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: ???????????????????????????
To answer the questions about electrolysis and the dissolution of iron in sulfuric acid, we need to apply some principles from electrochemistry and stoichiometry. Let's break down each question and explain how to arrive at the answers.
1. The minimum voltage needed to drive the electrolysis reaction can be determined using the Nernst equation. However, since the question states that only the activation potential for the hydrogen reaction is non-negligible, we can assume that the activation potential is the relevant parameter. To calculate the minimum voltage in volts, you need to know the activation potential, which is not provided in the question.
2. The current density in A/cm^2 at a voltage of 1.5 V can be calculated using the Tafel equation or Butler-Volmer equation, which relate the current density to the overpotential. However, since the question only provides the exchange current density (j0) and the transfer coefficient (α), we cannot calculate the current density at a specific voltage.
3. To determine the area of the cell required to produce a rate of H2 production of 1 mol/sec, you need to know the exchange current density (j0) and the transfer coefficient (α) of the reaction. The question provides the value of j0(H2) as 0.10 A/cm^2 and α(H2) as 0.50. The area (A) in cm^2 can be calculated using the equation: A = (j0(H2) * 1 mol/sec) / (α(H2) * F), where F is the Faraday constant.
For the second set of questions:
1. The de Broglie wavelength of an electron with a given kinetic energy can be calculated using the equation: λ = h / √(2mE), where h is the Planck's constant (6.626 x 10^(-34) J·s), m is the mass of the electron (9.11 x 10^(-31) kg), and E is the kinetic energy in joules. Once you have the wavelength in meters, you can convert it to picometers (pm) by multiplying by 10^12.
2. To determine the resistivity (ρ) of the coil required, you need to apply Ohm's Law and the equation for resistance. The resistance (R) can be calculated using the equation: R = (ρ * L) / A, where ρ is the resistivity, L is the length of the coil, and A is the cross-sectional area of the coil.
3. To find the number of electrons per Si atom, you need to know the electron concentration in the conduction band and the Avogadro's number (6.022 x 10^23 atoms/mol). The number of electrons per Si atom can be calculated by dividing the electron concentration by the Avogadro's number.
For the last set of questions:
d. The power generated by the solar cell can be calculated using the equation: P = (efficiency * incident sunlight power * cell area). Convert the incident sunlight power from W/m^2 to W by multiplying it by the cell area.
To calculate the energy produced during a day that receives the equivalent light of 4 hours of 1000 W/m^2 direct incident sunlight, multiply the power generated by the solar cell by the time (in hours) that the cell is exposed to the sunlight.
The energy that the battery can store can be calculated using the equation: E = (specific charge * battery voltage * battery mass), where the specific charge is the actual specific charge of the battery.
For the question about dissolving iron in sulfuric acid, the balanced reaction can be completed by adding the appropriate number of H2 molecules on the right side.
To calculate the amount of 1 molar sulfuric acid required to dissolve 1 kg of iron, you need to convert the mass of iron to moles, and then use the stoichiometric coefficients from the balanced reaction to determine the number of moles of sulfuric acid needed.
To calculate the electrical energy required to dissolve an additional 1 kg of iron, you can use Faraday's law of electrolysis, which states that the amount of substance (in moles) that is oxidized or reduced at an electrode is directly proportional to the amount of electrical charge (in coulombs) passed through the electrolyte.
To determine the minimum total voltage needed to drive the reaction at a higher current, you need to consider the excess potential due to activation losses and the exchange current (I0). You also need to know the transfer coefficient (α). However, the values for these parameters are not provided in the question.
Unfortunately, without the specific values and parameters required for the calculations, we cannot provide the answers to the questions.