Final answer:
The molar mass of metal M in MCl3 is calculated to be approximately 88.85 g/mol after finding the molar mass of Cl and subtracting it from the total molar mass of MCl3.
Step-by-step explanation:
To calculate the molar mass of metal M in MCl3, start with the fact that MCl3 is 54.47% Cl by mass. Since there are three Cl atoms in MCl3, you can calculate the mass of Cl in one mole of MCl3 using the atomic mass of Cl (approximately 35.45 g/mol).
Multiplying the atomic mass by three, you get 3 x 35.45 g/mol of Cl = 106.35 g/mol of Cl.
With MCl3 being 54.47% Cl, the total molar mass of MCl3 can be found by dividing the mass of Cl by this percentage (106.35 g/mol / 0.5447), resulting in approximately 195.20 g/mol for the molar mass of MCl3.
To find the molar mass of M, deduct the mass of Cl from the molar mass of MCl3:
195.20 g/mol - 106.35 g/mol = 88.85 g/mol.
Therefore, the molar mass of M is approximately 88.85 g/mol.