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. (e) What are the formula and molecular weight of MCl_x?

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Step 1: Use the ideal gas law to determine the number of moles of gas evolved. Convert the given volume of gas to liters, temperature to Kelvin, and pressure to atmospheres. Use the formula: \( PV = nRT \), where \( R \) is the ideal gas constant.

Step 2: Determine the number of moles of HCl that reacted with the metal M. Since the gas evolved is likely hydrogen, use the stoichiometry of the reaction between metal M and HCl to find the moles of M that reacted.

Step 3: Calculate the molality of the solution using the freezing point depression formula: \( \Delta T_f = i \cdot K_f \cdot m \), where \( \Delta T_f \) is the change in freezing point, \( i \) is the van't Hoff factor, \( K_f \) is the cryoscopic constant for water, and \( m \) is the molality. Solve for \( m \).

Step 4: Use the molality to find the moles of MClx in the solution. Since molality is moles of solute per kilogram of solvent, use the mass of water to find the moles of MClx.

Step 5: Determine the formula and molecular weight of MClx by comparing the moles of M from the gas evolution with the moles of MClx from the freezing point depression. Use the ratio to find \( x \) in MClx and calculate the molar mass.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the number of moles of gas evolved during the reaction, which can be determined from the given volume, temperature, and pressure of the gas. Understanding this relationship allows for the determination of the amount of metal M that reacted with HCl.

Colligative Properties

Colligative properties are properties of solutions that depend on the number of solute particles in a given amount of solvent, rather than the identity of the solute. The freezing point depression observed in the solution formed after dissolving MClx in water can be used to calculate the molality of the solution, which is crucial for determining the number of moles of MClx and, subsequently, the molecular weight of the compound.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced chemical equations. In this context, stoichiometry is used to relate the moles of the metal M that reacted with HCl to the moles of MClx produced. Understanding stoichiometric relationships is vital for determining the formula of MClx and calculating its molecular weight based on the mass of the unknown metal.

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Textbook Question

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 dissolving the compound in 25.0 g of water, the melting point of the resulting solution was - 3.53 °C. (b) What mass of MClx is formed? (a) How many moles of H₂ gas are evolved?

Textbook Question

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. (c) What is the molality of particles (ions) in the solution of MCl_x?

Textbook Question

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?

Textbook Question

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