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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1. Calculate the de Broglie wavelength in picometers (1 picometer =10^−12 meters) of an electron that has kinetic energy of 10 keV. The mass of an electron is 9.11 x 10^−31 kg
2. Winter is coming, so I want to make a 1500 W heating coil which will plug into a 120 V wall outlet. The coil will have a cross sectional area of 0.01 cm^2 and a length (when fully unwound) of 5 m.
Determine the resistivity of the coil required, in Ωcm:
3. 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: ???????????????????????????
No idea. But i want to know. Does anyone have an idea??
1. To find the minimum voltage needed, we can use the Nernst equation for the hydrogen reaction: E = E0 + (RT/nF) ln(Q), where E0 is the standard potential, R is the gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred, F is Faraday's constant, and Q is the reaction quotient.
First, let's find the standard potential for the hydrogen reaction. Since the other potentials are negligible, we can assume the standard potential for the hydrogen reaction is 0 V.
Next, we can calculate the reaction quotient Q, which is the ratio of the concentrations of products to reactants raised to their stoichiometric coefficients. In this case, Q = (PH2) / (PO2^(1/2)), where PH2 is the partial pressure of H2 and PO2 is the partial pressure of O2.
Given that the pressure of H2 is 1 atm and the pressure of O2 is also 1 atm, we can substitute these values into the equation for Q.
Using the given values:
E = 0 V + (8.314 J/(mol*K) * 350 K) / (2 * 96485 C/mol) * ln(1 / (1^(1/2)))
E = 0 V + (8.314 J/(mol*K) * 350 K) / (2 * 96485 C/mol) * ln(1)
E ≈ 0.141 V
Therefore, the minimum voltage needed to drive the reaction at these conditions is approximately 0.141 volts.
2. To find the current density at a voltage of 1.5 V, we can use the Tafel equation: j = j0 * exp((α * n * F * η) / (RT)), where j0 is the exchange current density, α is the charge transfer coefficient, n is the number of moles of electrons transferred, F is Faraday's constant, R is the gas constant, T is the temperature in Kelvin, and η is the overpotential.
Since the activation potential for the hydrogen reaction is non-negligible, we can assume that the exchange current density is 0.10 A/cm2 and α is 0.50.
Given that the temperature is 350 K and the voltage is 1.5 V, we can substitute these values into the Tafel equation.
Using the given values:
j = 0.10 A/cm2 * exp((0.50 * 2 * 96485 C/mol * (1.5 V - 0.141 V)) / (8.314 J/(mol*K) * 350 K))
j ≈ 4.174 A/cm2
Therefore, the current density at a voltage of 1.5 V is approximately 4.174 A/cm2.
3. To find the area of the cell 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 electrons transferred (which is equal to the rate of H2 production in mol/sec), I is the current in amperes, t is the time in seconds, F is Faraday's constant, and A is the area of the cell.
Given that the rate of H2 production is 1 mol/sec and the current density is 4.174 A/cm2, we can use the equation n = (I * t) / (F * A) to solve for A.
Rearranging the equation, we have A = (I * t) / (F * n).
Since we want to produce 1 mol/sec of H2, we can substitute the given values into the equation.
Using the given values:
A = (4.174 A/cm2 * t) / (96485 C/mol * 1 mol/sec)
A = 4.322 * t cm2
Therefore, the area of the cell needed to get a rate of H2 production of 1 mol/sec is given by 4.322 times the time in seconds in cm2.