In the process of electrolysis, electrical power is used to separate water into oxygen and hydrogen molecules via the reaction:
H2O --> H2 + ½O2
This is very much like running a hydrogen fuel cell in reverse. We assume that only the activation potential for the hydrogen reaction is non-negligible. All other potentials are negligible. Hence the relevant parameters are :
PO2 PH2 Temp j0(H2) α(H2)
1 atm 1 atm 350 K 0.10 A/cm2 0.50
What is the minimum voltage needed to drive this reaction at these conditions, in volts?
What is the current density in A/cm2 at a voltage of 1.5 V?
What area of the cell, in cm2, do we need in order to get a rate of H2 production of 1 mol/sec?
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At 300 K we see the electron concentration in the conduction band for pure (undoped) Si is 10^10/cm^3. How many electrons per Si atom is this? You can use scientific notation, as in A.AAeB
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A competing technology uses a photovoltaic cell to charge a battery which can then be used to power a LED light. To compare these technologies, we make some reasonable assumptions. We assume the solar cell is 10 cm on a side, and that it has an efficiency of 15%. We assume the battery is a LaNi5 nickel metal hydride rechargeable battery with a mass of 50 grams, and we assume that the battery has an actual specific charge of 50% of its theoretical specific charge. We also assume that the battery produces an average voltage of 1.1 V.
d. How much power (in watts) will be generated by our solar cell if we place it in 1000 W/m2 direct incident sunlight? A: 1.5
How much energy can the solar cell produce during a day that receives the equivalent light of 4 hours of 1000 W/m2 direct incident sunlight, in kJ? A: 21.6
How much energy can the battery store, in kJ?
ENERGY STORE ANSWER: ??????????
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In the TV show "Breaking Bad" the characters attempt to use HF acid to dissolve guns (among other things). Here we consider instead dissolving guns (which we will assume are pure iron) with sulfuric acid.
Complete the balanced reaction for reacting iron in dilute sulfuric acid to form aqueous FeSO4. Do not worry about formatting subscripts (i.e. O2 to represent diatomic oxygen gas is fine).
Fe + H2SO4 → FeSO4 + __H2(g)___
How many liters of 1 molar sulfuric acid would be required to dissolve 1 kg of iron? Assume the reaction from the previous part goes to completion. The molecular mass of Fe is 55.85 g/mol.
ANSWER: ???????????????????????
It is apparent that they must use an outside source of electrical power to drive the dissolution of the iron. They use a small current so that the dissolution proceeds with the minimum voltage required. Assume standard values for the electrochemical potentials.
How much electrical energy supplied this way is thus required to dissolve an additional 1 kg of iron? Give your answer in kJ.
ANSWER: ????????????????????????????
The characters realize that their hideout has been discovered by the police and they still have a last handgun that weighs 0.25 kg to dissolve. The cops will get there in an hour, so they have to speed up the reaction, by driving it at a higher current. What is the minimum total voltage in volts they'll need to drive the reaction at to get rid of the gun in time? Consider excess potential because of activation losses only and the exchange current I0 to be 1 A for the reaction over the surface of the entire tank (not a current density). α is 0.5 and everything is being done at room temperature. Assume standard electrochemical potentials.
ANSWER: ???????????????????????????
To calculate the minimum voltage needed to drive the electrolysis reaction at the given conditions, we can use the Nernst equation:
E = E° - (RT / nF) ln(Q)
where:
E is the potential difference (voltage),
E° is the standard electrode potential,
R is the gas constant (8.314 J/(mol·K)),
T is the temperature in Kelvin (350 K),
n is the number of electrons transferred in the reaction (in this case, 2),
F is Faraday's constant (96485 C/mol),
and ln(Q) is the natural logarithm of the reaction quotient.
Since the activation potential for the hydrogen reaction is non-negligible and all other potentials are negligible, we can assume the reaction quotient (Q) is equal to 1. Therefore, ln(Q) = 0.
Given:
PO2 = 1 atm
PH2 = 1 atm
Temp = 350 K
j0(H2) = 0.10 A/cm2
α(H2) = 0.50
First, let's calculate the standard electrode potential (E°) for the hydrogen reaction. The standard electrode potential for the hydrogen reaction is 0 V.
Next, let's calculate the minimum voltage needed using the Nernst equation:
E = 0 V - ((8.314 J/(mol·K)) * (350 K) / (2 * 96485 C/mol)) * (0)
E ≈ 0 V
Therefore, the minimum voltage needed to drive the reaction at these conditions is approximately 0 volts.
To calculate the current density (j) at a voltage of 1.5 V, we can rearrange the Nernst equation:
E = E° - (RT / nF) ln(Q) + (RT / nF) ln(j / j0)
Rearranging, we have:
ln(j / j0) = (E - E°) / ((RT / nF))
Using the given values and assuming E° = 0 V:
ln(j / j0) = (1.5 V - 0 V) / ((8.314 J/(mol·K)) * 350 K / (2 * 96485 C/mol))
ln(j / j0) ≈ 0.000032
Taking the exponential of both sides:
j / j0 ≈ e^(0.000032)
j ≈ j0 * e^(0.000032)
j ≈ 0.10 A/cm2 * e^(0.000032)
Therefore, the current density at a voltage of 1.5 V is approximately 0.10 A/cm2 * e^(0.000032) A/cm2.
To calculate the area of the cell (A) needed to get a rate of H2 production of 1 mol/sec, we can use Faraday's law of electrolysis:
n = (I * t) / (F * A)
where:
n is the number of moles of H2 produced (1 mol/sec)
I is the current (in amperes)
t is the time (in seconds)
F is Faraday's constant (96485 C/mol)
A is the area of the cell (in cm2)
Rearranging, we have:
A = (I * t) / (n * F)
Given:
n = 1 mol/sec
I = j = 0.10 A/cm2 * e^(0.000032)
t = 1 sec
A = (0.10 A/cm2 * e^(0.000032) A/cm2 * 1 sec) / (1 mol/sec * 96485 C/mol)
A ≈ 0.10 * e^(0.000032) / 96485 cm^2
Therefore, the area of the cell needed to get a rate of H2 production of 1 mol/sec is approximately 0.10 * e^(0.000032) / 96485 cm^2.
Now let's move on to the next set of questions about solar cells and batteries.
To solve these questions, we need to use relevant equations and values provided.
1. Minimum voltage needed to drive the reaction:
The equation for the minimum voltage needed to drive the reaction is given by:
V = E(H2) - E(O2) + RT/αF * ln(PH2/PO2)
Where:
V = minimum voltage (in volts)
E(H2) = standard electrode potential of hydrogen
E(O2) = standard electrode potential of oxygen
R = gas constant
T = temperature (in Kelvin)
F = Faraday's constant
α = exchange current density ratio (j0(H2)/j0(O2))
PH2 = partial pressure of hydrogen
PO2 = partial pressure of oxygen
Using the given values, we can find the minimum voltage.
2. Current density at a voltage of 1.5 V:
To determine the current density, we can use the equation:
j = j0 * [exp((αFV)/(RT)) - exp(-(1 - α)FV)/(RT)]
Where:
j = current density (in A/cm^2)
j0 = exchange current density (in A/cm^2)
α = exchange current density ratio (j0(H2)/j0(O2))
F = Faraday's constant
V = voltage (in volts)
R = gas constant
T = temperature (in Kelvin)
Substituting the given values, we can find the current density.
3. Area of the cell needed for a rate of H2 production of 1 mol/sec:
The equation to calculate the area of the cell is given by:
A = I / (nFj)
Where:
A = area of the cell (in cm^2)
I = current (in A)
n = number of electrons transferred in the reaction
F = Faraday's constant
j = current density (in A/cm^2)
Given that the rate of H2 production is 1 mol/sec, we can calculate the area.
4. Electron concentration in the conduction band:
The number of electrons in the conduction band can be calculated using the equation:
n = N * exp(-(E-EF) / (kT))
Where:
n = electron concentration (in cm^-3)
N = total number of atoms (per cm^3)
E = energy level of conduction band
EF = Fermi energy level
k = Boltzmann constant
T = temperature (in Kelvin)
Given the values, we can calculate the number of electrons per Si atom.
5. Power generated by the solar cell:
The power generated by the solar cell can be calculated using the equation:
P = A * E * η
Where:
P = power (in watts)
A = area of the solar cell (in m^2)
E = irradiance (in W/m^2)
η = efficiency of the solar cell
Using the given values, we can calculate the power generated.
6. Energy produced by the solar cell during a day:
The energy produced by the solar cell during a day can be calculated by multiplying the power generated by the time (in seconds) equivalent to the given light conditions. Then converting it to kilojoules (kJ).
7. Energy stored by the battery:
The energy stored by the battery can be calculated by multiplying the battery's average voltage by its specific charge and mass, and converting it to kilojoules (kJ).
8. Balanced reaction for iron in dilute sulfuric acid:
The balanced reaction for iron in dilute sulfuric acid to form aqueous FeSO4 is:
Fe + H2SO4 → FeSO4 + H2(g)
9. Liters of 1 molar sulfuric acid to dissolve 1 kg of iron:
To calculate the liters of 1 molar sulfuric acid required to dissolve 1 kg of iron, we need to use stoichiometry and the molar mass of iron.
10. Electrical energy required to dissolve an additional 1 kg of iron:
The electrical energy required to dissolve an additional 1 kg of iron can be calculated using Faraday's law of electrolysis.
11. Minimum total voltage needed to dissolve the gun in time:
To find the minimum total voltage needed to dissolve the gun in time, we can use the equation:
V = E(cell) - E(Iron) - IR
Where:
V = total voltage (in volts)
E(cell) = cell potential
E(Iron) = standard electrode potential of Iron
I = current (in A)
R = resistance
Using the given values, we can calculate the minimum total voltage needed.