Question

All of the lanthanide metals react with HCl to form compounds having the formula MCl2,MCl3,or MCl4 (where M represents the metallic element). Each metal forms a single compound. A chemist has .250g sample of a transition metal, and wishes to identify the metal. She reacts the metal with excess HCl and obtains .427g of product. Based on this information, identify the metal and write the chemical formula of the product.

Answer 1

I would do this.
M + xHCl ==> MClx + Hx
If we started with 0.250 g M and ended with 0.427 g of the chloride, the amount of Cl added must be 0.427-0.250 = 0.177 grams. Convert that to moles by 0.177/35.453 = 0.00499 moles Cl atoms.

We know the formula is MCl2, MCl3 or MCl4; therefore, the 0.0499 moles Cl will have 1/4 moles of M if MCl4, 1/3 moles of M if MCl3, and 1/2 moles M if MCl2.
For 4, 0.00499/4 = 0.00112
For 3, 0.00499/3 = 0.00166
For 2, 0.00499/2 = 0.00250

moles M = grams/atomic mass and rearrange to atomic mass = grams/moles M and plug in the numbers.
For 4 (MCl4), 0.250/0.00112 = ??
For 3 (MCl3), 0.250/0.00166 = ??
For 2 (MCl2), 0.250/0.00250 = ??
Look on the periodic table and find the lanthanide element closest to one of your values.
There may be an easier way to solve this but this is the best I can think of at the moment.