By burning 52 g of Metal (III) in a chlorine atmosphere, 158.5 g of salt were obtained. What metal was burned?

We compose the reaction equation.
2 Ме + 3 Cl2 -> 2 MeCl3
Where Me is an unknown metal.
Let us denote the molar mass of the metal through x. Next, we find the molar mass from the reaction equation.
52 g Me – 158.5 g MeCl3
2 × x g / mol Me – (35.5 × 3 + x) × 2 g / mol MeCl3
52 × ((35.5 × 3 + x) × 2) = 158.5 × 2x.
52 × ((106.5 + x) × 2) = 317 x.
52 × (213 + 2x) = 317 x.
11076 + 104 x = 317 x.
11076 = 317 x – 104 x.
11076 = 213 x.
X = 11076 ÷ 213 = 52 g / mol Me.
This means that the molar mass of the unknown metal is 52 g / mol. The metal chromium has a molar mass of 52 g / mol. Chromium also has a valency of 3.
Answer: unknown metal chromium Cr.