Problem 11 - Chemistry and Chemical Reactivity

Question

Sodium sulfide, \(\mathrm{Na}_{2} \mathrm{S},\) is used in the leather industry to remove hair from hides. The \(\mathrm{Na}_{2} \mathrm{S}\) is made by the reaction $$\mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{s})+4 \mathrm{C}(\mathrm{s}) \rightarrow \mathrm{Na}_{2} \mathrm{S}(\mathrm{s})+4 \mathrm{CO}(\mathrm{g})$$ Suppose you mix \(15 \mathrm{g}\) of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) and \(7.5 \mathrm{g}\) of \(\mathrm{C}\) Which is the limiting reactant? What mass of \(\mathrm{Na}_{2} \mathrm{S}\) is produced?

Step-by-Step Solution

Answer

The limiting reactant is \( \text{Na}_2\text{SO}_4 \). Mass of \( \text{Na}_2\text{S} \) produced is about 8.28 g.

Step 1: Calculate Molar Masses

First, we calculate the molar masses of the reactants and products involved. - The molar mass of \( \text{Na}_2\text{SO}_4 \) is \( 2 \times 23.0 \text{ g/mol} + 32.1 \text{ g/mol} + 4 \times 16.0 \text{ g/mol} = 142.1 \text{ g/mol} \).- The molar mass of \( \text{C} \) is \( 12.0 \text{ g/mol} \).- The molar mass of \( \text{Na}_2\text{S} \) is \( 2 \times 23.0 \text{ g/mol} + 32.1 \text{ g/mol} = 78.1 \text{ g/mol} \).

Step 2: Calculate Moles of Reactants

Using the molar masses, calculate the number of moles of each reactant.- Moles of \( \text{Na}_2\text{SO}_4 \) = \( \frac{15\text{ g}}{142.1\text{ g/mol}} \approx 0.106 \text{ mol} \).- Moles of \( \text{C} \) = \( \frac{7.5\text{ g}}{12.0\text{ g/mol}} = 0.625 \text{ mol} \).

Step 3: Determine Limiting Reactant

Using the balanced chemical equation, determine which reactant is limiting.- According to the equation, 1 mole of \( \text{Na}_2\text{SO}_4 \) reacts with 4 moles of \( \text{C} \).- To react completely with 0.106 moles of \( \text{Na}_2\text{SO}_4 \), we need \( 4 \times 0.106 = 0.424 \text{ moles} \) of \( \text{C} \).- Since we have 0.625 moles of \( \text{C} \), \( \text{Na}_2\text{SO}_4 \) is the limiting reactant.

Step 4: Calculate Mass of Produced Na2S

Now that we know \( \text{Na}_2\text{SO}_4 \) is limiting, we calculate the mass of \( \text{Na}_2\text{S} \) produced.- From the equation, 1 mole of \( \text{Na}_2\text{SO}_4 \) produces 1 mole of \( \text{Na}_2\text{S} \).- Thus, 0.106 moles of \( \text{Na}_2\text{SO}_4 \) will produce 0.106 moles of \( \text{Na}_2\text{S} \).- Mass of \( \text{Na}_2\text{S} = 0.106 \text{ mol} \times 78.1 \text{ g/mol} \approx 8.28 \text{ g} \).

Key Concepts

Stoichiometry

Stoichiometry is a critical concept in chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. Think of it as the "recipe" for chemical reactions. Every balanced chemical equation has a specific stoichiometric ratio that shows how the amounts of different substances relate to each other. For instance, in the given reaction:\[ \mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{s})+4 \mathrm{C}(\mathrm{s}) \rightarrow \mathrm{Na}_{2} \mathrm{S}(\mathrm{s})+4 \mathrm{CO}(\mathrm{g}) \]The stoichiometry indicates that 1 mole of sodium sulfate (\mathrm{Na}_{2} \mathrm{SO}_{4}) reacts with 4 moles of carbon (\mathrm{C}) to produce 1 mole of sodium sulfide (\mathrm{Na}_{2} \mathrm{S}) and 4 moles of carbon monoxide (\mathrm{CO}). Understanding these ratios allows chemists to determine how much of each reactant is needed and what amount of product will form. Breaking it down step-by-step encourages accuracy in both chemical calculations and experimental design.

Molar Mass Calculation

Calculating the molar mass of compounds involved in a chemical reaction is a fundamental step in stoichiometric calculations. The molar mass tells us the mass of one mole of a substance, which is crucial for converting between grams and moles, the units used in stoichiometry. Here's how you calculate molar mass:- **Identify the atomic masses.** Look up the atomic masses of the individual elements on the periodic table. For example, the atomic mass of sodium (\mathrm{Na}) is approximately 23.0 g/mol, sulfur (\mathrm{S}) is 32.1 g/mol, and oxygen (\mathrm{O}) is 16.0 g/mol.- **Sum the masses according to the chemical formula.** For sodium sulfate (\mathrm{Na}_{2} \mathrm{SO}_{4}), the molar mass is calculated by adding the masses of its constituent elements: \( 2 \times 23.0 + 32.1 + 4 \times 16.0 = 142.1\) g/mol.This calculation allows us to convert a given mass of \mathrm{Na}_{2} \mathrm{SO}_{4} (15 g, in this case) into moles via the formula \( \text{moles} = \frac{\text{mass in grams}}{\text{molar mass in g/mol}} \). Armed with this data, we can progress to further stoichiometric calculations.

Chemical Reactions

Chemical reactions are transformative processes where substances, called reactants, convert into new substances known as products. These reactions can involve the rearrangement of atoms, breaking and forming of bonds, and changes in energy. In the provided problem, the chemical reaction is written as follows:\[ \mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{s})+4 \mathrm{C}(\mathrm{s}) \rightarrow \mathrm{Na}_{2} \mathrm{S}(\mathrm{s})+4 \mathrm{CO}(\mathrm{g}) \]This equation shows us:- **Reactants:** sodium sulfate (\mathrm{Na}_{2} \mathrm{SO}_{4}) and carbon (\mathrm{C}).- **Products:** sodium sulfide (\mathrm{Na}_{2} \mathrm{S}) and carbon monoxide (\mathrm{CO}).The balanced nature of this equation indicates that matter is conserved, meaning the same number of each type of atom appears on both sides. Understanding the balancing and purpose of chemical reactions helps determine the limiting reactant, the substance that fully reacts and limits the amount of product formed. This forms a critical part of analyzing any reaction, influencing practical applications in industrial processes, such as leather production in this scenario.