**Category:** Inorganic Chemistry  
**Subtype:** Stoichiometry and Chemical Reactions  
**Problem Description:** This problem involves the absorption of carbon dioxide (\(\mathrm{CO}_{2}\)) in a solution containing potassium hydroxide (KOH) and potassium carbonate (\(\mathrm{K}_{2}\mathrm{CO}_{3}\)). It requires calculating the amount of \(\mathrm{K}_{2}\mathrm{CO}_{3}\) (denoted as \(y\)) based on the reactions that occur when a portion of the resulting solution is mixed with hydrochloric acid (HCl) and barium hydroxide (\(\mathrm{Ba(OH)}_{2}\)). The problem provides specific volumes and concentrations, as well as the mass of precipitate formed, to determine the value of \(y\).