A 4.000 g sample of M₂S₃ is converted to MO₂ and loses 0.277 g. What is the atomic weight of M?

A different solution path:

1) Some facts that I can't think of a good title for:

a) The moles of M in M₂S₃ equals the moles of M in 2MO₂. (Notice the inclusion of the coefficient.)

b) Let x = the atomic weight of M.

2) more facts that I can't think of a good title for:

molar mass of M₂S₃ ⇒ 2x + 96 g mol¯¹

"molar mass" of 2MO₂ ⇒ 2x + 64 g mol¯¹

3) Determine moles of M₂O₃ and moles of 2MO₂:

M₂S₃ ⇒ 4.000 / (2x + 96)

2MO₂ ⇒ 3.723 / (2x + 64)

4) Set moles of M in M₂S₃ equal to moles of M in 2MO₂:

[4.000 / (2x + 96)] = [3.723 / (2x + 64)]

x = 183 g mol¯¹

For a bit of clarity with the numbers, I didn't pay close attention to putting units on numbers. I hope this didn't mess you up too much.