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?

Short answer

The Claus process with a 98% yield and given amounts of reactants would produce 27.657 grams of S8.

Step-by-step solution

Calculate the moles of reactants

Begin by calculating the moles of each reactant. Use the given masses and the molar masses. For H2S: Mass (g) = 30.0 g Molar mass = 34.08 g/mol (1.00784 g/mol for H, 32.065 g/mol for S) Moles of H2S = (30.0 g) / (34.08 g/mol) = 0.8804 moles For O2: Mass (g) = 50.0 g Molar mass = 32.00 g/mol (16.00 g/mol for O) Moles of O2 = (50.0 g) / (32.00 g/mol) = 1.5625 moles

Determine the limiting reactant

To determine the limiting reactant, we need to compare the mole ratios of the reactants to the required mole ratio according to the balanced equation. Divide the moles of each reactant by their stoichiometric coefficients. Moles ratio of H2S = (0.8804 moles) / 8 = 0.11005 Moles ratio of O2 = (1.5625 moles) / 4 = 0.390625 The smaller value indicates the limiting reactant, which is H2S in this case.

Calculate moles of S8 from limiting reactant

Using the moles of the limiting reactant (H2S) and the stoichiometry of the balanced equation, we can calculate the maximum moles of S8 produced. Since 8 moles of H2S react to form 1 mole of S8, the maximum moles of S8 produced are: Moles of S8 = (0.8804 moles of H2S) * (1 mole of S8 / 8 moles of H2S) = 0.11005 moles of S8

Calculate mass of S8 considering the yield

We know that the actual yield of the process is 98%. Therefore, we need to account for the yield in the calculation of the mass of S8 produced. First, calculate the molar mass of S8: Molar mass of S8 = 8 * 32.065 g/mol (From periodic table) = 256.52 g/mol Now, find the actual moles of S8 produced considering the yield: Actual moles of S8 = 0.11005 moles * 98% = 0.107849 moles Finally, calculate the mass of S8 produced: Mass of S8 = (0.107849 moles) * (256.52 g/mol) = 27.657 g Thus, 27.657 grams of S8 would be produced, assuming 98% yield.

Key concepts

Limiting Reactant

When two reactants are mixed, the limiting reactant is the one that gets used up first, stopping the chemical reaction from continuing. To find out which reactant is limiting in a chemical reaction like the Claus process for hydrogen sulfide, we use the balanced equation, and we compare the molar amounts of each reactant to their stoichiometric coefficients. The Claus process reaction is: $$8 \mathrm{H}_{2} \mathrm{S}(g) + 4 \mathrm{O}_{2}(g) \rightarrow \mathrm{S}_{8}(l) + 8 \mathrm{H}_{2} \mathrm{O}(g)$$In this formula, 8 moles of hydrogen sulfide (\(\mathrm{H}_{2} \mathrm{S}\)) react with 4 moles of oxygen (\(\mathrm{O}_2\)). To determine the limiting reactant, calculate the molar ratio for each of the reactants and choose the one with the smaller number.- Divide the moles of \(\mathrm{H}_{2} \mathrm{S}\) by its coefficient (8) and \(\mathrm{O}_2\) by its coefficient (4).- The reactant with the smaller ratio is the limiting reactant.Here, it was determined that \(\mathrm{H}_{2} \mathrm{S}\) is the limiting reactant, meaning it will be completely consumed first, determining the maximum amount of \(\mathrm{S}_8\) that can be formed.

Yield Calculation

Calculating the yield in a chemical reaction helps you understand the efficiency of that reaction. The theoretical yield is the maximum amount of product that can be formed from a given amount of reactants. However, in real-life scenarios, the actual yield is often lower due to inefficiencies or side reactions.In the Claus process applied to our exercise:- Given the optimal 98% yield, the product \(\mathrm{S}_8\) does not completely form as expected from the reactants.- To find the actual yield, use this key formula:\[\text{Actual moles of } \mathrm{S}_8 = \text{Theoretical moles of } \mathrm{S}_8 \times \frac{\text{Actual yield}}{100} = 0.11005 \times 0.98 = 0.107849\]Yield calculations such as these help predict the actual outcomes of chemical processes in industrial applications, where maximizing efficiency is crucial.

Stoichiometry

Stoichiometry is a central concept in chemistry that involves the calculation of reactants and products in chemical reactions. It relies heavily on the law of conservation of mass. In the Claus process equation, stoichiometry is used to find out how many moles of one reactant are needed to react completely with another and yield a product, such as \(\mathrm{S}_8\).- You use coefficients from the balanced chemical equation: - 8 moles of \(\mathrm{H}_{2} \mathrm{S}\) produce 1 mole of \(\mathrm{S}_8\).To find how much product is formed from a given amount of limiting reactant, you can follow this stoichiometric calculation:\[\text{Moles of } \mathrm{S}_8 = \frac{\text{Moles of } \mathrm{H}_{2} \mathrm{S}}{8}\]By understanding stoichiometry, one can deduce quantitative relationships in a reaction, ensuring the correct amounts of reactants lead to desired product quantities.

Molar Mass Calculation

The molar mass is the mass of a given substance divided by the amount of substance, often expressed in grams per mole (g/mol). In chemistry, it's crucial to convert between grams and moles for accurate calculations.In a reaction like the Claus process:- Determine the molar mass of each reactant and product, starting with the periodic table values: - \( \mathrm{H}_{2} \mathrm{S} \) has a molar mass of 34.08 g/mol. - \( \mathrm{O}_2 \) has a molar mass of 32.00 g/mol. - \( \mathrm{S}_8 \) is calculated as 256.52 g/mol, found by multiplying the atomic mass of sulfur (32.065 g/mol) by 8.Molar mass calculations help convert between the mass of a substance and the number of moles, a necessary step in determining limiting reactants and yields in chemical reactions.