An unidentified metal M reacts with an unidentified halogen X to form a compound MX2. When heated, the compound decomposes by the reaction: When 1.12 g of MX2 is heated, 0.720 g of MX is obtained, along with 56.0 mL of X2 gas. Under the conditions used, 1.00 mol of the gas has a volume of 22.41 L. (a) What is the atomic weight and identity of the halogen X?

Verified step by step guidance

1. Determine the moles of X2 gas produced using the ideal gas law relationship: \( \text{moles of } X_2 = \frac{56.0 \text{ mL}}{22.41 \text{ L/mol}} \).
2. Calculate the mass of X2 gas using the moles obtained and the molar mass of X2: \( \text{mass of } X_2 = \text{moles of } X_2 \times \text{molar mass of } X_2 \).
3. Use the mass of MX2 and MX to find the mass of X2: \( \text{mass of } X_2 = \text{mass of } MX_2 - \text{mass of } MX \).
4. Set up an equation using the molar mass of X2 to solve for the atomic weight of X: \( \text{molar mass of } X_2 = 2 \times \text{atomic weight of } X \).
5. Compare the calculated atomic weight of X with known halogen atomic weights to identify the halogen.

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the conservation of mass. It involves using balanced chemical equations to determine the relationships between the amounts of substances consumed and produced. In this question, stoichiometry will help relate the mass of MX2 decomposed to the moles of X2 gas produced, allowing for the determination of the halogen's identity.

Molar Volume of a Gas

The molar volume of a gas at standard conditions (0°C and 1 atm) is approximately 22.41 L for 1 mole. This concept is crucial for converting the volume of gas produced in the reaction into moles, which can then be used to find the molar mass of the halogen X. Understanding this relationship allows for the calculation of the identity of the halogen based on the amount of gas evolved.

Molar Mass and Identity of Elements

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). By calculating the molar mass of the halogen X from the stoichiometric data provided, one can compare it to known values of halogens to identify the element. This concept is essential for determining the identity of X based on the mass of the gas produced and the stoichiometry of the reaction.