Kp to Kc Converter – Equilibrium Constant Calculator
Convert between Kp (equilibrium constant in terms of partial pressure) and Kc (equilibrium constant in terms of concentration) for chemical equilibrium reactions. This calculator uses the relationship Kp = Kc(RT)Δn to perform accurate conversions.
Quick Conversions
Click on any example below to instantly calculate the conversion:
Kc = 0.0227 at 298 K, Δn = -2
Calculate Kp →
Kc = 4.5 at 500 K, Δn = 0
Calculate Kp →
Kc = 1.5×10-3 at 373 K, Δn = 1
Calculate Kp →
Kc = 2.8 at 400 K, Δn = 2
Calculate Kp →
Kp = 3.796×10-5 at 298 K, Δn = -2
Calculate Kc →
Kc = 0.15 at 298 K, Δn = -1
Calculate Kp →
Conversion Formula
The Relationship Between Kp and Kc:
Alternatively:
Where:
- Kp = Equilibrium constant in terms of partial pressure
- Kc = Equilibrium constant in terms of molar concentration
- R = Universal gas constant (value depends on pressure unit)
- T = Absolute temperature in Kelvin
- Δn = Change in number of moles of gas = (moles of gaseous products) – (moles of gaseous reactants)
Gas Constant Values
The gas constant R varies depending on the pressure unit used in your calculation. Select the appropriate value:
| Pressure Unit | Gas Constant (R) Value | Units |
|---|---|---|
| Atmospheres (atm) | 0.0820574614 | L·atm/(K·mol) |
| Kilopascals (kPa) | 8.314462 | L·kPa/(K·mol) |
| Bars (bar) | 0.083144621 | L·bar/(K·mol) |
| Torr | 62.36367 | L·Torr/(K·mol) |
| Millimeters of Mercury (mmHg) | 62.36367 | L·mmHg/(K·mol) |
Conversion Examples
Example 1: Converting Kc to Kp (Haber Process)
Reaction: N2(g) + 3H2(g) ⇌ 2NH3(g)
Given: Kc = 2.27 × 10-2 at 298 K
Find: Kp in atmospheres
- Calculate Δn: Δn = 2 – (1 + 3) = -2
- Identify R: R = 0.0820574614 L·atm/(K·mol) for atmospheres
- Apply formula: Kp = Kc × (RT)Δn
- Substitute values: Kp = 2.27 × 10-2 × (0.0820574614 × 298)-2
- Calculate: Kp = 2.27 × 10-2 × (24.453)-2 = 2.27 × 10-2 × 1.672 × 10-3
- Result: Kp ≈ 3.796 × 10-5
Example 2: Converting Kp to Kc
Reaction: H2O(g) + C(s) ⇌ H2(g) + CO(g)
Given: Kp = 0.236 atm at 1000 K
Find: Kc
- Calculate Δn: Δn = (1 + 1) – 1 = 1 (carbon is solid, not counted)
- Identify R: R = 0.0820574614 L·atm/(K·mol)
- Apply formula: Kc = Kp × (RT)-Δn
- Substitute values: Kc = 0.236 × (0.0820574614 × 1000)-1
- Calculate: Kc = 0.236 × (82.0574614)-1 = 0.236 / 82.0574614
- Result: Kc ≈ 2.876 × 10-3
Example 3: When Δn = 0
Reaction: H2(g) + I2(g) ⇌ 2HI(g)
Given: Kc = 54.3 at 700 K
Find: Kp
- Calculate Δn: Δn = 2 – (1 + 1) = 0
- Apply formula: Kp = Kc × (RT)0 = Kc × 1
- Result: Kp = 54.3 (same as Kc)
When the change in moles equals zero, Kp and Kc are numerically equal regardless of temperature or pressure.
Common Chemical Equilibrium Conversions
| Reaction Type | Typical Δn | Temperature Range | Notes |
|---|---|---|---|
| Synthesis reactions (A + B → C) | Negative | Varies | Kp < Kc when Δn < 0 |
| Decomposition reactions (C → A + B) | Positive | Varies | Kp > Kc when Δn > 0 |
| Isomerization reactions | Zero | Varies | Kp = Kc |
| Haber process (N₂ + 3H₂ ⇌ 2NH₃) | -2 | 400-500°C | Industrial ammonia production |
| Water gas shift (CO + H₂O ⇌ CO₂ + H₂) | 0 | 800-1000 K | Important for hydrogen production |
| PCl₅ decomposition (PCl₅ ⇌ PCl₃ + Cl₂) | +1 | 200-300°C | Kp > Kc at all temperatures |
Frequently Asked Questions
What is the difference between Kp and Kc?
Kp is the equilibrium constant expressed in terms of partial pressures of gases, while Kc is expressed in terms of molar concentrations. Both describe the same equilibrium state but use different units. Kp is used when working with gas pressures, while Kc is used when working with solution concentrations.
When are Kp and Kc equal?
Kp equals Kc when the change in the number of moles of gas (Δn) is zero. This occurs when the number of moles of gaseous products equals the number of moles of gaseous reactants in the balanced chemical equation.
Why do we only count gaseous species when calculating Δn?
Only gaseous species are counted because the ideal gas law (PV = nRT) applies only to gases. Solids and liquids have negligible vapor pressures under standard conditions and do not contribute significantly to the pressure-based equilibrium constant. Their activities are taken as unity (1) in equilibrium expressions.
Which gas constant value should I use?
The gas constant R value you use must match the pressure units in your Kp value. For atmospheres, use R = 0.08206 L·atm/(K·mol). For kilopascals, use R = 8.314 L·kPa/(K·mol). Always verify that your R value matches your pressure unit to avoid calculation errors.
Can I use Celsius instead of Kelvin for temperature?
No, you must use absolute temperature in Kelvin for the formula Kp = Kc(RT)Δn. The ideal gas law requires absolute temperature. To convert Celsius to Kelvin, add 273.15 to the Celsius temperature: K = °C + 273.15.
What if Δn is negative?
If Δn is negative (more gaseous reactants than products), Kp will be smaller than Kc at the same temperature. This is because (RT)Δn becomes a fraction when Δn is negative. The more negative Δn is, the smaller Kp will be relative to Kc.
Do Kp and Kc have units?
Technically, both Kp and Kc should have units based on their definitions, but by convention, they are often reported as dimensionless numbers. This is because concentrations and pressures are typically expressed relative to standard states. When converting between them, however, you must be careful with the units of R to get correct numerical values.
How does temperature affect the relationship between Kp and Kc?
Temperature directly affects the conversion factor (RT)Δn. As temperature increases, if Δn is positive, Kp increases relative to Kc. If Δn is negative, Kp decreases relative to Kc. However, both Kp and Kc themselves change with temperature according to the van ‘t Hoff equation, which is independent of this conversion relationship.
Related Equilibrium Constants
Besides Kp and Kc, there are other equilibrium constants used in chemistry:
Ka (Acid Dissociation Constant)
Measures the strength of an acid in solution. It represents the equilibrium constant for the dissociation of an acid into its conjugate base and a proton. Larger Ka values indicate stronger acids.
Kb (Base Dissociation Constant)
Measures the strength of a base in solution. It represents the equilibrium constant for the reaction of a base with water to form its conjugate acid and hydroxide ion. Larger Kb values indicate stronger bases.
Ksp (Solubility Product Constant)
Describes the equilibrium between a solid and its ions in a saturated solution. It is used to calculate the solubility of sparingly soluble salts. Lower Ksp values indicate lower solubility.
Kw (Water Dissociation Constant)
The equilibrium constant for the self-ionization of water: H₂O ⇌ H⁺ + OH⁻. At 25°C, Kw = 1.0 × 10-14. It relates to pH calculations and acid-base chemistry.