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?

Verified step by step guidance

1. Identify the balanced chemical equation: \( \text{Fe (s)} + 2 \text{HCl (aq)} \rightarrow \text{FeCl}_2 \text{(aq)} + \text{H}_2 \text{(g)} \).
2. 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.
3. Convert the temperature from Celsius to Kelvin: \( T(K) = 22 + 273.15 \).
4. 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 \( \text{H}_2 \).
5. 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).

Key Concepts

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.