Stoichiometry: Identify the metal and formula of it

[Sho Kano]

Homework Statement

All of the lanthanide metals (La through Lu) react with HCL to form compounds having eithe the formula MCl2, MCl3, MCl4, (where M represents the metallic element). Each metal forms a single compound. A chemist has a 0.250g sample of a lanthanide metal, and she wishes to identify the metal. She reacts the metal with excess HCl and obtains 0.427g of the product. Based on this information, identify the metal and write the chemical formula of the product.

Homework Equations

The Attempt at a Solution

I'm not sure the below equation is correct. I originally wrote the equation without the H2, but it did not seem to be right with conservation of mass.
M + HCL —> MCl2 (or MCl3, MCl4) + H2
Basically, if the H2 does belong there, then I'd just have to guess MCl2, 3, or 4, then balance the equation, then randomly guess an element right? Seems like a lot of work.

 

[Bystander]

and obtains 0.427g of the product.

2, 3, or 4, then balance

 

[Sho Kano]

I can't see anything on your post

 

[Bystander]

MCl_n is all you need; ignore the H₂, and just start cutting and trying.

 

[Sho Kano]

MCl_n is all you need; ignore the H₂, and just start cutting and trying.

I'm getting Sm as the unknown metal; is that right?

 

[Bystander]

Samarium? Mental arithmetic checks out.

 

[Sho Kano]

Samarium? Mental arithmetic checks out.

Awesome. What happens to the hydrogen though?

 

[Bystander]

What happens to the hydrogen though?

It "fizzes" away up the chimney/hood/exhaust system.

 

[Sho Kano]

It "fizzes" away up the chimney/hood/exhaust system.

I mean why is it not represented in the chemical equation

 

[Bystander]

"M" + nHCl = (n/2)H₂ + "M"Cl_n; it is.

 

[Borek]

Hydrogen is present in the reaction equation and we can even easily calculate its amount. We just ignore it as it is not necessary for solving the problem (just like the amount of HCl doesn't matter, as long as there is enough of it).

The only part of the equation that matters is

Sm → SmCl₃

It preserves the only important information here - stoichiometric ratio between Sm and SmCl₃. When solving this particular problem everything else is just a noise.