Calculate the concentration polarization for the electrolysis of 0.9 M AgNO3 with silver electrode at 18 °C and ia = ia = 0.1 mA/cm². The activity coefficient of Agt is 0.731, diffusion coefficient of Agt is 5*10-6 m/sec and an effective thickness of diffuse layer is 0.0176 cm.
angelZ8469
To calculate the concentration polarization for the electrolysis of AgNO3, we can use the Butler-Volmer equation:
i = i0 * (exp((α * F * η) / (RT)) - exp((-α * F * η) / (RT)))
Where:
i = Current density (mA/cm²)
i0 = Exchange current density (mA/cm²)
α = Transfer coefficient (assumed to be 0.5 for this calculation)
F = Faraday constant (96485 C/mol)
η = Overpotential (V)
R = Gas constant (8.314 J/(mol*K))
T = Temperature (K)
First, we need to calculate the exchange current density (i0) using the formula:
i0 = 0.1 * (1 - exp((-α * F * η0) / (RT))) = 0.1 * (1 - exp((-0.5 * 96485 * 0.0) / (8.314 * 291)))
Since the overpotential (η0) is 0 for this calculation (no polarization), the exchange current density (i0) is simply equal to 0.1 mA/cm².
Next, we can calculate the polarization current density (ip) using the formula:
ip = i0 * (exp((α * F * η) / (RT)) - 1)
To calculate the overpotential (η), we need to use the Nernst equation:
η = (RT / (α * F)) * ln((Ct0 / Ct) * (γt / γt0))
Where:
Ct0 = Initial concentration of Agt (0.9 M)
Ct = Concentration of Agt at the electrode surface (assumed to be 0 M due to depletion)
γt0 = Activity coefficient of Agt in the bulk solution (0.731)
γt = Activity coefficient of Agt at the electrode surface (assumed to be the same as γt0 due to depletion)
First, we calculate the value inside the natural logarithm:
((Ct0 / Ct) * (γt / γt0)) = (0.9 / 0) * (0.731 / 0.731) = undefined (since Ct is 0)
Since Ct is 0 due to depletion, the value inside the logarithm is undefined. This means that the overpotential (η) is also undefined for this calculation.
Therefore, we cannot calculate the concentration polarization for this specific scenario.
To calculate the concentration polarization for the electrolysis of AgNO3, we can use the Butler-Volmer equation:
i = i0 * (exp((α * F * η) / (RT)) - exp((-α * F * η) / (RT)))
Where:
- i is the total current density (mA/cm²)
- i0 is the exchange current density (mA/cm²)
- α is the transfer coefficient (dimensionless)
- F is Faraday's constant (C/mol)
- η is the overpotential (V)
- R is the gas constant (8.314 J/(mol·K))
- T is the temperature (K)
The exchange current density (i0) can be calculated using the Tafel equation:
i0 = ia / (exp((β * F * η) / (RT)))
Where:
- ia is the anodic current density (mA/cm²)
- β is the symmetry factor (dimensionless)
First, let's calculate the exchange current density (i0):
ia = 0.1 mA/cm²
β = 0.5 (assuming a symmetrical system)
i0 = ia / (exp((β * F * η) / (RT)))
= 0.1 / (exp((0.5 * 96500 * η) / (8.314 * 293)))
Next, let's calculate the overpotential (η). The overpotential is related to the concentration polarization (ε) by the following equation:
ε = (η - ηeq) / ηeq
Where:
- ηeq is the equilibrium overpotential (V)
The equilibrium overpotential (ηeq) can be calculated using the Nernst equation:
ηeq = (RT / (α * F)) * ln(aA / aA0)
Where:
- aA is the activity of Ag+ at the electrode surface
- aA0 is the standard activity of Ag+ (assumed to be 1)
To calculate aA, we need to consider the activity coefficient (γ) and the concentration of Ag+ (CAg+).
γ = 0.731 (given)
CAg+ = 0.9 M (given)
aA = γ * CAg+
= 0.731 * 0.9
Now, let's calculate ηeq:
ηeq = (RT / (α * F)) * ln(aA / aA0)
= (8.314 * 293 / (1 * 96500)) * ln((0.731 * 0.9) / 1)
Now, we can calculate the overpotential (η) using the concentration polarization (ε) equation:
η = ε * ηeq + ηeq
To calculate ε, we need to know the effective thickness of the diffuse layer (L) and the diffusion coefficient of Agt (D).
L = 0.0176 cm (given)
D = 5 * 10^(-6) m/sec (given)
ε = (2 * L * i) / (F * D * ηeq)
Finally, we can substitute the calculated values into the Butler-Volmer equation to get the concentration polarization (i):
i = i0 * (exp((α * F * η) / (RT)) - exp((-α * F * η) / (RT)))