To find the mass of sodium carbonate required, we can use the formula:
Mass = Molarity × Volume × Molar Mass
Step 1: Calculate the molar mass of sodium carbonate (Na2CO3).
2 × Na = 2 × 23 = 46 g/mol
1 × C = 1 × 12 = 12 g/mol
3 × O = 3 × 16 = 48 g/mol
Molar mass of Na2CO3 = 46 + 12 + 48 = 106 g/mol
Step 2: Calculate the number of moles of sodium carbonate using the molarity and volume of the solution.
Molarity = Number of moles / Volume
Number of moles = Molarity × Volume
Given:
Molarity = 0.1 mol/dm³ (or 0.1 M)
Volume = 500 cm³ (or 0.5 dm³)
Number of moles = 0.1 × 0.5 = 0.05 moles
Step 3: Calculate the mass of sodium carbonate using the number of moles and molar mass.
Mass = Number of moles × Molar mass
Mass = 0.05 moles × 106 g/mol = 5.3 grams
Therefore, the mass of sodium carbonate required is 5.3 grams.