The total volume of hydrogen gas needed to fill the Hidenbrug was 2.0e8 L at 1.0 atm and 25 degrees Celsius. How much heat was evolved when the Hidenburg exploded, assuming all the hydrogen reacted?
To calculate the amount of heat evolved when the Hidenburg exploded, we need to know the enthalpy change per mole of hydrogen gas. However, this information is not provided in the question. Without that information, it is not possible to accurately determine the heat evolved.
However, if we assume that the reaction involved is the combustion of hydrogen gas (2H2 + O2 -> 2H2O), we can estimate the heat evolved using the standard enthalpy of formation values for the reactants and products involved.
The standard enthalpy of formation (∆H˚f) for H2O(g) is -241.8 kJ/mol. Since 2 moles of H2O are formed for every 2 moles of hydrogen gas, the heat evolved (∆H˚) can be calculated using the following formula:
∆H˚ = (∆Hf˚(H2O) × 2 moles) / (2 moles)
Now, let's estimate the moles of hydrogen gas present in the Hidenburg.
Given:
Volume of hydrogen gas = 2.0e8 L
Pressure = 1.0 atm
Temperature = 25 degrees Celsius = 298 K
To convert the volume of hydrogen gas to moles, we need to use the ideal gas law equation:
PV = nRT
Rearranging the equation:
n = PV / RT
n = (1.0 atm) × (2.0e8 L) / [(0.0821 L·atm/mol·K) × (298 K)]
n ≈ 8248 moles
Now, we can use this value of moles to calculate the heat evolved (∆H˚):
∆H˚ = (∆Hf˚(H2O) × 8248 moles) / (2 moles)
Calculating the approximate value:
∆H˚ ≈ (-241.8 kJ/mol × 8248 moles) / (2 moles)
∆H˚ ≈ -998081.6 kJ
Therefore, approximately 998,082 kJ of heat was evolved when the Hidenburg exploded, assuming all the hydrogen reacted.