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?
To determine the minimum voltage needed to drive the electrolysis reaction, we can use the Nernst equation for the hydrogen reaction:
E = E° + (RT/nF) ln(Q)
Where:
E is the cell potential
E° is the standard potential
R is the ideal gas constant (8.314 J/mol·K)
T is the temperature in Kelvin
n is the number of electrons transferred in the reaction
F is Faraday's constant (96,485 C/mol)
Q is the reaction quotient
In this case, n = 2 for the hydrogen reaction and Q = [H2]/[H2O]. Since we assume the only non-negligible potential is for hydrogen, we can assume Q = 1 since the concentration of H2O remains constant.
Rearranging the equation to solve for E:
E = E° + (RT/2F) ln(1)
Since all other potentials are assumed negligible, the standard potential for the hydrogen reaction is the relevant parameter. However, the given data does not include the standard potential for the reaction. Therefore, it is not possible to determine the minimum voltage without knowing the standard potential.
Moving on to the second question, to determine the current density at a given voltage, we can use the Butler-Volmer equation:
j = j0(H2) × exp((α(H2) × F × η) / (RT))
Where:
j is the current density
j0(H2) is the exchange current density for the hydrogen reaction
α(H2) is the transfer coefficient for the hydrogen reaction
η is the overpotential (ΔE), which is the difference between the applied voltage and the minimum voltage required for the reaction to occur.
Since we were not given the exchange current density (j0(H2)), we cannot calculate the current density at a voltage of 1.5 V without this information.
Lastly, to determine the area of the cell required to achieve a hydrogen production rate 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 hydrogen produced
I is the current in amperes
t is the time in seconds
A is the area of the cell in square centimeters
Rearranging the equation to solve for A:
A = (I × t) / (F × n)
Given that the rate of H2 production is 1 mol/sec (n = 1) and assuming a time interval of 1 second, we can substitute the given current density (0.10 A/cm2) into the equation:
A = (0.10 A/cm2 × 1 s) / (96,485 C/mol × 1 mol)
Simplifying the equation, the area required to achieve 1 mol/sec of H2 production is:
A = 0.10 cm2.