Problem 68 - Chemistry: The Central Science

Question

(a) Why are tables of standard enthalpies of formation so useful? (b) What is the value of the standard enthalpy of formation of an element in its most stable form? (c) Write the chemical equation for the reaction whose enthalpy change is the standard enthalpy of formation of sucrose (table sugar), \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s), \Delta H_{f}^{\circ}\left[\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right]\).

Step-by-Step Solution

Answer

(a) Tables of standard enthalpies of formation are useful because they allow for convenient calculation of enthalpy changes in chemical reactions using Hess's Law, providing valuable thermodynamic information for various applications. (b) The standard enthalpy of formation for an element in its most stable form is defined as zero. (c) The chemical equation for the formation of sucrose is: 12 \(\mathrm{C}(s, \text{graphite})\) + 11 \(\mathrm{O}_{2}(g)\) + 11 \(\mathrm{H}_{2}(g)\) → \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)\).

Step 1: Answer (a): Usefulness of tables of standard enthalpies of formation

Tables of standard enthalpies of formation are useful because they provide a convenient and standardized way of calculating the enthalpy change for various chemical reactions. By knowing the enthalpy of formation values for the reactants and the products in a reaction, we can determine the overall enthalpy change for the reaction using Hess's Law. This information is crucial in understanding the thermodynamic properties of a reaction, which can be helpful in various industrial, environmental, and research applications.

Step 2: Answer (b): Enthalpy of Formation for an Element in its Most Stable Form

The standard enthalpy of formation for an element in its most stable form is always defined as zero (0). This is because the formation of an element in its standard state from itself requires no change in energy, as no chemical transformation or bonds breaking/forming occurs. As standard enthalpies of formation are relative values based on the formation of a compound from its constituent elements, a reference point needs to be established. By convention, this reference point is set as zero for elements in their most stable forms.

Step 3: Answer (c): Chemical Equation for Sucrose Formation

To write the chemical equation for the formation of sucrose from its constituent elements, we must consider the fact that it has a chemical formula of \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)\). To find its enthalpy of formation, we need to form it from its constituent elements in their most stable states: Carbon in the form of graphite (\(\mathrm{C}(s, \text{graphite})\)), Hydrogen as H2 gas (\(\mathrm{H}_{2}(g)\)), and Oxygen as O2 gas (\(\mathrm{O}_{2}(g)\)). The chemical equation for the formation of sucrose is: 12 \(\mathrm{C}(s, \text{graphite})\) + 11 \(\mathrm{O}_{2}(g)\) + 11 \(\mathrm{H}_{2}(g)\) → \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)\)

Key Concepts

Enthalpy Change

Enthalpy change, denoted by \( \Delta H \), represents the heat absorbed or released during a chemical reaction at constant pressure. It is a thermodynamic quantity that gives insights into the energy changes occurring in a reaction. The sign of \( \Delta H \), positive or negative, indicates whether the process is endothermic (heat absorbed) or exothermic (heat released), respectively. In educational contexts, mastering the concept of enthalpy change is crucial for predicting the feasibility and spontaneity of reactions. Understanding \( \Delta H \), students can infer much about a reaction's behavior without performing it, which is pivotal in planning and analyzing chemical processes.

In the case of formation reactions, the \( \Delta H_{f}^{\circ} \) of a compound is particularly significant as it reveals the energy required to form one mole of that compound from its elements in their standard states. For sucrose, the enthalpy change of formation would inform us about the energy dynamics involved in its creation from carbon (graphite), hydrogen (gas), and oxygen (gas).

Hess's Law

Hess's Law is a foundational concept in thermodynamics stating that the total enthalpy change for a chemical reaction is the same, regardless of the route by which the chemical reaction occurs, assuming that the initial and final conditions are the same. This principle essentially means that if a reaction can be expressed as a series of steps, the sum of the enthalpy changes for each step will equal the overall enthalpy change for the complete reaction.

This law allows chemists to calculate the enthalpy change of a complex reaction by breaking it down into a series of simpler reactions for which standard enthalpies of formation are available. It is especially useful when direct measurement of the enthalpy change for a reaction is not feasible. For students struggling to grasp this concept, envisioning energy levels as steps that must always add up to the same overall change, regardless of the path taken, can facilitate comprehension.

Thermodynamic Properties

Understanding Thermodynamic Properties

Thermodynamic properties of substances, such as enthalpy, internal energy, entropy, and Gibbs free energy, serve as critical parameters for understanding and predicting the behavior of chemical reactions. These properties can help determine whether a reaction will occur spontaneously and the extent to which it will proceed. For students, it can be helpful to think of thermodynamic properties as the 'personality traits' of a chemical process, defining how it will 'act' under various conditions.

For example, the standard enthalpy of formation is a thermodynamic property that can be utilized to calculate the energy changes in reactions through Hess's Law. In educational settings, emphasizing the interrelation between thermodynamic properties and real-world applications, such as in energy generation, material synthesis, and environmental sciences, can help students appreciate their practical significance.

Chemical Reaction Equation

Dissecting the Chemical Reaction Equation

The chemical reaction equation serves as a symbolic representation of a chemical reaction, where reactants are transformed into products. It conveys essential information such as the nature and quantity of the involved substances and the stoichiometry of the reaction. Grasping this concept is foundational in chemistry education, as it forms the basis for understanding how different elements combine and transform into new compounds.

For the formation of sucrose, the reaction equation outlines the exact elements and their specific states needed to synthesize a mole of sucrose. The coefficients in the reaction equation indicate the proportion of moles required for each reactant. Proper interpretation and balancing of these equations are crucial skills in chemistry education to predict the outcomes of reactions and to comprehend the changes in enthalpy associated with the process.