Suppose a hydrogen-oxygen fuel-cell generator was used to produce electricity for a house. Use the balanced redox reactions and the standard cell potential to predict the volume of hydrogen gas (at STP) required each month to generate the electricity needed for a typical house. Assume the home uses 1200 of electricity per
To determine the volume of hydrogen gas required each month to generate the electricity needed for a typical house, we need to follow a few steps:
1. Determine the balanced redox reaction for the hydrogen-oxygen fuel cell:
In a hydrogen-oxygen fuel cell, the reaction can be represented as follows:
2H₂ (g) + O₂ (g) -> 2H₂O (l)
2. Determine the standard cell potential (E°) for the reaction:
The standard cell potential for the hydrogen-oxygen fuel cell is 1.23 V.
3. Calculate the number of electrons transferred in the reaction:
Since 2 moles of hydrogen gas are required for every mole of oxygen gas, and each mole of H₂ releases 2 electrons, the number of electrons transferred in the reaction is 4.
4. Calculate the charge transferred in the reaction:
The charge transferred in the reaction can be obtained using Faraday's constant (F), which is 96,500 C/mol. Therefore, the charge transferred is 4 * F.
5. Calculate the energy produced from the given amount of electricity:
Given that the house uses 1200 kWh of electricity per month, we convert it to joules using the conversion factor: 1 kWh = 3.6 x 10^6 J. So, the energy produced is 1200 kWh * 3.6 x 10^6 J/kWh.
6. Calculate the moles of electrons required to produce the given amount of energy:
Since 1 mole of electrons carries a charge of F, the number of moles of electrons required can be calculated by dividing the energy produced by the charge transferred (step 4).
7. Calculate the moles of hydrogen gas required:
Since every 2 moles of hydrogen gas release 4 moles of electrons, the number of moles of hydrogen gas required is half the number of moles of electrons required.
8. Calculate the volume of hydrogen gas at STP:
Using the ideal gas law, pV = nRT, where p is the pressure (1 atm), V is the volume, n is the moles, R is the ideal gas constant (0.0821 L·atm·K⁻¹·mol⁻¹), and T is the temperature (273.15 K at STP). Solve the equation for V to find the volume of hydrogen gas in liters.
Follow these steps, substituting the values given in the problem, to find the volume of hydrogen gas required each month to generate the electricity needed for a typical house.