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 :1 atm
PH2: 1 atm
Temp: 350K
j0(H2): 0.1A/cm2
α(H2): 0.50
1. What is the current density in A/cm2 at a voltage of 1.5 V?
2. What area of the cell, in cm2, do we need in order to get a rate of H2 production of 1 mol/sec?
To answer these questions, we need to use the Butler-Volmer equation, which relates the current density to the overpotential (difference between the actual cell voltage and the thermodynamic equilibrium voltage). The equation is as follows:
j = j0 * [exp((α * F * η) / (RT)) - exp((- (1 - α) * F * η) / (RT))]
where:
- j is the current density in A/cm2
- j0 is the exchange current density in A/cm2, representing the maximum current density at zero overpotential
- α is the charge transfer coefficient, representing the fraction of charge transferred during the reaction
- F is Faraday's constant (96485 C/mol)
- η is the overpotential in volts
- R is the gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin
Now, let's proceed to solve each question:
1. What is the current density in A/cm2 at a voltage of 1.5 V?
Given:
- Voltage (η) = 1.5 V
- j0 (H2) = 0.1 A/cm2
- α (H2) = 0.50
- R = 8.314 J/(mol·K)
- T = 350 K
We can plug in these values into the Butler-Volmer equation to find the current density (j):
j = 0.1 * [exp((0.5 * 96485 * 1.5) / (8.314 * 350)) - exp((-(1 - 0.5) * 96485 * 1.5) / (8.314 * 350))]
After performing the calculations using a scientific calculator or software, you will find the current density (j) in A/cm2 at a voltage of 1.5 V.
2. What area of the cell, in cm2, do we need in order to get a rate of H2 production of 1 mol/sec?
To find the area of the cell (A), we can rearrange the equation for current density:
j = I / A
where:
- I is the current in amperes
- A is the area in cm2
Given:
- Rate of H2 production (I) = 1 mol/sec
- Current density (j) = Calculated in question 1
We can rearrange the equation to find the area (A):
A = I / j
Substituting the values:
A = 1 / (current density obtained in question 1)
After performing the calculations, you will find the area of the cell (A) in cm2 required to get a rate of H2 production of 1 mol/sec.
Remember, it's crucial to use the correct units and perform the calculations accurately to get accurate results.