Question 1: Batteries

I want to use a galvanic cell to power a 60-watt light bulb. Complete the following steps to determine how long the galvanic cell will power the light bulb before running out.

a.) The galvanic cell uses the following solutions: 0.81 L 1.5 M Cr₂(SO₄)₃ solution and 1.2 L 0.81 M Au(NO₃)₃ solution. Write down the balanced chemical equations of the dissolution of Cr₂(SO₄)₃ and Au(NO₃)₃ into ions in water:

b.) The galvanic cell includes solid bars of gold (Au) and chromium (Cr). Using your answer in part a and the table of standard reduction potentials (see the last page of this homework), write the following:

Oxidation half-reaction:

Reduction half reaction:

Overall balanced reaction:

Voltage of the galvanic cell:

c.) Recall that at the cathode, positive ions in solution are reduced into the solid form. The galvanic cell will stop working when all of the ions in solution are reduced to the solid form. Identify the ion that is being reduced at the cathode and calculate the total number of moles of the ion in solution at the beginning of the reaction:

d.) Based on the half-reaction in part b, how many total moles of electrons will be transferred when all of the ions at the cathode are reduced? How many coulombs of charge are transferred? Recall that 1 mol of electrons = 96,485 coulombs

e.) Using the equation P=I*V, where P is the power (watts), I is the current (unit of amps) and V is the voltage (volts), calculate the current needed to power a 60-watt light bulb:

f.) Recall that Current (A) = Charge (C)/time (s). Combining your answers in parts d and e, calculate the total amount of time that the 60-watt light bulb can be powered by the galvanic cell:

Question 2: Electrolytic cells

An electrical current can be used to decompose water into oxygen gas and hydrogen gas. In an electrolyzer, the oxidation / reduction processes are described by the following equations:

2 H₂O → 4 H⁺ + 4 e^- + O₂ OXIDATION
2 H⁺ + 2 e^- → H₂ REDUCTION

You've had practice calculating the grams of hydrogen gas, but it is also possible to calculate the amount of oxygen gas produced. What volume of O₂ will be produced if we supply the electrolyzer with a current of 0.201 amps (A) for 1 hour? Give your answer in units of milliliters (mL).

Reference information:

• Current (A) = Charge (C)/time (s)
• 1 mole of electrons has a total charge of 96, 485 C.
• 1 mole of any gas at 1 atmosphere pressure and 25^oC (room temperature) occupies approximately 24.5 liters.
• 1000 milliliters = 1 liter

Question 3: Electricity from solar cells

If solar cells were 100% efficient, every photon that hits the solar cell would produce 1 electron. Commercial polycrystalline silicon solar cells, however, are only 15% efficient; if 100 photons hit the solar cell, only 15 electrons are produced. Complete the following steps to estimate the current output of a 15% efficient solar cell exposed to sunlight.

a.) Recall that sunlight contains many different wavelengths of light. For the purposes of this calculation, we will assume that sunlight only has a single wavelength of 600 nm. Calculate the energy of a photon (in units of joules) with a wavelength of 600 nm.

Useful equation: E = h*c/ λ, where h = 6.6x10^-34 J*s, c= speed of light = 3.0x10⁸ m/s

b.) The average intensity of sunlight is 100 W/m², where 1 watt = 1 Joule/second. Calculate the total number of watts hitting a 1.5 m² solar cell.

c.) Using the energy of a photon you calculated in part a and your answer in part b, calculate the number of photons hitting the solar cell per second.

d.) If 15% of the photons hitting the solar cell produce electrons, calculate the current produced by the 1.5 m² solar cell. Recall that current has units of amps, where Current (A) = Charge (C)/time (s). (1 mole of electrons has a total charge of 96, 485 C. 1mol e- has 6.022 x 10²³ electrons)