Thermodynamics Solutions: #16

16.* (1995 F 13) The ocean is littered with sunken treasure ships. The "Float-By-Night Treasure Salvage Company" has approached you with the proposal to raise sunken ships by placing pontoons within the ship by means of a surface-controlled robotic submarine. According to their scheme, the pontoons would then be filled by H2 gas formed by the electrolysis of seawater. It is estimated that 1.0 x 108 moles of H2 are required to provide enough buoyancy to raise a treasure ship (filled presumably with silver and gold, etc.) You are being asked to consider an investment in this company.

The following information will prove useful to you:

Half-reaction

E0 (volts)

H+ + e = 1/2 H2 (g, 1 atm)

0.00 (by definition)

O2 + 4H+ + 4e- = 2H2O (l)

1.23

1 mol electrons = 96,500 Coulombs

1 amp = 1 coulomb/sec

One watt = 1 Joule/second = 1 amp x 1 volt

A. How many coulombs of electrical charge would be required to generate 1 x 108 moles of H2?

B. What is the minimum voltage required at sea level (1 atm pressure) to generate H2 and O2 from the electrolysis of water?

E°=-1.23 V

E°=0.00V

E°=-1.23 V

C. Actually, the sunken treasure that Float-By-Night Treasure Salvage Co. proposes to recover is located at the bottom of the ocean at a depth of 2 miles! Given that 1 atm pressure is equivalent to the pressure of about 30 feet of water, calculate the pressure at the bottom of the ocean where the sunken treasure lies. There are 5280 feet in a mile.

D. What is the minimum voltage required to generate H2 and O2 from the electrolysis of water at this depth?

For the reaction

,

Therefore,

 

E. What is the minimum electrical energy required to raise the treasure ship by electrolytic reflotation? What is the minimum cost if the rate is 25 cents per kilowatt hour?

F. Make a rough estimate of the weight (in tons) of a ship at a depth of 2 miles in the ocean that can be refloated using 1.0 x 108 moles of H2 to displace water. Some useful conversion information is 1 mL of water weighs 1 g, 454g = 1lb, 2000lbs = 1 ton, and Archimedes principle states that "when a body is immersed in a fluid it experiences an upward thrust equal to the weight of the volume of fluid displaced." Take the temperature of the water at the bottom of the ocean as the same as on the surface of the ocean.