Question

Hydrogen reacts with oxygen to produce electrical energy in a fuel cell.

2H₂(g) -> 4H⁺ + 4e^-

O₂(g) + 4e^- -> 2O^2-

2H₂(g) + O₂(g) -> 2H₂O(l)    E^o = +1.23 V

Due to losses (typically heat) a fuel cell may actually produce about 1.0 V, but it is still more efficient than an internal combustion engine.

The power in hydrogen can be expressed in units of Watts. The Watt in electricity is defined as the volts times current (amperes)

1 Watt = 1 Volt X 1 Amp

We can calculate the amount of current that a single hydrogen fuel cell needs to produce one Watt of power knowing the voltage produced is 1 volt. It is simply 1 amp.

From our study of electrochemistry, we know the definition of an amp is the amount of charge passed per second.

1 amp = 1 coulomb/sec = 1 Q/sec

Faraday’s law of electrolysis allows us to convert charge into moles of electrons.

Q = n x F

Where Q is the amount of charge, n is the number of moles of electrons and F is Faraday’s constant equal to 94485 coulombs per mole. Using these relationships calculate the number of moles of H₂ needed per Kwh of energy. Be sure to show your calculations and show units.

Initially it asks for actual H₂ cell voltage which I have down as +1.23 V and it also asks current needed to produce 1 watt which from the information provided leads me to believe 1 amp.

How much charge is transferred when one H₂ cell is discharged for one hour at the current calculated to produce 1 Watt? 3600 C is what I arrived at using 1 amp x 3600 seconds = 3600 C

How many holes of electrons and how many moles of H₂ are transferred in one hour?

Answer 1

We know

Q = n * F

Now, Q = 3600 c

F = 94485 c / mole

then, n = 3600/94485 = 0.0381 mol

hence , number of electrons transferred = 0.0381

now,

2 H₂ (g) 4 H⁺ + 4e

or, H₂ (g) 2 H⁺ + 2e

From the given half reaction we can say that, 1 mole H₂  is transferred when 2 moles of electrons are transferred.

Hence, number of H₂ transferred in 1 hour = moles of electrons / 2 = 0.0381 / 2 = 0.019 moles

1 KwH = 1000 watt hour = 3600*1000 = 3600000 c

now , moles of Hydrogen needed to produce 1 KwH of energy = 0.019*1000 = 19 moles