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Understanding Equilibrium Constants: Kp and Kc

In reversible chemical reactions, the equilibrium state can be described by an equilibrium constant, which can be expressed either in terms of molar concentration (Kc) or in terms of partial pressure (Kp). The Equilibrium Constant Calculator and Kp to Kc Converter tool simplifies the conversion between these two forms, allowing you to quickly obtain the correct value for your reaction.

The Concentration-Based Constant Kc

For a general reaction:

the equilibrium constant in terms of concentration is:

where $[A]$ and $[B]$ are the molar concentrations of the reactants, and $[C]$ and $[D]$ are the molar concentrations of the products. The Chemical Equilibrium Calculator on this page automatically handles these expressions.

The Partial-Pressure Constant Kp

When dealing with gases, it is often more convenient to measure partial pressures. The equilibrium constant in terms of partial pressure follows an analogous form:

where $P_A$ and $P_B$ are the partial pressures of the gaseous reactants, and $P_C$ and $P_D$ are those of the gaseous products.

The Relationship Between Kp and Kc

The conversion between Kp and Kc uses the equation:

where:

• $R$ is the universal gas constant,
• $T$ is the absolute temperature (in Kelvin),
• $\Delta n$ is the change in the number of moles of gas, defined as:

If $\Delta n = 0$, then Kp equals Kc directly. For any other value, you can rely on the Kp Calculator to compute the conversion quickly and accurately.

Step-by-Step Conversion Example (Haber Process)

Consider the synthesis of ammonia:

At 298 K, the equilibrium constant Kc is $2.27 \times 10^{-2}$. To find Kp:

1. Choose the correct gas constant according to the pressure unit you intend to use. For atmospheres, $R = 0.082057 \ \text{L·atm·K}^{-1}\text{·mol}^{-1}$.
2. Calculate $\Delta n$:
   $\Delta n = 2 - (3 + 1) = -2$.
3. Apply the formula: $$K_p = 2.27 \times 10^{-2} \times (0.082057 \times 298)^{-2}$$ This yields $K_p \approx 3.796 \times 10^{-5}$.

The same procedure works for any gaseous reaction; just ensure you only include species in the gas phase.

Important Considerations

• Only gases matter: In heterogeneous reactions, solids and liquids do not appear in the Kp expression. For example, in the reaction $2H_2(g) + O_2(g) \rightleftharpoons 2H_2O(s)$, the Kp expression is simply: $$K_p = \frac{1}{P_{H_2}^2 \cdot P_{O_2}}$$
• Unit consistency is crucial. The table below lists the most common pressure units and their corresponding gas constants for the Kp–Kc conversion.

Using the Partial Pressure Calculator ensures these constants are applied correctly, so you can focus on your chemical equilibrium problem without manual unit conversions.

Summary

Whether you need to convert Kc to Kp or vice versa, the fundamental relationship $K_p = K_c (RT)^{\Delta n}$ is your guide. With the Kp to Kc Converter and the information above, you can handle any reversible gaseous reaction efficiently. Remember to verify your units and to include only gaseous species in the equilibrium expression.