In a chemical reaction involving chromium(III) oxide and hydrogen sulfide, the goal is to determine the mass of chromium(III) sulfide produced when given amounts of the reactants. The balanced reaction can be represented as:

Cr₂O₃ + 3 H₂S → 2 Cr₂S₃ + 3 H₂O

To solve the problem, we start with the provided masses of chromium(III) oxide (14.20 grams) and hydrogen sulfide (12.80 grams). The first step is to convert these masses into moles using their respective molar masses. The molar mass of chromium(III) oxide (Cr₂O₃) is calculated as follows:

Cr: 2 × 51.996 g/mol + O: 3 × 16.00 g/mol = 151.992 g/mol

Next, we convert the mass of chromium(III) oxide to moles:

Number of moles of Cr₂O₃ = 14.20 g × (1 mol / 151.992 g) ≈ 0.0934 mol

For hydrogen sulfide (H₂S), the molar mass is:

H: 2 × 1.008 g/mol + S: 32.07 g/mol = 34.086 g/mol

Now, convert the mass of hydrogen sulfide to moles:

Number of moles of H₂S = 12.80 g × (1 mol / 34.086 g) ≈ 0.375 mol

With the moles of both reactants calculated, we perform a mole-to-mole conversion based on the stoichiometry of the balanced equation. For chromium(III) sulfide (Cr₂S₃), the stoichiometric ratio from the balanced equation indicates that 1 mole of Cr₂O₃ produces 1 mole of Cr₂S₃. Thus, we can calculate the moles of chromium(III) sulfide produced from chromium(III) oxide:

0.0934 mol Cr₂O₃ × (2 mol Cr₂S₃ / 1 mol Cr₂O₃) = 0.1868 mol Cr₂S₃

Next, we convert moles of chromium(III) sulfide to grams. The molar mass of chromium(III) sulfide is calculated as:

Cr: 2 × 51.996 g/mol + S: 3 × 32.07 g/mol = 202.21 g/mol

Thus, the mass of chromium(III) sulfide produced from chromium(III) oxide is:

0.1868 mol Cr₂S₃ × 202.21 g/mol ≈ 37.8 g

Now, we perform the same calculations for hydrogen sulfide. According to the balanced equation, 3 moles of H₂S produce 1 mole of Cr₂S₃. Therefore, we calculate the moles of chromium(III) sulfide produced from hydrogen sulfide:

0.375 mol H₂S × (1 mol Cr₂S₃ / 3 mol H₂S) = 0.125 mol Cr₂S₃

Converting this to grams gives:

0.125 mol Cr₂S₃ × 202.21 g/mol ≈ 25.3 g

Now, we compare the two amounts of chromium(III) sulfide produced. The smaller amount, 25.3 grams, indicates that hydrogen sulfide is the limiting reagent, while chromium(III) oxide is in excess. The theoretical yield of chromium(III) sulfide is determined by the limiting reagent, which in this case is hydrogen sulfide.

Thus, the final answer for the mass of chromium(III) sulfide formed is 25.3 grams.