Suppose a fuel-cell generator was used to produce electricity for a house. If each H2 molecule produces 2e- , how many kilograms of hydrogen would be required to generate the electricity needed for a typical house? Assume the home uses about 850 kWh of electricity per month, which corresponds to approximately of 2.65 x 10^4 mol of electrons at the voltage of a fuel cell.
To find out how many kilograms of hydrogen would be required to generate the electricity needed for a typical house, we can follow these steps:
Step 1: Calculate the number of electrons produced.
To calculate the number of electrons produced, we use the given information: each H2 molecule produces 2e-. The number of moles of electrons is given as 2.65 x 10^4 mol. To find the total number of electrons, we can multiply this by Avogadro's number (6.022 x 10^23 electrons per mole).
Number of electrons = (2.65 x 10^4 mol) x (6.022 x 10^23 electrons/mol)
Step 2: Convert electrons to kilograms of hydrogen.
From the given information, we know that each H2 molecule produces 2 electrons. Therefore, to convert the number of electrons to kilograms of hydrogen, we divide the number of electrons by 2.
Number of hydrogen molecules = Number of electrons / 2
To convert the number of hydrogen molecules to kilograms, we can use the molar mass of hydrogen (2.02 g/mol) and Avogadro's number.
Mass of hydrogen (kg) = (Number of hydrogen molecules) x (2.02 g/mol) / (6.022 x 10^23 molecules/mol) / (1000 g/kg)
Now, we can plug in the values and calculate the result:
Number of electrons = (2.65 x 10^4 mol) x (6.022 x 10^23 electrons/mol)
Number of hydrogen molecules = Number of electrons / 2
Mass of hydrogen (kg) = (Number of hydrogen molecules) x (2.02 g/mol) / (6.022 x 10^23 molecules/mol) / (1000 g/kg)
Solving these equations will give you the final result of how many kilograms of hydrogen would be required to generate the electricity needed for a typical house.