Treatment of 1.385 g of an unknown metal M with an excess of aqueous HCl evolved a gas that was found to have a volume of 382.6 mL at 20.0 °C and 755 mm Hg pressure. Heating the reaction mixture to evaporate the water and remaining HCl then gave a white crystalline compound, MCl_x. After dis- solving the compound in 25.0 g of water, the melting point of the resulting solution was - 3.53 °C. (f) What is the identity of the metal M?

Verified step by step guidance

1. Determine the moles of gas evolved using the ideal gas law: PV = nRT. Convert the given pressure from mm Hg to atm and the volume from mL to L. Use R = 0.0821 L·atm/mol·K and convert the temperature to Kelvin.
2. Calculate the moles of MClx formed using the freezing point depression formula: ΔT_f = iK_fm, where ΔT_f is the change in freezing point, i is the van't Hoff factor (assume i = 2 for MClx), K_f is the freezing point depression constant for water (1.86 °C·kg/mol), and m is the molality of the solution.
3. Use the moles of gas evolved to determine the moles of metal M reacted, assuming the gas is hydrogen (H2) and the reaction is M + xHCl → MClx + x/2 H2.
4. Calculate the molar mass of the metal M by dividing the mass of the metal (1.385 g) by the moles of metal M determined in the previous step.
5. Identify the metal M by comparing the calculated molar mass to known molar masses of metals.

Key Concepts

Gas Laws

Gas laws describe the behavior of gases in relation to pressure, volume, and temperature. The ideal gas law (PV=nRT) is particularly relevant here, as it allows us to calculate the number of moles of gas produced during the reaction. Understanding how to manipulate these variables is crucial for determining the amount of metal reacted and the identity of the metal M.

Molar Mass and Stoichiometry

Molar mass is the mass of one mole of a substance, which is essential for converting between grams and moles. Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. By determining the moles of gas evolved and relating it to the mass of metal M, we can calculate the molar mass of M and identify the metal.

Freezing Point Depression

Freezing point depression is a colligative property that describes how the addition of a solute lowers the freezing point of a solvent. In this case, the melting point of the solution formed by dissolving MClx in water is given, which can be used to calculate the molality of the solution. This information helps in determining the number of moles of solute, which is necessary for identifying the metal M.