Both Jacques Charles and Joseph Louis Guy-Lussac were avid balloonists. In his original flight in 1783, Jacques Charles used a balloon that contained approximately 31,150 L of H2. He generated the H2 using the reaction between iron and hydrochloric acid: Fe1s2 + 2 HCl1aq2 ¡ FeCl21aq2 + H21g2 How many kilograms of iron were needed to produce this volume of H2 if the temperature was 22 °C?

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Identify the balanced chemical equation: \( \text{Fe (s)} + 2 \text{HCl (aq)} \rightarrow \text{FeCl}_2 \text{(aq)} + \text{H}_2 \text{(g)} \).

Use the ideal gas law to find the number of moles of \( \text{H}_2 \): \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is moles, \( R \) is the gas constant, and \( T \) is temperature in Kelvin.

Convert the temperature from Celsius to Kelvin: \( T(K) = 22 + 273.15 \).

Assume standard pressure (1 atm) unless otherwise specified, and use \( R = 0.0821 \text{ L atm mol}^{-1} \text{ K}^{-1} \). Solve for \( n \), the moles of \( \text{H}_2 \).

Use stoichiometry to convert moles of \( \text{H}_2 \) to moles of \( \text{Fe} \) using the balanced equation, then convert moles of \( \text{Fe} \) to mass using the molar mass of iron (55.85 g/mol).

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Key Concepts

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

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It allows us to calculate the amount of substances consumed and produced in a reaction based on balanced chemical equations. In this case, understanding stoichiometry is essential to determine how much iron is needed to produce a specific volume of hydrogen gas.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law is crucial for calculating the volume of hydrogen gas produced at a given temperature and pressure, which is necessary for solving the problem.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is used to convert between the mass of a substance and the number of moles. In this question, knowing the molar mass of iron (approximately 55.85 g/mol) is important for calculating how many kilograms of iron are required to produce the desired volume of hydrogen gas.

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