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Kp Equilibrium Constant Calculator

Calculate the equilibrium constant (Kp) for gas-phase reactions based on partial pressures. This tool helps chemists and students determine reaction spontaneity and predict product formation at equilibrium.

Temperature at which the reaction occurs (in Kelvin)
Standard Gibbs free energy change (in kJ/mol)
Change in moles of gas (products - reactants)

How to Use This Calculator

  1. Enter the temperature of the reaction in Kelvin
  2. Input the standard Gibbs free energy change (ΔG°) in kJ/mol
  3. Enter the change in moles of gas (products minus reactants)
  4. Select whether you want to calculate Kp from ΔG° or convert from Kc
  5. If converting from Kc, enter the Kc value
  6. Click Calculate to see the Kp value and reaction equilibrium information

Formula Used

Kp = e^(-ΔG°/(RT))

Where:

  • Kp = Equilibrium constant based on partial pressures
  • ΔG° = Standard Gibbs free energy change (J/mol)
  • R = Gas constant (8.314 J/(mol·K))
  • T = Temperature (K)
Kp = Kc(RT)^Δn

Where:

  • Kc = Equilibrium constant based on concentrations
  • Δn = Change in moles of gas (products - reactants)

Example Calculation

Real-World Scenario:

For the synthesis of ammonia (NH₃) from nitrogen (N₂) and hydrogen (H₂) at 700K, with a standard Gibbs free energy change of -33.3 kJ/mol and a change in moles of gas of -2, we can calculate the equilibrium constant Kp.

Given:

  • Temperature (T) = 700 K
  • ΔG° = -33.3 kJ/mol = -33,300 J/mol
  • Δn = -2 (2 moles of reactants to 1 mole of product)

Calculation:

Kp = e^(-ΔG°/(RT))

Kp = e^(-(-33,300 J/mol)/(8.314 J/(mol·K) × 700 K))

Kp = e^(33,300/(5,819.8))

Kp = e^(5.72)

Kp = 3.05 × 10²

Result: The equilibrium constant Kp is 3.05 × 10², indicating that at equilibrium, the reaction favors the formation of ammonia at this temperature.

Why This Calculation Matters

Practical Applications

  • Predicting the direction of chemical reactions at equilibrium
  • Optimizing industrial chemical processes for maximum yield
  • Determining the feasibility of new synthetic routes
  • Designing catalytic systems for chemical manufacturing

Key Benefits

  • Helps determine optimal reaction conditions
  • Enables prediction of product yields at equilibrium
  • Guides the selection of temperature and pressure for industrial processes
  • Assists in understanding reaction thermodynamics

Common Mistakes & Tips

Always use Kelvin for temperature calculations. If your temperature is in Celsius, add 273.15 to convert to Kelvin. Using the wrong temperature unit will lead to incorrect Kp values.

Pay close attention to the signs of ΔG° and Δn. A negative ΔG° indicates a spontaneous reaction, while a positive value indicates a non-spontaneous reaction. For Δn, calculate it as (moles of gaseous products) - (moles of gaseous reactants), which can be positive, negative, or zero.

Ensure consistent units when using the formula. If your ΔG° is in kJ/mol, convert it to J/mol by multiplying by 1000. The gas constant R is 8.314 J/(mol·K), so using J/mol for ΔG° ensures unit consistency.

Frequently Asked Questions

Kp is the equilibrium constant based on partial pressures of gases, while Kc is based on concentrations. They are related by the equation Kp = Kc(RT)^Δn, where Δn is the change in moles of gas. For reactions where Δn = 0, Kp = Kc.

Temperature has a significant effect on Kp. For exothermic reactions (negative ΔH°), increasing temperature decreases Kp, shifting the equilibrium toward reactants. For endothermic reactions (positive ΔH°), increasing temperature increases Kp, shifting the equilibrium toward products. This relationship is described by the van't Hoff equation.

A large Kp value (>> 1) indicates that at equilibrium, the reaction favors the formation of products. A small Kp value (<< 1) indicates that at equilibrium, the reaction favors the reactants. When Kp = 1, the concentrations of reactants and products are approximately equal at equilibrium.

Kp is specifically for gas-phase reactions and only includes the partial pressures of gaseous species. Pure solids and liquids are not included in the equilibrium expression because their concentrations are essentially constant. For reactions involving both gases and condensed phases, only the gaseous components are included in the Kp expression.

References & Disclaimer

Chemistry Disclaimer

This calculator provides theoretical values based on ideal gas behavior and standard conditions. Real-world chemical systems may deviate from these idealizations due to factors such as non-ideal gas behavior, activity coefficients, and side reactions. For critical applications, consult with a qualified chemist and consider experimental data.

References

Accuracy Notice

This calculator assumes ideal gas behavior and standard conditions. Results may not be accurate for reactions at extreme pressures, temperatures, or for systems with significant non-ideal behavior. For precise calculations, consider using activity coefficients and consult specialized thermodynamic software or databases.

About the Author

Kumaravel Madhavan

Web developer and data researcher creating accurate, easy-to-use calculators across health, finance, education, and construction and more. Works with subject-matter experts to ensure formulas meet trusted standards like WHO, NIH, and ISO.

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science chemistry equilibrium constant formula