Calculate the entropy change \((\mathrm{J} / \mathrm{mol} \mathrm{K})\) of the given reaction. The molar entropies [J/K-mol] are given in brackets after each substance. \(2 \mathrm{PbS}(s)[91.2]+3 \mathrm{O}_{2}(g)[205.1] \longrightarrow 2 \mathrm{PbO}(s)[66.5]+2 \mathrm{SO}_{2}(g)[248.2]\) (a) \(-113.5\) (b) \(-168.3\) (c) \(+72.5\) (d) \(-149.2\)

Chemical thermodynamics is a sub-discipline of thermodynamics that focuses on the energy changes associated with chemical reactions and changes in physical state. The fundamental principles of thermodynamics such as the first and the second law are applied to chemical processes to predict the spontaneity of reactions, to understand equilibrium conditions, and to calculate various state functions like enthalpy, entropy, and Gibbs free energy.

Understanding the thermodynamics of chemical reactions is crucial because it enables chemists and engineers to design processes that optimize energy use and minimize environmental impact, leading to more sustainable practices. Moreover, concepts like entropy change offer insight into the disorder and randomness within a system, impacting the feasibility and direction of a chemical reaction.

Molar entropy is a thermodynamic property representing the amount of disorder or randomness in a substance per mole. Measured in units of joules per mole per kelvin (\( \text{J/mol} \text{K} \)), it's a state function, meaning its value depends only on the state of the system and not how it arrived at that state.

In the context of a reaction, you can consider the molar entropies of the reactants and products to determine if a reaction will result in a higher or lower level of disorder in the system. Generally, an increase in the number of gas molecules or a change from a more ordered solid state to a less ordered gaseous state increases entropy. Conversely, the formation of solids from gases or the decrease in the number of gas molecules reduces entropy.

Problems in physical chemistry often involve calculating the changes in thermodynamic quantities for chemical reactions or phase changes. These include exercises like entropy and enthalpy calculations, determining equilibrium constants, or predicting reaction spontaneity using Gibbs free energy.

For successful problem-solving, it is essential to have a firm grasp of thermodynamic principles and mathematical skills to manipulate equations effectively. Applying these concepts to solve physical chemistry problems not only helps students to understand the fundamental science behind chemical reactions but also hones their analytical skills, which are applicable in various scientific fields.

Stoichiometric coefficients refer to the numbers written in front of chemical species in a balanced chemical equation. These numbers denote the ratio in which reactants combine and products form. Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction.

In thermodynamic calculations, stoichiometric coefficients are used to determine the quantity of each substance involved in a reaction. They play an essential role in calculating properties like the total entropy of reactants and products, as they tell us how many moles of each substance participate in the reaction. Correctly applying stoichiometric coefficients ensures accurate computation of entropy changes, which is a vital step to predict the direction and spontaneity of a reaction.