The first step in the industrial recovery of zinc from the zinc sulfide ore is roasting, that is, the conversion of \(\mathrm{ZnS}\) to \(\mathrm{ZnO}\) by heating: $$\begin{array}{r}2 \mathrm{ZnS}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{ZnO}(s)+2 \mathrm{SO}_{2}(g) \\ \Delta H=-879 \mathrm{~kJ} / \mathrm{mol}\end{array}$$ Calculate the heat evolved (in kJ) per gram of ZnS roasted.

Chemical reaction stoichiometry is a branch of chemical science that involves the quantitative relationships between the reactants and products in a chemical reaction. Understanding stoichiometry is essential for predicting how much product will form from a given amount of reactants, which is crucial in industrial processes such as the roasting of zinc sulfide ore to produce zinc oxide.

In the example of the zinc sulfide ore roasting, the balanced chemical equation $$2 \mathrm{ZnS}(s) + 3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{ZnO}(s) + 2 \mathrm{SO}_{2}(g)$$illustrates the stoichiometric relationship. The coefficients in front of each substance indicate their respective molar ratios. For every 2 moles of zinc sulfide (\(\mathrm{ZnS}\)), 3 moles of oxygen gas (\(\mathrm{O}_{2}\)) are required, and the reaction will yield 2 moles of zinc oxide (\(\mathrm{ZnO}\)) and 2 moles of sulfur dioxide (\(\mathrm{SO}_{2}\)).

Understanding the stoichiometry is not just about balancing chemical equations; it's also critical in determining the efficiency and yield of the industrial process. For instance, if you start with an excess of \(\mathrm{ZnS}\), not all of it will be converted to \(\mathrm{ZnO}\) unless there is enough \(\mathrm{O}_{2}\) present. Therefore, accurate calculation and measurement are key to ensuring the chemical process is both effective and cost-efficient.

Thermochemistry is the study of the heat energy associated with chemical reactions and physical transformations. The change in enthalpy (\(\Delta H\)) of a reaction, which is the heat absorbed or released under constant pressure, is a fundamental concept in this field.

In the context of our roasting reaction of zinc sulfide, the given enthalpy change is \(-879 \mathrm{~kJ/mol}\), indicating that the reaction is exothermic; it releases heat to the surroundings. This amount of energy is substantial when considering the industrial application, as it impacts the energy requirements and overall sustainability of the process. For instance, the heat evolved can be harnessed to power other stages of ore processing, enhancing energy efficiency.

Understanding the enthalpy change is also vital for safety considerations in industrial settings where controlling the temperature is crucial to prevent accidents. It can dictate the need for cooling systems to manage excess heat or insulation strategies to maintain optimal temperatures for the reaction to proceed.

Molar mass calculation is a process used to determine the mass of one mole of a substance, expressed typically in grams per mole (\(g/mol\)). It is an essential aspect of chemical stoichiometry, as it allows chemists to convert between the mass of a substance and the amount in moles.

For example, the molar mass of zinc sulfide (\(\mathrm{ZnS}\)) is found by adding the atomic masses of zinc (\(\mathrm{Zn}\), 65.38 \(g/mol\)) and sulfur (\(\mathrm{S}\), 32.06 \(g/mol\)). Therefore, the molar mass of \(\mathrm{ZnS}\) is \(65.38 + 32.06 = 97.44 \, g/mol\).

When calculating the heat evolved per gram of \(\mathrm{ZnS}\) roasted, we use this molar mass in conjunction with the thermochemical data to find that \(4.51 \, kJ/g\) of energy is released. This information is critical for adjusting the scale of the operation to the desired output and for ensuring the correct amount of ore is processed to meet energy requirements. In any industrial process, accurate molar mass calculation underpins the ability to standardize reactions, ensure product quality, and control production costs.