The hydrogen-filled dirigible Hindenburg had a volume of 1.99 * 108 L. If the hydrogen used was produced by the reaction of carbon with steam, how many kilograms of carbon would have been needed to produce enough hydrogen to fill the dirigible at 20 °C and 740 mm pressure?

Verified step by step guidance

1. Step 1: Write the balanced chemical equation for the reaction of carbon with steam to produce hydrogen gas. The reaction is typically represented as: \[ \text{C(s)} + \text{H}_2\text{O(g)} \rightarrow \text{CO(g)} + \text{H}_2(g) \].
2. Step 2: Use the ideal gas law to calculate the number of moles of hydrogen gas needed to fill the dirigible. The ideal gas law is given by \( PV = nRT \), 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.
3. Step 3: Convert the given temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. Thus, \( T = 20 + 273.15 \).
4. Step 4: Convert the pressure from mmHg to atm, since the ideal gas constant \( R \) is typically given in terms of atm. Use the conversion factor: \( 1 \text{ atm} = 760 \text{ mmHg} \).
5. Step 5: Solve the ideal gas law equation for \( n \), the number of moles of hydrogen gas. Then, use stoichiometry from the balanced equation to determine the moles of carbon needed, and convert this to kilograms using the molar mass of carbon (12.01 g/mol).

Key Concepts

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 amount of gas produced or required under specific conditions, such as the volume of hydrogen needed to fill the dirigible at given temperature and pressure.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced equations. Understanding stoichiometry is crucial for determining how much carbon is needed to produce the required amount of hydrogen from the reaction of carbon with steam.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole. It is important for converting between moles of a substance and its mass, allowing for the calculation of how many kilograms of carbon are necessary to produce the hydrogen needed for the dirigible.