Kc to Kp: Converting Equilibrium Constants

This calculator converts an equilibrium constant in terms of concentration (Kc) to an equilibrium constant in terms of partial pressure (Kp) for a gas-phase reaction. Enter the Kc value, the temperature in kelvin, and the change in moles of gas (Δn) for your reaction, and you get the corresponding Kp. The conversion uses the relationship Kp = Kc(RT)^Δn, where R is the ideal gas constant.

Formula

The conversion formula is:

Kp = Kc × (RT)^Δn

Where:

• Kp = equilibrium constant in terms of partial pressures (unit depends on Δn)
• Kc = equilibrium constant in terms of molar concentrations (mol/L)
• R = ideal gas constant = 0.08206 L·atm/(mol·K) (when pressure is in atm)
• T = absolute temperature in kelvin (K)
• Δn = (moles of gaseous products) − (moles of gaseous reactants) from the balanced equation

If you use pressure in atm, use R = 0.08206. If you use pressure in bar, use R = 0.08314. The calculator uses atm by default.

Worked Example

Consider the reaction: N₂(g) + 3H₂(g) ⇌ 2NH₃(g). Here, Δn = 2 − (1+3) = −2. Suppose Kc = 1.0 at T = 298 K.

Step 1: Identify Δn = −2, T = 298 K, R = 0.08206.

Step 2: Calculate RT = 0.08206 × 298 = 24.45 (L·atm/mol).

Step 3: Raise to Δn: (24.45)^(−2) = 1 / (24.45²) = 1 / 597.8 = 0.001673.

Step 4: Multiply by Kc: Kp = 1.0 × 0.001673 = 0.001673.

So Kp ≈ 0.001673. The calculator gives the same result (0.0017 when rounded to 4 decimals).

Why Convert Between Kc and Kp?

Equilibrium constants can be expressed in different ways. Kc uses molar concentrations (mol/L) and is common in solution chemistry. Kp uses partial pressures (atm, bar, or mmHg) and is preferred for gas-phase reactions because pressure is easier to measure than concentration in a gas mixture. The conversion lets you use data from one form to calculate the other, which is often needed when comparing results from different sources or when applying equilibrium expressions to industrial processes like the Haber process.

How to Choose the Right R Value

The value of R must match the pressure unit you want for Kp. Common choices:

• atm: R = 0.08206 L·atm/(mol·K) – most common in chemistry textbooks.
• bar: R = 0.08314 L·bar/(mol·K) – used in some advanced and international contexts.
• mmHg (torr): R = 62.36 L·mmHg/(mol·K) – if you work with mmHg pressures.

Always check the units of your Kc and the pressure unit you need. The calculator uses atm, but you can adjust the formula manually if you need a different R.

Common Mistakes and Misconceptions

A frequent error is forgetting that Δn only counts gaseous species, not solids or liquids. For example, in the reaction CaCO₃(s) ⇌ CaO(s) + CO₂(g), Δn = 1 (only CO₂ is gas). Another mistake is using Celsius instead of kelvin – always convert T(K) = T(°C) + 273.15. Also, when Δn = 0, Kp = Kc because (RT)^0 = 1. Some students mistakenly think Kp and Kc are always equal; they are only equal when Δn = 0.

Limitations of the Conversion

The formula assumes ideal gas behavior, which is valid at low pressures and high temperatures. At very high pressures or low temperatures, real gases deviate, and the conversion becomes approximate. Also, the units of Kp depend on Δn: if Δn = 1, Kp has units of atm; if Δn = −1, units of atm�¹, etc. The numerical value of Kp changes if you change the pressure unit (e.g., from atm to bar), so always state the units. Finally, the conversion does not change the equilibrium position – it only changes how the constant is expressed.

Frequently Asked Questions

Q: When is Kp equal to Kc?
A: When Δn = 0, meaning the number of moles of gaseous products equals the number of moles of gaseous reactants. Then (RT)^0 = 1, so Kp = Kc.

Q: What if my reaction has solids or liquids?
A: Only include gaseous species when calculating Δn. Solids and liquids do not appear in the equilibrium expression for Kc or Kp, so they are ignored in Δn.

Q: Do I need to use kelvin or Celsius?
A: Always use kelvin. The gas constant R has units that include kelvin, so temperature must be in K. Convert from Celsius by adding 273.15.

Q: Can I convert Kp to Kc using the same formula?
A: Yes, just rearrange: Kc = Kp / (RT)^Δn. The same Δn and R apply.

Q: Why does the unit of Kp change with Δn?
A: Because (RT)^Δn has units of (pressure)^Δn. When Δn = 1, Kp has pressure units; when Δn = 2, pressure²; when Δn = −1, pressure�¹. This is why Kp values are often reported without units in textbooks, but technically they have units.

Q: What if I don’t know Δn?
A: You need the balanced chemical equation to find Δn. Count the total moles of gaseous products minus gaseous reactants. Without the equation, you cannot convert.

Related

• What GPU Do You Need for DLSS and Neural Rendering?
• Fair Trivia Questions for Fast-Paced Games
• Get Pixel Material You Theme on Chrome and Firefox

in kc | Kc (concentration) | - | 1.0 | 0
in temp | Temperature | K | 298 | 0
in dn | Δn (moles of gas products - reactants) | mol | 0 | -10
out kp | Kp (pressure) | - | kc * (0.08206 * temp)^dn | 4