermic.Option (d) proposes a fraction involving multiplication of enthalpy changes, which doesn't match with any thermodynamic principles.

Choose the Correct Answer

By Hess's Law, the overall enthalpy change \(\Delta_{r} H\) of a reaction going from X to Y along multiple routes (with individual enthalpy changes \(\Delta_{r} H_{1}, \Delta_{r} H_{2}, \Delta_{r} H_{3}\ldots\)) would be the algebraic sum of those changes. Therefore, the correct expression is the one that adds up all the individual enthalpy changes. So, option (a) is the correct answer.

Key concepts

Enthalpy Change

Understanding enthalpy change is crucial for grasping the essence of chemical thermodynamics. Enthalpy change, denoted as \( \Delta H \), refers to the heat absorbed or released in a chemical reaction at constant pressure. It's an indicator of whether a reaction is exothermic (releasing heat) or endothermic (absorbing heat). For example, when you feel heat while a bonfire burns, that's an exothermic reaction taking place.

Chemists use enthalpy changes to predict the feasibility of reactions and to calculate how much energy is required or will be produced. By convention, an exothermic reaction has a negative enthalpy change, as it releases heat to the surroundings, while endothermic reactions have a positive enthalpy change, indicating the absorption of heat.

Thermodynamics

Diving into the realm of thermodynamics, we venture into the study of energy, heat, work, and how they interplay within the universe. It essentially sets the stage for understanding enthalpy change, as previously mentioned. Thermodynamics encompasses laws that govern energy transformations and provides key concepts such as enthalpy, entropy, and Gibbs free energy.

First Law of Thermodynamics

The first law of thermodynamics, also known as the law of energy conservation, tells us that energy cannot be created or destroyed, only transformed. This principle underlies Hess's Law in chemistry, reinforcing the idea that the total change in enthalpy is the same regardless of the path taken during a chemical reaction.

Chemical Reactions

The chemical reactions topic unwraps the core of chemical transformations. Reactions can be simple, involving just a rearrangement of atoms, or complex, entailing multiple steps and intermediates. Each reaction comes with its own enthalpy change, reflecting the energy differences between reactants and products.

Understanding reactions on an enthalpic level is akin to working with a budget of energy: some steps give out energy (exothermic), while others consume it (endothermic). The beauty of Hess's Law lies in its provision for calculating overall reactions' enthalpies by simply adding up the enthalpy changes for each step, regardless of the complexities or the number of intermediate stages involved in a reaction's pathway.