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 2.65 x 10^4 mol of electrons at the voltage of a fuel cell.

Question

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 2.65 x 10^4 mol of electrons at the voltage of a fuel cell.

Answer 1

Each mole of H2 provides 2 moles of electrons.

so how many moles of H2?
molesH2=2.65E4molese-/2molese-

molesH2= 1.37E4moles

how many grams of H2 is that? how many kg?

Answer 2

To find out how many kilograms of hydrogen would be required to generate the electricity needed for a typical house using a fuel-cell generator, we can follow these steps:

Step 1: Calculate the total number of electrons required

Given that each H2 molecule produces 2e-, and the home uses approximately 2.65 x 10^4 mol of electrons, we can calculate the total number of electrons needed by multiplying the number of moles by Avogadro's number.

Number of electrons = (2.65 x 10^4 mol) x (6.022 x 10^23 e-/mol)

Step 2: Calculate the total charge in Coulombs

Since each electron carries a charge of 1.602 x 10^-19 Coulombs, we can determine the total charge required by multiplying the number of electrons by the charge of each electron.

Total charge = (Number of electrons) x (1.602 x 10^-19 C/e-)

Step 3: Calculate the total amount of hydrogen in moles

Considering that in a fuel cell, each water molecule (H2O) yields 2 H2 molecules, and each H2 molecule consists of 2 H atoms, we can calculate the number of moles of H2 required by dividing the total number of electrons by 4.

Number of moles of H2 = (Number of electrons) / 4

Step 4: Convert moles of H2 to kilograms

The molar mass of hydrogen (H2) is approximately 2 g/mol. To convert the number of moles to kilograms, we need to multiply the number of moles by the molar mass of hydrogen and divide by 1000 for unit conversion.

Mass of H2 = (Number of moles of H2) x (2 g/mol) / 1000

Now, let's calculate the result:

Number of electrons = (2.65 x 10^4 mol) x (6.022 x 10^23 e-/mol)
Total charge = (Number of electrons) x (1.602 x 10^-19 C/e-)
Number of moles of H2 = (Number of electrons) / 4
Mass of H2 = (Number of moles of H2) x (2 g/mol) / 1000

Plug in the values and calculate the answer.