Problem 83 - Chemistry The Central Science

Question

Hydrogen sulfide is an impurity in natural gas that must be removed. One common removal method is called the Claus process, which relies on the reaction: $$ 8 \mathrm{H}_{2} \mathrm{~S}(g)+4 \mathrm{O}_{2}(g) \longrightarrow \mathrm{S}_{8}(l)+8 \mathrm{H}_{2} \mathrm{O}(g) $$ Under optimal conditions the Claus process gives \(98 \%\) yield of \(\mathrm{S}_{8}\) from \(\mathrm{H}_{2} \mathrm{~S}\). If you started with 30.0 grams of \(\mathrm{H}_{2} \mathrm{~S}\) and 50.0 grams of \(\mathrm{O}_{2}\), how many grams of \(\mathrm{S}_{8}\) would be produced, assuming \(98 \%\) yield?

Step-by-Step Solution

Answer

Under optimal conditions with 98% yield, 27.66 grams of S₈ would be produced.

Step 1: Convert the grams of each reactant to moles

We can use the molar masses of H₂S and O₂ to convert the given masses to moles. Molar mass of H₂S = 1.01 g/mol (for H) + 32.07 g/mol (for S) = 34.08 g/mol Moles of H₂S = (30.0 g) / (34.08 g/mol) = 0.880 mol Molar mass of O₂ = 2 * 16 g/mol (for O) = 32 g/mol Moles of O₂ = (50.0 g) / (32 g/mol) = 1.563 mol

Step 2: Determine the limiting reactant

Next, we'll find the limiting reactant. We can do this by dividing the moles of each reactant by their respective stoichiometric coefficients given in the balanced chemical equation and finding the lowest value. For H₂S: (0.880 mol) / 8 = 0.110 For O₂: (1.563 mol) / 4 = 0.391 Since the value for H₂S is lower, H₂S is the limiting reactant.

Step 3: Calculate the theoretical yield of S₈ in moles

Now, we will calculate the theoretical yield of S₈ using the stoichiometry of the reaction. Since H₂S is the limiting reactant, we will base our calculation on its moles. The stoichiometric ratio of S₈ to H₂S from the balanced equation is 1:8, meaning 1 mol of S₈ is produced for every 8 mol of H₂S consumed. Moles of S₈ produced = (0.880 mol H₂S) * (1 mol S₈ / 8 mol H₂S) = 0.110 mol S₈

Step 4: Convert the theoretical yield to grams and find the actual yield

Next, we need to convert the moles of S₈ into grams. The molar mass of S₈ is 8 * 32.07 g/mol (for S) = 256.56 g/mol. Theoretical yield of S₈ = (0.110 mol S₈) * (256.56 g/mol) = 28.22 g Now, we know that the actual yield is 98% of the theoretical yield. Actual yield of S₈ = 0.98 * 28.22 g = 27.66 g So, under optimal conditions with 98% yield, 27.66 grams of S₈ would be produced.

Key Concepts

Stoichiometry

Stoichiometry is closely related to the concept of a recipe in cooking; it refers to the quantitative relationship between reactants and products in a chemical reaction. In simple terms, stoichiometry tells us how much of each reactant is needed to produce a certain amount of product. It's essential for predicting the yields of reactions and for scaling up from laboratory to industrial production.

Using the Claus process as an example, the stoichiometry of the reaction can be deciphered from the balanced equation, which indicates that eight moles of hydrogen sulfide react with four moles of oxygen to form one mole of octasulfur and eight moles of water. These molar ratios are fundamental to determining the amount of each substance involved in the reaction.

Limiting Reactant

The limiting reactant in a chemical reaction is the substance that is completely consumed first and thus determines the amount of product that can be formed. Identifying the limiting reactant is a critical step in stoichiometry because it allows for the calculation of the theoretical yield. In the Claus process example, the limiting reactant is determined by comparing the mole ratio of each reactant to its stoichiometric coefficient. If hydrogen sulfide is the limiting reactant, it means all of it will be used up when the reaction proceeds, while there will be some remaining oxygen.

Theoretical Yield

The theoretical yield is the maximum amount of product that can be generated from a given amount of reactants under perfect conditions. It is calculated by assuming all the limiting reactant is converted into the product, without any losses or side reactions. The theoretical yield provides a benchmark for the efficiency of the reaction. In calculating the theoretical yield for the formation of octasulfur, the stoichiometry of the reaction is applied to the amount of the limiting reactant (hydrogen sulfide), as shown in the exercise.

Actual Yield

The actual yield is the amount of product actually obtained from a chemical reaction. It is often less than the theoretical yield due to factors such as incomplete reactions, side reactions, or loss of product during processing. In practice, the actual yield is expressed as a percentage of the theoretical yield, known as the percent yield. For the Claus process problem, 98% yield means that the actual amount of octasulfur produced is 98% of the calculated theoretical yield.

Chemical Reaction Balancing

Balancing a chemical reaction involves adjusting the coefficients of the reactants and products to ensure that the number of atoms for each element is the same on both sides of the equation. This reflects the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. The Claus process reaction is already balanced, with equal numbers of atoms on both sides—this balanced equation is used to determine the stoichiometry, the theoretical yield, and ultimately, the actual yield of sulfur produced.