A sample of magnesium metal reacts with aqueous HCl to yield H2 gas: Mg1s2 + 2 HCl1aq2¡MgCl21aq2 + H21g2 The gas that forms is found to have a volume of 3.557 L at 25 °C and a pressure of 747 mm Hg. Assuming that the gas is saturated with water vapor at a partial pressure of 23.8 mm Hg, what is the partial pressure in millimeters of mercury of the H2? How many grams of magnesium metal were used in the reaction?

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Calculate the partial pressure of hydrogen gas (H2) by subtracting the partial pressure of water vapor from the total pressure. Use the formula: Partial Pressure of H2 = Total Pressure - Partial Pressure of Water Vapor.

Convert the temperature from Celsius to Kelvin for use in gas law calculations. Use the formula: Temperature in Kelvin = Temperature in Celsius + 273.15.

Apply the Ideal Gas Law to find the moles of hydrogen gas produced. Use the formula: PV = nRT, where P is the partial pressure of hydrogen, V is the volume, n is the number of moles, R is the gas constant (0.0821 L atm K-1 mol-1), and T is the temperature in Kelvin.

Determine the moles of magnesium used in the reaction by using the stoichiometry of the balanced chemical equation. Since 1 mole of Mg produces 1 mole of H2, the moles of Mg used will be equal to the moles of H2 produced.

Calculate the mass of magnesium used in the reaction by multiplying the moles of magnesium by its molar mass (24.305 g/mol). Use the formula: Mass of Mg = Moles of Mg × Molar Mass of Mg.

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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 behavior of gases under various conditions. In this question, it will help determine the number of moles of hydrogen gas produced from the given volume, temperature, and pressure.

Dalton's Law of Partial Pressures

Dalton's Law states that in a mixture of gases, the total pressure is equal to the sum of the partial pressures of each individual gas. In this scenario, it is crucial to calculate the partial pressure of hydrogen gas by subtracting the vapor pressure of water from the total pressure, allowing for accurate determination of the gas's contribution to the overall pressure.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced equations. In this case, it is used to relate the moles of hydrogen gas produced to the moles of magnesium consumed, allowing for the determination of the mass of magnesium that reacted, using its molar mass.

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