Equilibrium Partial Pressure Calculator for CO2 + H2 ⇌ CO + H2O
Calculate equilibrium partial pressures of CO2, H2, and H2O (plus CO) for the reverse water-gas shift reaction using temperature-derived or manual Kp.
How to Calculate the Equilibrium Partial Pressure of CO2, H2, and H2O
If you are trying to calculate the equilibrium partial pressure of CO2, H2, and H2O, you are almost always dealing with a reaction-network problem in chemical thermodynamics. One of the most important systems is the reverse water-gas shift (RWGS) reaction: CO2 + H2 ⇌ CO + H2O. This equation appears in carbon capture utilization, synthetic fuel production, methanol pathways, and catalytic reactor optimization. The calculator above is built around that equilibrium relationship and can be used as a practical engineering tool for rapid design decisions.
In equilibrium calculations, partial pressure is central because reaction quotients and equilibrium constants are frequently written in pressure terms for gas-phase systems. For the RWGS reaction, the pressure-form equilibrium constant is: Kp = (PCO × PH2O) / (PCO2 × PH2). Solving this equation with mass balances gives you the equilibrium composition. Once you have mole fractions, each partial pressure is simply Pi = yi × Ptotal.
Why this calculation matters in real plants and laboratories
Engineers use equilibrium partial pressure calculations to set feed ratios, temperature windows, and conversion expectations before pilot testing. In many CO2 utilization systems, the equilibrium limit is often as important as catalyst activity. A high-activity catalyst cannot exceed thermodynamic limits. That is why design teams calculate equilibrium first, then evaluate kinetics and transport. In hydrogen-rich systems, the partial pressures of CO2 and H2 directly control how far the reaction can proceed, while generated H2O can suppress conversion if not managed by process design.
- Carbon utilization projects use equilibrium estimates to define realistic conversion ceilings.
- Electrolyzer-integrated e-fuel systems use the model to size hydrogen supply.
- Catalyst screening programs compare measured conversion to equilibrium conversion to identify kinetic bottlenecks.
- Reactor operators use equilibrium predictions to evaluate recycle and staging strategies.
Core equations used in the calculator
Start with initial moles: nCO2,0, nH2,0, nCO,0, nH2O,0. Let reaction extent be ξ. For RWGS:
- nCO2 = nCO2,0 – ξ
- nH2 = nH2,0 – ξ
- nCO = nCO,0 + ξ
- nH2O = nH2O,0 + ξ
Because there are two moles of gas on each side, total moles remain constant for this idealized stoichiometric basis, which simplifies the algebra. Substituting into Kp gives a quadratic expression in ξ. The physically valid root is the one that keeps all species moles non-negative and satisfies the equilibrium expression most closely.
If Kp is not supplied, the calculator estimates it from temperature using a van’t Hoff style approximation: ln(Kp) = -ΔG°/(RT), with ΔG° = ΔH° – TΔS°. This is a useful first-pass engineering estimate, especially for concept screening. For highly accurate work, pull temperature-dependent properties from detailed databases and include non-ideal fugacity corrections at elevated pressures.
Thermodynamic reference data at 298 K
The following values are commonly used as a starting point (compiled from NIST-style standard thermochemistry conventions). They support quick checks for sign and magnitude of ΔH° and ΔS° in RWGS modeling.
| Species | ΔHf° (kJ/mol, 298 K) | S° (J/mol-K, 298 K) |
|---|---|---|
| CO2(g) | -393.5 | 213.7 |
| H2(g) | 0.0 | 130.7 |
| CO(g) | -110.5 | 197.7 |
| H2O(g) | -241.8 | 188.8 |
From these values, RWGS has a positive ΔH° near +41 kJ/mol (endothermic), so increasing temperature generally favors products thermodynamically. That aligns with observed industrial behavior where higher temperatures support higher equilibrium CO formation.
Estimated Kp trend versus temperature for RWGS
The values below illustrate a representative trend from a constant ΔH° and ΔS° approximation. Exact values vary with heat-capacity corrections and chosen data source, but the direction is robust and useful for engineering intuition.
| Temperature (K) | Estimated Kp | Interpretation |
|---|---|---|
| 600 | 0.12 | Reactants favored; limited CO and H2O generation |
| 700 | 0.30 | Conversion improves but still reactant-lean equilibrium |
| 800 | 0.58 | Balanced region; meaningful forward conversion |
| 900 | 0.97 | Near unity; products and reactants similarly weighted |
| 1000 | 1.48 | Products favored; stronger CO and H2O formation |
Step-by-step method to calculate equilibrium partial pressures
- Define the reaction and confirm stoichiometry: CO2 + H2 ⇌ CO + H2O.
- Collect initial amounts or mole fractions for all four species.
- Determine temperature and total pressure.
- Obtain Kp from trusted thermodynamic data or use a validated approximation.
- Write species moles in terms of extent ξ and enforce non-negative constraints.
- Insert expressions into Kp formula to get a polynomial equation in ξ.
- Solve for ξ and select the physically valid root.
- Compute equilibrium mole fractions yi and then partial pressures Pi = yi × Ptotal.
- Validate by re-substituting equilibrium partial pressures into the Kp expression.
Common mistakes and how to avoid them
- Ignoring product inlets: If feed already contains CO or H2O, equilibrium shifts significantly.
- Unit inconsistency: Keep temperature in kelvin and pressure basis consistent with your Kp convention.
- Assuming pressure always changes equilibrium: For RWGS, Δn = 0, so total pressure has limited direct effect on ideal Kp expression.
- Using only kinetics: Fast kinetics cannot surpass equilibrium limits.
- Skipping non-ideality at high pressure: Use fugacity-based methods in rigorous reactor design.
Practical interpretation of results
Suppose you run a hydrogen-rich feed with no initial water. If temperature increases from 700 K to 1000 K, the expected Kp rise indicates stronger forward RWGS tendency, increasing equilibrium PH2O and PCO while reducing PCO2 and PH2. If your plant objective is maximizing CO for downstream Fischer-Tropsch or methanol synthesis pathways, this trend can guide stage temperatures and water management strategy. If your objective is minimizing CO, such as protecting a downstream catalyst from CO poisoning, lower temperatures and alternative process routes become more attractive.
You should also distinguish between equilibrium-limited and kinetics-limited behavior. Many real reactors, especially compact systems and short-contact-time units, may not reach equilibrium. However, equilibrium remains the benchmark ceiling. By plotting measured outlet against equilibrium predictions, you can identify whether catalyst improvement, residence time, or thermal management gives the largest performance gain.
Authoritative sources for deeper validation
For rigorous calculations and report-grade documentation, consult primary data and technical resources:
- NIST Chemistry WebBook (.gov) for thermochemical reference properties and species data.
- NOAA Global Monitoring Laboratory CO2 Trends (.gov) for measured atmospheric CO2 context relevant to carbon conversion systems.
- U.S. Department of Energy Hydrogen Production Resources (.gov) for process and infrastructure context where H2 and CO2 equilibrium chemistry is applied.
Final engineering takeaway
To calculate equilibrium partial pressure of CO2, H2, and H2O reliably, combine stoichiometric balances with a trustworthy equilibrium constant and enforce physical constraints on composition. The calculator on this page implements exactly that workflow for the RWGS system and visualizes how species partial pressures redistribute at equilibrium. Use it for pre-design screening, sensitivity studies, and educational analysis, then move to high-fidelity fugacity and reactor models for final process design.