Equilibrium Partial Pressure Calculator: CO and CO2
This calculator solves the gas-phase equilibrium for the Boudouard reaction with solid carbon present: CO2(g) + C(s) ⇌ 2CO(g). Enter feed composition, temperature, and system pressure to compute equilibrium partial pressures.
How to Calculate the Equilibrium Partial Pressures of CO and CO2
Calculating equilibrium partial pressures of carbon monoxide (CO) and carbon dioxide (CO2) is a core task in combustion engineering, metallurgical processing, gasification, and high-temperature reactor design. The most common equilibrium framework is the Boudouard reaction:
CO2(g) + C(s) ⇌ 2CO(g)
In this equilibrium, solid carbon participates as a pure phase, so its activity is treated as approximately 1. That means it does not explicitly appear in the equilibrium constant expression. The gas-phase equilibrium is then controlled by temperature, total pressure, and initial gas composition. If you can estimate or model the equilibrium constant at temperature, you can solve directly for equilibrium mole fractions and partial pressures.
Why this equilibrium matters in real systems
- Blast furnace and direct-reduction operations rely on CO rich gas chemistry.
- Biomass and coal gasification performance depends on CO and CO2 distribution.
- Heat treatment furnaces use CO and CO2 control to tune carbon potential.
- High temperature catalytic systems can shift selectivity based on CO/CO2 equilibrium.
Core equation used in the calculator
For the reaction CO2 + C ⇌ 2CO, the pressure-based equilibrium constant is:
Kp = (P_CO)^2 / P_CO2
where partial pressures are in atm relative to a 1 atm standard state. The calculator estimates Kp from a thermodynamic approximation:
ΔG°(T) = ΔH° – TΔS°, then Kp = exp(-ΔG° / RT)
using representative reaction values near standard reference conditions: ΔH° ≈ 172.45 kJ/mol and ΔS° ≈ 175.84 J/(mol·K). This is a practical engineering approximation over common industrial temperature windows.
Mass balance and extent of reaction approach
Let initial moles be n_CO2,0 and n_CO,0. If ξ is reaction extent:
- n_CO2 = n_CO2,0 – ξ
- n_CO = n_CO,0 + 2ξ
- n_total = n_CO2 + n_CO + n_inert
Partial pressures follow from mole fractions:
- P_CO2 = (n_CO2 / n_total) P_total
- P_CO = (n_CO / n_total) P_total
The unknown ξ is solved numerically so that the equilibrium function equals zero:
f(ξ) = (P_CO^2 / P_CO2) – Kp(T) = 0
Step by step method for accurate equilibrium partial pressure calculation
- Choose reaction model and verify solid carbon presence in excess.
- Convert temperature to Kelvin and pressure to atm for consistent units.
- Compute Kp(T) from thermodynamic data or trusted tabulated values.
- Write stoichiometric mole balances with reaction extent ξ.
- Express partial pressures in terms of ξ and total moles.
- Solve equilibrium equation numerically (bisection, Newton, or secant).
- Back-calculate P_CO and P_CO2 and report composition with validation checks.
Thermodynamic reference data you should know
The table below shows representative standard values (298 K) used frequently in engineering thermodynamics references. These values support the direction and temperature sensitivity of the Boudouard equilibrium.
| Quantity | Representative Value | Interpretation |
|---|---|---|
| ΔH° for CO2 + C → 2CO | +172.45 kJ/mol | Endothermic reaction, favored by higher temperature. |
| ΔS° for CO2 + C → 2CO | +175.84 J/(mol·K) | Entropy increase due to higher gas moles on product side. |
| ΔG° at 298 K (approx.) | +120 kJ/mol | Not favorable at low temperature under standard conditions. |
Data compiled from standard thermodynamic references and compatible with values reported by NIST chemistry databases.
How temperature changes the CO and CO2 equilibrium split
Temperature is the dominant lever in this reaction. Because the forward direction is endothermic and entropy increasing, rising temperature strongly pushes equilibrium toward CO. The table below provides approximate values at 1 atm total pressure using the simple ΔH° and ΔS° model.
| Temperature (K) | Estimated Kp | Estimated P_CO (atm) at 1 atm total | Estimated P_CO2 (atm) at 1 atm total |
|---|---|---|---|
| 700 | 0.00021 | 0.014 | 0.986 |
| 900 | 0.15 | 0.320 | 0.680 |
| 1000 | 1.50 | 0.686 | 0.314 |
| 1100 | 9.88 | 0.915 | 0.085 |
| 1300 | 179 | 0.995 | 0.005 |
These results explain why high temperature reduction zones generate CO-rich atmospheres. In practical reactors, kinetic limits, mixing, and residence time can delay approach to equilibrium, but the thermodynamic target remains clear.
Pressure effect and Le Chatelier interpretation
The reaction creates more moles of gas on the product side (1 mole CO2 to 2 moles CO). At higher total pressure, the equilibrium shifts toward fewer moles, favoring CO2 relative to CO. At lower pressure, CO becomes even more favored. This pressure effect is weaker than temperature in many designs but is still significant in pressurized gasifiers.
| Total Pressure (atm) | Estimated y_CO at 1100 K (Kp ≈ 9.88) | Estimated y_CO2 at 1100 K |
|---|---|---|
| 0.2 | 0.975 | 0.025 |
| 1.0 | 0.915 | 0.085 |
| 5.0 | 0.730 | 0.270 |
Common mistakes when computing equilibrium partial pressures
- Using Celsius directly in the exponential Kp expression instead of Kelvin.
- Ignoring unit conversion for pressure and mixing atm, bar, and kPa inconsistently.
- Forgetting that pure solid carbon does not appear in Kp expression.
- Assuming mole fractions equal partial pressures without multiplying by total pressure.
- Skipping feasibility limits for reaction extent, causing negative moles numerically.
- Applying low temperature constants to high temperature systems without correction.
Engineering practice tips
- For rigorous design, use temperature-dependent heat capacities and integrate to get ΔG°(T).
- Compare equilibrium prediction against reactor outlet data to identify kinetic constraints.
- If other reactions are active (water-gas shift, methanation), solve full multireaction equilibrium.
- Include inert dilution effects because they change mole fractions and therefore partial pressures.
- Validate against a benchmark software package before final equipment sizing.
Authoritative references for deeper study
- U.S. National Institute of Standards and Technology (NIST): NIST Chemistry WebBook
- U.S. Environmental Protection Agency technical resources: EPA.gov
- MIT OpenCourseWare thermodynamics materials: ocw.mit.edu
Final takeaway
To calculate equilibrium partial pressures of CO and CO2 correctly, combine thermodynamics with stoichiometric mole balances and careful unit handling. In the Boudouard system, higher temperature generally increases CO strongly, while higher pressure tends to suppress it. The calculator above automates these steps and provides both numerical output and visual comparison so you can evaluate how feed and operating conditions affect the equilibrium gas composition.