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Roasting is a critical initial step in the process of extracting zinc from zinc sulfide (\(\text{ZnS}\)) ore. It involves heating the zinc sulfide in the presence of oxygen to transform it into zinc oxide (\(\text{ZnO}\)) along with the release of sulfur dioxide (\(\text{SO}_2\)). This reaction step is represented as:
2\(\text{ZnS(s)} + 3\text{O}_2(g) \rightarrow 2\text{ZnO(s)} + 2\text{SO}_2(g)\)
The roasting process is not only important for zinc extraction but also contributes to the overall environmental impact due to the emission of sulfur dioxide, which can lead to air pollution if not managed properly. This step liberates a considerable amount of energy, known as the enthalpy change or \(\Delta H_{\text{rxn}}\), which is provided as -879 kJ/mol for this reaction.
It's essential to control the roasting conditions carefully to maximize the yield of ZnO and minimize energy costs and emissions, ensuring a more sustainable and efficient process.

Understanding molar mass is fundamental to performing various chemical calculations, such as determining amounts in reactions or conversions between grams and moles. In this exercise, we calculate the molar mass of zinc sulfide (\(\text{ZnS}\)).
Here's how the calculation works:

• The atomic mass of zinc (\(\text{Zn}\)) is approximately 65.38 g/mol.
• The atomic mass of sulfur (\(\text{S}\)) is approximately 32.07 g/mol.

Thus, the molar mass of \(\text{ZnS}\) is calculated by adding these atomic masses together:
\(65.38 \text{ g/mol} + 32.07 \text{ g/mol} = 97.45 \text{ g/mol}\).
This molar mass serves as a conversion factor to understand the relationship between the weight of zinc sulfide and the number of moles, which is crucial for further calculations, such as determining the heat evolved per gram.

Calculating heat evolved in a chemical reaction provides insight into the energy changes taking place. For the roasting of zinc sulfide, we need to determine how much heat is released per gram of \(\text{ZnS}\) roasted.
As given, the enthalpy change for the roasting of 2 moles of \(\text{ZnS}\) is -879 kJ. Thus, per mole of \(\text{ZnS}\), the heat evolved is:
\(-\frac{879 \text{ kJ}}{2} = -439.5 \text{ kJ/mol}\).
To convert from per mole to per gram, we use the molar mass of \(\text{ZnS}\):

• Divide the heat evolved per mole \(-439.5 \text{ kJ/mol}\) by the molar mass \(97.45 \text{ g/mol}\), resulting in:

\(-439.5 \text{ kJ/mol} \div 97.45 \text{ g/mol} = -4.51 \text{ kJ/g}\).
This conversion tells us the energy change on a more practical scale and allows industries to gauge energy efficiency for different quantities of raw materials used in their processes.