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?

검증된 단계별 안내

Step 1: Use the ideal gas law to calculate the moles of H2 gas evolved. The ideal gas law is given by the equation \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.

Step 2: Convert the given pressure from mm Hg to atm. Use the conversion factor \( 1 \text{ atm} = 760 \text{ mm Hg} \).

Step 3: Convert the given volume from mL to L by dividing by 1000, since \( 1 \text{ L} = 1000 \text{ mL} \).

Step 4: Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature.

Step 5: Substitute the converted values into the ideal gas law equation to solve for \( n \), the number of moles of \( H_2 \) gas evolved. Use \( R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1} \) for the ideal gas constant.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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 hydrogen gas evolved in the reaction, as it allows us to use the measured volume, temperature, and pressure to find the moles of gas produced.

Molar Mass and Stoichiometry

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole. In this problem, determining the molar mass of the unknown metal M and the resulting compound MClx is crucial for calculating the mass of MClx formed after the reaction. Stoichiometry involves using balanced chemical equations to relate the amounts of reactants and products.

Freezing Point Depression

Freezing point depression is a colligative property that describes how the addition of a solute to a solvent lowers the freezing point of the solution. In this question, the change in freezing point of the water after dissolving MClx can be used to determine the molality of the solution, which is necessary for calculating the mass of MClx formed based on the number of moles of solute present.