Final answer:
To determine the formula of the hydrated sodium carbonate compound, the masses of water and anhydrous Na2CO3 were compared, and moles of each substance were calculated. The mole-to-mole ratio suggested that there are approximately 10 moles of water for every mole of Na2CO3, indicating the formula Na2CO3⋅10H2O for the hydrated compound.
Step-by-step explanation:
The student seeks to determine the formula of the hydrated sodium carbonate compound by comparing the mass of the hydrated form with the mass of the anhydrous form after heating.
The problem provides the initial mass of the hydrated compound (4.640 g) and the final mass of the anhydrous sodium carbonate (1.720 g). By calculating the mass of the water of hydration removed, we can find the number of water molecules in the hydrated compound.
The mass of the water of hydration is:
Mass of hydrated compound - Mass of anhydrous compound = 4.640 g - 1.720 g = 2.920 g
Next, we calculate the molar mass of anhydrous Na₂CO₃ (105.99 g/mol) and water (H₂O, 18.01 g/mol). To find the number of moles of water, we divide the mass of water (2.920 g) by the molar mass of water:
Moles of water = 2.920 g / 18.01 g/mol = 0.162 moles of water
We do the same for anhydrous Na₂CO₃:
Moles of Na₂CO₃ = 1.720 g / 105.99 g/mol = 0.0162 moles of Na₂CO₃
Dividing the moles of water by the moles of sodium carbonate gives us the ratio of water to Na₂CO₃:
Number of water molecules per Na₂CO₃ = 0.162 moles / 0.0162 moles ≈ 10
Therefore, for every mole of anhydrous Na₂CO₃ there are approximately 10 moles of water, indicating the formula is Na₂CO₃⋅10H₂O.