1. Balanced Chemical Equation:
The balanced chemical equation for the reaction is:
CH₄ + 4S → CS₂ + 2H₂S
2. Calculate Moles of Reactants:
* Moles of CH₄:
- Molar mass of CH₄ = 12.01 g/mol (C) + 4 * 1.01 g/mol (H) = 16.05 g/mol
- Moles of CH₄ = 120 g / 16.05 g/mol = 7.47 mol
* Moles of S:
- Molar mass of S = 32.07 g/mol
- Moles of S = 120 g / 32.07 g/mol = 3.74 mol
3. Identify the Limiting Reactant:
- From the balanced equation, 1 mole of CH₄ reacts with 4 moles of S.
- We have 7.47 moles of CH₄, which would require 7.47 * 4 = 29.88 moles of S.
- Since we only have 3.74 moles of S, sulfur is the limiting reactant.
4. Calculate Theoretical Yield of CS₂:
- The balanced equation shows that 4 moles of S produce 1 mole of CS₂.
- Since we have 3.74 moles of S, we can produce 3.74 mol S / 4 = 0.935 mol of CS₂.
5. Convert Moles of CS₂ to Grams:
- Molar mass of CS₂ = 12.01 g/mol (C) + 2 * 32.07 g/mol (S) = 76.15 g/mol
- Theoretical yield of CS₂ = 0.935 mol * 76.15 g/mol = 71.2 g
Therefore, the theoretical yield of carbon disulfide in this reaction is 71.2 g.
