Calculate gas-phase equilibrium constants (Kp), convert between concentration Kc and Kp via Kp = Kc(RT)^Δn, evaluate Dalton's law partial pressures, and solve standard Gibbs free energy (ΔG°) with our free Kp Calculator.
Scientific: 2.370 × 10^0 • Products Favored (Kp > 1)
Spontaneous
[M] units
Δng = 2 - 4
25.0 °C
L·atm/mol
Kp > 1
The Gas-Phase Equilibrium Constant (\(K_p\)) is the thermodynamic mass action ratio expressed in terms of partial pressures of reacting gases at dynamic chemical equilibrium:
By Dalton's law of partial pressures (\(P_i = \chi_i P_{\text{total}}\)), each constituent gas in a closed vessel contributes a partial pressure directly proportional to its molar fraction. While \(K_c\) tracks molar concentrations (\(\text{mol/L}\)), \(K_p\) governs gas-phase industrial reactors, jet combustion, and atmospheric chemistry where pressure and temperature fluctuations drive reaction yields.
Eliminates exponent inversion errors when calculating \(\Delta n_g = \sum \nu_{\text{products}} - \sum \nu_{\text{reactants}}\) during \(K_c \leftrightarrow K_p\) conversions.
Applies \(R = 0.082057\text{ L}\cdot\text{atm/(mol}\cdot\text{K)}\) for gas volumes and \(R = 8.314\text{ J/(mol}\cdot\text{K)}\) for thermodynamic Gibbs free energy without unit conflicts.
Automatically excludes condensed solid catalysts and pure liquids whose thermodynamic activities equal \(1.0\) from partial pressure quotients.
Compute \(K_p\) directly from equilibrium partial pressures (\(\text{atm/bar}\)) or interconvert from concentration equilibrium constants (\(K_c\)) via \(K_p = K_c(RT)^{\Delta n_g}\).
Calculates standard Gibbs free energy changes (\(\Delta G^\circ = -RT \ln K_p\)) in \(\text{kJ/mol}\), determining thermodynamic spontaneity at any specified temperature.
Handles ultra-high (e.g. \(10^{15}\)) and ultra-low (e.g. \(10^{-12}\)) equilibrium constants with automatic scientific notation formatting.
Displays complete mathematical derivations including partial pressure ratios, temperature substitutions, and logarithmic Gibbs energy derivations in real time.
| Pressure Unit | Gas Constant Value (\(R\)) | Standard State (\(P^\circ\)) | Primary Field of Use |
|---|---|---|---|
| Atmospheres (\(\text{atm}\)) | \(0.082057\text{ L}\cdot\text{atm/(mol}\cdot\text{K)}\) | \(1.000\text{ atm}\) | General Chemistry & Classical Thermodynamics |
| Bar (\(\text{bar}\)) | \(0.083145\text{ L}\cdot\text{bar/(mol}\cdot\text{K)}\) | \(1.000\text{ bar} = 100\text{ kPa}\) | IUPAC Standard State & Petrochemical Refining |
| Joules (\(\text{J}\)) / Gibbs Energy | \(8.31446\text{ J/(mol}\cdot\text{K)}\) | \(\Delta G^\circ = -RT \ln K\) | Free Energy & Chemical Enthalpy Calculations |
Choose Partial Pressures for experimental gas data or Convert from \(K_c\) for thermodynamic interconversion.
Enter individual gas partial pressures in atmospheres/bars or specify \(K_c\), temperature (Kelvin or Celsius), and \(\Delta n_g\).
Click "Compute Equilibrium Constant" to evaluate \(K_p\), scientific notation, and full mathematical KaTeX derivations.
Inspect standard Gibbs free energy \(\Delta G^\circ\) in \(\text{kJ/mol}\) to confirm product favorability, and copy results with one click.
Problem: In the industrial contact process for sulfuric acid manufacturing, sulfur dioxide and oxygen reach equilibrium at \(700\text{ K}\): \(2\text{SO}_2(g) + \text{O}_2(g) \rightleftharpoons 2\text{SO}_3(g)\). Equilibrium partial pressures are \(P_{\text{SO}_2} = 0.30\text{ atm}\), \(P_{\text{O}_2} = 0.20\text{ atm}\), and \(P_{\text{SO}_3} = 1.20\text{ atm}\). Calculate \(K_p\), equivalent \(K_c\), and standard Gibbs energy \(\Delta G^\circ\).
1. Calculate \(K_p\):
2. Interconvert to \(K_c\) (\(\Delta n_g = 2 - 3 = -1\)):
3. Standard Gibbs Free Energy \(\Delta G^\circ\):
Problem: At \(298.15\text{ K}\), colorless \(\text{N}_2\text{O}_4\) dissociates into brown \(\text{NO}_2\) gas with \(\Delta n_g = 2 - 1 = +1\). If \(P_{\text{N}_2\text{O}_4} = 0.80\text{ atm}\) and \(P_{\text{NO}_2} = 0.40\text{ atm}\):
1. Equilibrium Constant: \(K_p = \frac{(P_{\text{NO}_2})^2}{P_{\text{N}_2\text{O}_4}} = \frac{0.16}{0.80} = 0.2000\)
2. Standard Gibbs Energy:
Always evaluate \(\Delta n_g = \text{Moles of Gaseous Products} - \text{Moles of Gaseous Reactants}\). Forgetting the negative sign in reactions like \(\text{N}_2 + 3\text{H}_2 \to 2\text{NH}_3\) (\(\Delta n_g = -2\)) inverts \(K_p\) by orders of magnitude.
Use \(R = 0.082057\text{ L}\cdot\text{atm/(mol}\cdot\text{K)}\) when interconverting \(K_c\) and \(K_p\), and switch to \(R = 8.31446\text{ J/(mol}\cdot\text{K)}\) when computing thermodynamic \(\Delta G^\circ\).
Gas laws require absolute temperature in Kelvin (\(T = \text{}^\circ\text{C} + 273.15\)). Substituting Celsius directly will produce entirely false thermodynamic outputs.
Heterogeneous solid reactants (such as \(\text{C}(s)\) or \(\text{CaCO}_3(s)\)) possess constant chemical activities of \(1.0\) and must be omitted from partial pressure products.
Because \(\Delta n_g = -2\) for \(\text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g)\), chemical plants operate reactors at elevated pressures (\(150\text{--}250\text{ bar}\)) to exploit Le Chatelier's principle, forcing higher equilibrium conversions toward ammonia.
Hydrogen production facilities react natural gas with steam: \(\text{CH}_4(g) + \text{H}_2\text{O}(g) \rightleftharpoons \text{CO}(g) + 3\text{H}_2(g)\) (\(\Delta n_g = +2\)). High operating temperatures (\(800\text{--}900\text{ }^\circ\text{C}\)) drive \(K_p\) higher to maximize hydrogen output.
Authoritative answers to common questions regarding gas-phase equilibrium constants and thermodynamics.
