Problem 27 - Chemistry

Question

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:$$\begin{aligned}2 \mathrm{ZnS}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{ZnO}(s)+2 \mathrm{SO}_{2}(g) & \Delta H=-879 \mathrm{~kJ} / \mathrm{mol}\end{aligned}$$ Calculate the heat evolved (in kJ) per gram of \(\mathrm{ZnS}\) roasted.

Step-by-Step Solution

Answer

The heat evolved per gram of ZnS is approximately -4.511 kJ/g.

Step 1: Calculate Molar Mass of ZnS

First, we need to find the molar mass of ZnS to determine how much energy is released per mole. The atomic mass of Zn is approximately 65.38 g/mol and S is approximately 32.07 g/mol. Add these values to get the molar mass of ZnS:\[ \text{Molar mass of ZnS} = 65.38 + 32.07 = 97.45 \text{ g/mol} \]

Step 2: Determine the Heat Evolved for 1 mole of ZnS

The given enthalpy change \( \Delta H \) for the roasting process is -879 kJ for the reaction of 2 moles of \( \mathrm{ZnS} \). To find the heat evolved per mole of \( \mathrm{ZnS} \), divide the total enthalpy change by 2 (because the equation involves 2 moles):\[ \Delta H_{\text{per mole}} = \frac{-879 \text{ kJ}}{2} = -439.5 \text{ kJ/mol} \]

Step 3: Calculate Heat Evolved per Gram of ZnS

Now, use the molar mass to find the heat evolved per gram. Divide the heat evolved per mole by the molar mass of ZnS:\[ \text{Heat per gram} = \frac{-439.5 \text{ kJ/mol}}{97.45 \text{ g/mol}} \approx -4.511 \text{ kJ/g} \]

Key Concepts

Roasting Process

The roasting process plays a crucial role in metallurgical extraction, particularly for ores like zinc sulfide (\(\text{ZnS}\)). It involves heating ore in the presence of oxygen to convert the sulfide minerals into oxides. For zinc extraction, \(\text{ZnS}\) is transformed into zinc oxide (\(\text{ZnO}\)) by a reaction with oxygen:\[ 2\,\mathrm{ZnS}(s) + 3\,\mathrm{O}_{2}(g) \longrightarrow 2\,\mathrm{ZnO}(s) + 2\,\mathrm{SO}_{2}(g) \]This process is beneficial because it results in substances that are easier to chemically reduce to pure metal. Another benefit of roasting is its ability to remove unwanted sulfur and produce sulfur dioxide (\(\text{SO}_2\)), which can be captured and utilized in other industrial processes. Understanding how these chemical changes occur is fundamental for comprehending the environmental and industrial aspects of metal extraction.

Enthalpy Change

Enthalpy change (\(\Delta H\)) is a pivotal thermodynamic concept used in chemistry to describe the heat absorbed or released during a reaction at constant pressure. It helps us understand the energy dynamics of processes like roasting. For the reaction where \(\text{ZnS}\) is converted into \(\text{ZnO}\), the enthalpy change is -879 \(\text{kJ/mol}\) for the complete equation. This negative value indicates that the process is exothermic, meaning it releases heat. To find out how much energy is given off per mole of \(\text{ZnS}\), you need to consider that two moles of \(\text{ZnS}\) participate in the reaction. Therefore, divide the total \(\Delta H\) by 2, yielding \(-439.5 \text{ kJ/mol}\). Recognizing the negative sign helps predict the reaction behavior: it will naturally proceed as it releases energy to the surroundings.

Molar Mass Calculation

Calculating molar mass is fundamental in determining the energy changes per unit mass of a chemical substance. For zinc sulfide (\(\text{ZnS}\)), calculating the molar mass involves summing up the atomic masses of zinc and sulfur. Zinc has an atomic mass of 65.38 \(\text{g/mol}\) and sulfur's atomic mass is 32.07 \(\text{g/mol}\). Thus, the molar mass of \(\text{ZnS}\) can be calculated as follows:- Zinc: 65.38 \(\text{g/mol}\)- Sulfur: 32.07 \(\text{g/mol}\)- Molar mass of \(\text{ZnS}\) = 65.38 + 32.07 = 97.45 \(\text{g/mol}\)Understanding how to calculate molar mass is essential not just in extraction processes but in various chemical calculations as it allows for conversions between mass and moles, which are crucial for quantifying chemical reactions.

Energy Calculation in Reactions

Energy calculation in reactions helps quantify how much energy is involved per gram of a substance like zinc sulfide (\(\text{ZnS}\)). After finding the energy released per mole, you divide this value by the molar mass to determine the energy change per gram:- Enthalpy (\(\Delta H\)) per mole of \(\text{ZnS}\) = \(-439.5 \text{ kJ/mol}\)- Molar mass of \(\text{ZnS}\) = 97.45 \(\text{g/mol}\)- Energy per gram = \(-439.5 \text{kJ/mol} \div 97.45 \text{g/mol} \approx -4.511 \text{kJ/g}\)This calculation allows us to know how much energy is released for every gram of \(\text{ZnS}\) roasted. This detailed information is pivotal in industrial contexts as it helps design processes to be energy efficient, and it ensures that engineers and scientists can plan the correct scaling for large operations.