Final answer:
The atomic mass of element D is calculated by subtracting the mass contribution of aluminum from the molar mass of Al2D3, and then dividing by the number of D atoms per formula unit. The result is approximately option 4). 15.42 g/mol, which matches option (4) from the given choices.
Step-by-step explanation:
To calculate the atomic mass of element D in the compound Al2D3, we use the given data: 48.04 x 1023 molecules of Al2D3 have a mass of 800 g. We know that 1 mole of Al has an atomic mass of approximately 26.98 g. Since 1 mole of a substance contains Avogadro's number of entities (6.022 x 1023), we can first find out the number of moles of Al2D3 we have.
Number of moles of Al2D3 = (48.04 x 1023 molecules) / (6.022 x 1023 molecules/mol) = roughly 7.98 mol.
To find the molar mass of Al2D3, we divide the total mass by the number of moles: Molar mass of Al2D3 = 800 g / 7.98 mol = 100.25 g/mol.
Next, we calculate the molar mass of two Al atoms: 2 (26.98 g/mol) = 53.96 g/mol. Now, we subtract this from the molar mass of Al2D3 to find the molar mass of 3 atoms of D: 100.25 g/mol - 53.96 g/mol = 46.29 g/mol.
Therefore, the molar mass of one atom of D = 46.29 g/mol / 3 = 15.43 g/mol, which rounds to 15.42 g/mol if we consider significant figures. The closest answer from the provided options would be (4) 15.42.