Final answer:
The molar mass of magnesium sulfate heptahydrate (MgSO₄7H₂O) is calculated by summing the molar masses of the anhydrous compound and the water molecules. Subtracting the mass of anhydrous compound from the initial hydrate mass gives the water mass, which is then converted to moles to find the number of water molecules.
Step-by-step explanation:
To calculate the molar mass of a hydrate such as magnesium sulfate heptahydrate (MgSO₄⋅7H₂O), you need to add the molar masses of all the atoms in the formula. First, find the molar mass of anhydrous MgSO₄ by adding the atomic masses of magnesium (Mg), sulfur (S), and oxygen (O) within the sulfate (SO₄) ion. The molar mass of MgSO₄ is 24.305 g/mol for Mg, plus 32.065 g/mol for S, plus 4 times 15.999 g/mol for O, totaling 120.367 g/mol. Then, factor in the seven water molecules, H₂O, each with a molar mass of 18.015 g/mol, which totals 126.105 g/mol for the seven waters. The total molar mass of the hydrate is the sum: 120.367 g/mol + 126.105 g/mol = 246.472 g/mol.
To determine the number of water molecules originally in a sample, you can subtract the final mass after heating (mass of anhydrous MgSO₄) from the initial mass of the hydrate. In this case, 5.0 g - 2.6 g = 2.4 g represents the mass of water lost. By dividing this mass by the molar mass of water (18.015 g/mol), we find the number of moles of water, which can then be multiplied by Avogadro's number to find the number of water molecules.