how to calculate OCV for 20 % CO2+ 10 % CO + 70% N2 gases mixture at 1000 o C. with 0.1 mpa pressure.

To calculate the open circuit voltage (OCV) for a gas mixture containing 20% CO2, 10% CO, and 70% N2 at 1000 °C and 0.1 MPa, we need to consider the thermodynamic properties of the gases involved, particularly their partial pressures and the Nernst equation. The OCV is often used in electrochemical cells, especially in fuel cells, to determine the voltage produced under specific conditions.

Understanding the Components

In this case, we have three components in our gas mixture:

• CO2 (Carbon Dioxide): 20%
• CO (Carbon Monoxide): 10%
• N2 (Nitrogen): 70%

At 0.1 MPa (which is equivalent to 1 bar), we can calculate the partial pressures of each gas using their respective mole fractions.

Calculating Partial Pressures

The total pressure is 0.1 MPa, so we can find the partial pressures as follows:

• Partial pressure of CO2: \( P_{CO2} = 0.2 \times 0.1 \, \text{MPa} = 0.02 \, \text{MPa} \)
• Partial pressure of CO: \( P_{CO} = 0.1 \times 0.1 \, \text{MPa} = 0.01 \, \text{MPa} \)
• Partial pressure of N2: \( P_{N2} = 0.7 \times 0.1 \, \text{MPa} = 0.07 \, \text{MPa} \)

Using the Nernst Equation

The Nernst equation is crucial for calculating the OCV in electrochemical reactions. It can be expressed as:

E = E° - (RT/nF) * ln(Q)

Where:

• E = cell potential (OCV)
• E° = standard cell potential
• R = universal gas constant (8.314 J/(mol·K))
• T = temperature in Kelvin (1000 °C = 1273 K)
• n = number of moles of electrons transferred in the reaction
• F = Faraday's constant (96485 C/mol)
• Q = reaction quotient

Calculating the Reaction Quotient (Q)

The reaction quotient for the reaction involving CO and CO2 can be represented as:

Q = (P_{CO}) / (P_{CO2})

Substituting the partial pressures we calculated:

Q = (0.01) / (0.02) = 0.5

Plugging Values into the Nernst Equation

Assuming a standard cell potential (E°) for the reaction (for example, let’s say it’s 0.5 V for the CO/CO2 couple), we can now substitute all known values into the Nernst equation:

E = 0.5 V - (8.314 J/(mol·K) * 1273 K / (n * 96485 C/mol)) * ln(0.5)

To proceed, we need to know the value of n, which depends on the specific reaction. For the CO/CO2 reaction, n is typically 2.

Final Calculation

Substituting n = 2 into the equation:

E = 0.5 V - (8.314 * 1273 / (2 * 96485)) * ln(0.5)

Calculating the term:

E = 0.5 V - (0.0511) * (-0.693)

E = 0.5 V + 0.0354 V

E ≈ 0.5354 V

Conclusion

The open circuit voltage (OCV) for the gas mixture of 20% CO2, 10% CO, and 70% N2 at 1000 °C and 0.1 MPa is approximately 0.5354 V. This value can vary based on the specific conditions and the standard potential used, but it gives a good estimate for the OCV under the given parameters.