Final answer:
To find the grams of potassium carbonate produced, use stoichiometry and the given masses of KOH and CO₂ to calculate the moles of K₂CO₃ produced. Then, convert the moles of K₂CO₃ to grams using its molar mass. The answer is approximately 138.21 grams.
Step-by-step explanation:
To find the number of grams of potassium carbonate produced, we need to use stoichiometry to calculate the moles of potassium carbonate produced from the given masses of KOH and CO₂. First, balance the equation:
2KOH + CO₂ → K₂CO₃ + H₂O
From the balanced equation, we can see that 2 moles of KOH react with 1 mole of CO₂ to produce 1 mole of K₂CO₃. We can use the molar masses to convert the given masses of KOH and CO₂ to moles:
Given mass of KOH = 224.4 g
Molar mass of KOH = 56.11 g/mol
Moles of KOH = (given mass of KOH) / (molar mass of KOH) = 224.4 g / 56.11 g/mol = 4 moles
Given mass of CO₂ = 88.0 g
Molar mass of CO₂ = 44.0 g/mol
Moles of CO₂ = (given mass of CO₂) / (molar mass of CO₂) = 88.0 g / 44.0 g/mol = 2 moles
Since the reaction produces 1 mole of K₂CO₃ for every 2 moles of CO₂, we can determine the moles of K₂CO₃ produced using the given moles of CO₂:
Moles of K₂CO₃ = (given moles of CO₂) × (1 mole of K₂CO₃ / 2 moles of CO₂) = 2 moles × (1 mole of K₂CO₃ / 2 moles of CO₂) = 1 mole
Finally, we convert the moles of K₂CO₃ to grams using its molar mass:
Molar mass of K₂CO₃ = 138.21 g/mol
Mass of K₂CO₃ = (moles of K₂CO₃) × (molar mass of K₂CO₃) = 1 mole × 138.21 g/mol = 138.21 g
Therefore, 138.21 grams of potassium carbonate are produced in the reaction.