**Category:** Inorganic Chemistry  
**Subtype:** Chemical Reactions, Stoichiometry  

**Problem Overview:**  
This problem involves a chemical reaction where a mixture of elements (carbon, phosphorus, and sulfur) is reacted with concentrated nitric acid. The products include a solution and a gas mixture. The problem requires calculating the mass percentage of carbon in the original mixture based on the resulting products and the amount of precipitate formed when a barium hydroxide solution is added. 

**Key Points to Address:**  
- The initial mass of the mixture (12.49 g)  
- The products formed (solution Y and gas Z)  
- The mass of the precipitate formed (91.675 g)  
- The amount of sodium hydroxide solution needed to absorb the gas produced (2.55 mol)  

**Goal:**  
Determine the mass percentage of carbon in the original mixture X.