An element, X, can form a chloride (XCl3) and an iodide (XI3). The chloride can be converted quantitatively into the iodide when heated and exposed to excess iodine. If 0.760 grams of XCl3 are heated with iodine, 1.610 g of XI3 are produced. What is the chemical symbol for this element

The chemical symbol for this element is La

Explanation:

Step 1: Data given

Mass of XCl3 = 0.760 grams

Mass of XI3 = 1.610 grams

Molar mass Cl = 35.45 g/mol

Step 2: The balanced equation

2XCl3 + 3I2 → 2XI3 + 3Cl2

The mol ratio for XCl3: XI3 = 2:2 or 1:1

Step 3: Calculate moles

Moles = mass / molar mass

Moles XCl3 = mass XCl3 / molar mass XCl3

Moles XCl3 = 0.760 grams / (X + 3*35.45 g/mol)

Moles XI3 = 1.610 grams / (X + 3*126.9 g/mol)

0.760 grams / (X + 3*35.45 g/mol) = 1.610 grams / (X + 3*126.9 g/mol)

0.760 / (X + 106.35) = 1.610 / (X + 380.7)

0.760 (X +380.7) = 1.610 ( X + 106.35)

0.760X + 289.3 = 1.610X + 171.2

118.1 = 0.85X

X = 138.9 g/mol

If we look for an element with atomic mass of 138.9 g/mol we  find Lanthanum (La)

2LaCl3 + 3I2 → 2LaI3 + 3Cl2