Problem 54 - Chemical Principles: The Quest for Insight

Question

Write the thermochemical equations that give the values of the standard enthalpies of formation for (a) \(\mathrm{CH}_{2} \mathrm{COOH}\) (I); (b) \(\mathrm{SO}_{2}\) (g); (c) \(\mathrm{CO}_{2}\) (g).

Step-by-Step Solution

Answer

The standard enthalpies of formation are: (a) \(\mathrm{2C}+2\mathrm{H}_2+\mathrm{O}_2 \rightarrow \mathrm{CH}_{2}\mathrm{COOH} \), (b) \(\mathrm{S}+\mathrm{O}_2 \rightarrow \mathrm{SO}_2 \), (c) \(\mathrm{C}+\mathrm{O}_2 \rightarrow \mathrm{CO}_2 \).

Step 1 - Understanding Standard Enthalpies of Formation

The standard enthalpy of formation, \( \Delta H_f^\circ \), of a compound is the change in enthalpy when one mole of the compound is formed from its elements in their standard states. The standard state of an element is its state at 1 atm and 25°C (298 K).

Step 2 - Writing Equation for \( \mathrm{CH}_{2}COOH \) Formation

The chemical formula for acetic acid is \( \mathrm{C_2H_4O_2} \). Its formation from its elements in standard states can be represented as: \[\mathrm{2C_{(s)}} + \mathrm{2H_{2(g)}} + \mathrm{O_{2(g)}} \rightarrow \mathrm{C_2H_4O_2_{(l)}}\] Note that carbon is in its standard state as graphite, hydrogen as gas, and oxygen as gas. Acetic acid is in its liquid state.

Step 3 - Writing Equation for \( \mathrm{SO}_{2} \) (g) Formation

Sulfur dioxide is formed from its elements in their standard states by the reaction: \[\mathrm{S_{(s)}} + \mathrm{O_{2(g)}} \rightarrow \mathrm{SO_{2(g)}}\] Sulfur's standard state is solid, and oxygen's standard state is diatomic gas.

Step 4 - Writing Equation for \( \mathrm{CO}_{2} \) (g) Formation

Carbon dioxide is formed from its elements in their standard states by the reaction: \[\mathrm{C_{(s)}} + \mathrm{2O_{2(g)}} \rightarrow \mathrm{CO_{2(g)}}\] Here, carbon is in its standard state as graphite and oxygen as diatomic gas.

Key Concepts

Thermochemical Equations

In chemistry, thermochemical equations are representations of chemical reactions that also show the enthalpy change (\( \triangle H \)). These equations are essential for understanding the energy aspects of chemical reactions. A typical thermochemical equation includes not just the reactants and products but also the states they are in and the enthalpy change associated with the reaction.

For instance, when acetic acid (vinegar's active component) forms from its elemental components carbon, hydrogen, and oxygen, the thermochemical equation would not only list these substances but also the heat absorbed or released during the formation. This incorporation of thermal information transforms a standard chemical equation into a tool for energetics analysis in chemical thermodynamics, providing insights into energy efficiency and the driving forces behind chemical processes.

Enthalpy Change

The concept of enthalpy change is central to thermochemistry and represents the heat content that is either absorbed or released during a chemical reaction at constant pressure. This quantity is denoted as \( \triangle H \) and is measured in units of joules per mole. An enthalpy change can be of two types: exothermic (\( \triangle H < 0 \tt\trightarrow\text{heat released}\tt\trightarrow\text{heat released} \tt\trightarrow\text{heat released} \)) or endothermic (\( \triangle H > 0 \tt\trightarrow\text{heat absorbed}\tt\trightarrow\text{heat absorbed} \tt\trightarrow\text{heat absorbed} \)).

Interpreting these enthalpy changes helps us to predict whether a reaction will be spontaneous or non-spontaneous. By applying Hess's Law, we can even calculate the enthalpy change of a complex reaction through the sum of simpler reactions. This aids in understanding the energetic feasibility of industrial processes and biological functions.

Chemical Thermodynamics

Chemical thermodynamics is the branch of science that deals with the study of energy and enthalpy changes associated with chemical reactions and phase transitions. It allows scientists and engineers to understand how energy is exchanged and transformed in chemical processes.

One of the fundamental principles of chemical thermodynamics is that energy cannot be created or destroyed, only converted from one form to another—a reflection of the first law of thermodynamics. Energy changes in reactions are influenced by factors such as temperature, pressure, and the nature of the reactants and products. Mastery of chemical thermodynamics is crucial in predicting the spontaneity of a reaction, optimizing reaction conditions, and ultimately, designing processes across industries ranging from pharmaceuticals to renewable energy.

Standard States

In the context of chemical thermodynamics, standard states refer to specific reference conditions used to measure properties like enthalpy, entropy, and Gibbs free energy. These standard states are defined for a substance at one atmosphere of pressure (1 atm) and, commonly, a temperature of 298.15 K (25°C).

Different elements and compounds have different standard states depending on their most stable form at the specified conditions. For example, the standard state for carbon is graphite, not diamond, because graphite is more stable at 1 atm and 25°C. The concept of standard states provides a reference point that ensures consistency and comparability in thermodynamic calculations and tabulated thermochemical data.