A salt contains only magnesium and one of the halide ions. A 0.0776-g sample of the salt was dissolved in water, and an excess of sulfuric acid was added to form magnesium sulfate (MgSO4), which was filtered, dried, and weighed. Its mass was found to be 0.150 g. What is the formula of the magnesium halide

The formula of the magnesium halide is MgF₂

Explanation:

All halides, X, produce a salt with Mg with the formula:

MgX₂

-There are 2 moles of the halide ion per mole of Mg-

With the mass of the MgSO₄ we can find moles of magnesium sulfate  = Moles Mg.

With moles of Mg we can know the moles of the halide -1 mole Mg = 2 moles of Halide-

And we can find the mass of Mg in the 0.0776g sample. Subtracting we can find the mass of the halide and, with the mass and moles of the halide we can find its molecular weight and its identity:

Moles MgSO₄ -Molar mass: 120.366g/mol- = Moles Mg:

0.150g * (1mol / 120.366g) = 1.2462x10⁻³ moles Mg

Moles halide:

1.2462x10⁻³ moles Mg * 2 = 2.4924x10⁻³ moles Halide

Mass Mg -Molar mass: 24.305g/mol:

1.2462x10⁻³ moles Mg * (24.305g / mol) = 0.0303g Mg

Mass halide:

0.0776g - 0.0303g Mg = 0.0473g

Molecular weight of the halide:

0.0473g / 2.4924x10⁻³ moles =

18.98g/mol

This molecular weight is the molecular weight of Fluoride ion, F⁻,