

Determine the total charge required: Multiply the current (100 A) by the operating time (24 hours) to get the total charge. Total charge = 100 A * 24 hours = 2400 Amperehours (Ah)

Calculate the total moles of electrons: Since 1 Faraday is equivalent to 96,485 coulombs, divide the total charge (in Coulombs) by the Faraday constant to obtain the total moles of electrons. Total moles of electrons = 2400 Ah / (96,485 C/mol) = 0.0249 moles

Determine the stoichiometry of hydrogen consumption: The balanced equation for the electrochemical reaction in a hydrogen fuel cell is typically 2H2 + O2 > 2H2O. This means that for every mole of electrons transferred, 2 moles of hydrogen gas are consumed.

Calculate the moles of hydrogen required: Multiply the total moles of electrons by the stoichiometric ratio of hydrogen. Moles of hydrogen required = 0.0249 moles * 2 = 0.0498 moles

Convert moles of hydrogen to volume: Use the ideal gas law to convert the moles of hydrogen to volume at the given pressure and temperature conditions. The ideal gas law equation is 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.
Given: Pressure (P) = 0.006 to 0.012 bar = 0.0006 to 0.0012 MPa (since 1 bar = 0.1 MPa) Volume (V) = ? Moles of hydrogen (n) = 0.0498 moles Ideal gas constant (R) = 0.0821 LMPa/(molK) (at standard conditions) Temperature (T) = Assumed to be room temperature, around 298 K
Using the ideal gas law, we can solve for the volume: V = (nRT) / P
V_min = (0.0498 mol * 0.0821 LMPa/(molK) * 298 K) / 0.0012 MPa V_max = (0.0498 mol * 0.0821 LMPa/(molK) * 298 K) / 0.0006 MPa
V_min = 11.5327 L V_max = 23.0655 L
Therefore, you would need a minimum of approximately 11.53 liters and a maximum of around 23.07 liters of hydrogen to operate the fuel cell for 24 hours and generate 100 A of current.

Small error :

Total charge = 100 A * 24 hours * 3600 s/hour = 8,640,000 C
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