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Kp & Kc Equilibrium Constant Calculator

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### Chemical Thermodynamics & Gas Equilibrium Metrology Equilibrium constants relate concentrations and partial pressures through the Ideal Gas Law: - **1. Kp to Kc.

Reviewed by Ahmad Faraz · BSCS
Last updated:
Editorial Guidelines

⚙ Input Values

moles
moles
K

📊 Results

Kp (Gas Pressure Equilibrium Constant)
0
atm^Δn
Kc (Molar Concentration Constant)
0.042
M^Δn
Change in Moles of Gas (Δn)
-2
moles
Thermal Gas Factor (R × T)
63.443
L·atm/mol
Standard Gibbs Free Energy (ΔG°)
73.74
kJ/mol
✦ IUPAC Chemical Thermodynamics Diagnostic Summary
IUPAC Chemical Thermodynamics Profile (Haber Ammonia Synthesis (500°C)): Kp = 1.0435e-5 (atm^-2) | Kc = 0.04200 (M^-2). Thermodynamic Metrology: Gas Mole Change Δn = -2 (2 product moles - 4 reactant moles) with RT Factor = 63.443 L·atm/mol at T = 773.1 K (500.0°C). Standard Gibbs Free Energy ΔG° = 73.74 kJ/mol. Le Chatelier Equilibrium Insight: Because Δn < 0 (-2), increasing total system pressure shifts the equilibrium position toward the right (products) to minimize gas volume.
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📐 Formula

If deltaN == 0, Kp = Kc. For deltaG calculation, use Kp (thermodynamic activity standard)

💡 Practical Example

✅

A chemical engineer modeling ammonia production at 500°C (773.15 K) with $K_c = 0.042$ applies $\Delta n = -2$ to find $K_p = 1.044 \times 10^{-5}$, recognizing that high operating pressure is thermodynamically required to drive product yield.

📖 About Kp & Kc Equilibrium Constant Calculator

Chemical Thermodynamics & Gas Equilibrium Metrology

Equilibrium constants relate concentrations and partial pressures through the Ideal Gas Law:

  • **
  • Kp to Kc Fundamental Conversion Formula (IUPAC Standards)**:

K_p = K_c · (R · T)^Δ n_gas

K_c = K_p · (R · T)^-Δ n_gas

Δ n_gas = Σ n_gas, products - Σ n_gas, reactants

and T is absolute temperature in Kelvin).

  • **
  • Thermodynamic Gibbs Free Energy Link**:

Δ G^ = -R_joules · T · K_p )

  • **
  • Standard Chemical Equilibrium Benchmarks**:
  • HI Synthesis: K_p = K_c = 50.000
  • NO₂ Dimerization: K_c = 170.0 K_p = 6.947
  • PCl₅ Decomposition: K_c = 0.0415 K_p = 1.781
  • Haber Ammonia: K_c = 0.0420 K_p = 1.044 × 10^-5

How to Use This Calculator

Enter your Calculation & Conversion Direction — choose from Given Kc (Concentration) → Solve for Kp (Pressure), Given Kp (Pressure) → Solve for Kc (Concentration), Known Equilibrium Constant Value (Kc or Kp) (e.g. 0.042), Total Stoichiometric Moles of Gas Products (Σ n_prod) (e.g. 2 in moles), Total Stoichiometric Moles of Gas Reactants (Σ n_react) (e.g. 4 in moles), Reaction Temperature (Kelvin - K) (e.g. 773.15 in K), and Chemical Equilibrium Benchmark — choose from Custom Reaction System, Haber Ammonia (N₂ + 3H₂ ⇌ 2NH₃ at 500°C / 773K, Kc=0.042) → Δn = -2 | Kp = 1.045 × 10⁻⁵, NO₂ Dimerization (2NO₂ ⇌ N₂O₄ at 25°C / 298.15K, Kc=170) → Δn = -1 | Kp = 6.

  • Verify your units match the formula standard (SI vs imperial) before entering values.

The Formula

If deltaN == 0, Kp = Kc. For deltaG calculation, use Kp (thermodynamic activity standard)

Worked Example

A chemical engineer modeling ammonia production at 500°C (773.15 K) with K_c = 0.042 applies Δ n = -2 to find K_p = 1.044 × 10^-5, recognizing that high operating pressure is thermodynamically required to drive product yield.

Understanding Your Result

Scientific calculations require careful attention to significant figures and units. Your result is only as precise as your least precise input — expressing the result with more significant figures than the inputs implies false precision. For laboratory or regulatory work, verify which measurement standard applies (SI, ASTM, ISO) and whether temperature, pressure, or concentration conditions affect the formula. Cross-reference results against published reference values for your specific material or compound.

💡 Methodological Standards & Calculation Accuracy

  • All calculations are performed client-side in your browser using verified, standards-compliant mathematical algorithms.
  • Results are provided for educational and informational analysis; verify critical applications with certified domain specialists.
  • Ensure input values are entered in consistent units matching the selector options to guarantee accurate outputs.
  • Periodic recalibration is recommended whenever baseline assumptions, operating parameters, or external conditions change.
Sources: NIST Standards · ISO International Standards

Results are for informational and educational purposes only. Always verify critical decisions with a qualified professional.

❓ Frequently Asked Questions

When does Kp equal Kc?
Kp is identically equal to Kc whenever the change in moles of gas is zero, because (RT)^0 = 1. An example is H2(g) + I2(g) ⇌ 2HI(g), where 2 reactant gas moles equal 2 product gas moles.

Which value of the gas constant R should be used for Kp = Kc(RT)^Δn?
Use R = 0.0820574 L·atm/(mol·K) when partial pressures are expressed in standard atmospheres (atm). Use R = 0.0831446 L·bar/(mol·K) when pressures are in bars.

Do pure solids and pure liquids count in Δn?
No. Pure solids (s) and pure liquids (l) have constant thermodynamic activities equal to 1 and do not appear in Kp or Kc expressions. Only gaseous species (g) are included in the Δn calculation.

How does temperature affect Kp?
According to the Van 't Hoff equation, for endothermic reactions, increasing temperature increases Kp. For exothermic reactions, increasing temperature decreases Kp.

What is the physical meaning of ΔG° = -RT ln(Kp)?
A large Kp (Kp >> 1) produces a negative ΔG°, indicating that formation of products is thermodynamically favored at standard state conditions. A small Kp (Kp << 1) produces a positive ΔG°, meaning reactants predominate at equilibrium.

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