• The partition coefficient (K_pc) is the ratio of the concentrations of a solute in two different immiscible solvents in contact with each other when equilibrium has been established (at a particular temperature)
• For example, methylamine (CH₃NH₂) is dissolved in two immiscible solvents:
  • Water
  • An organic solvent
• A separating funnel is shaken with the organic solvent and aqueous methylamine
• The methylamine is soluble in both solvents, so when the mixture is left to settle an equilibrium is established
  • The rate of methylamine molecules moving from the organic layer into the aqueous layer is equal to the rate of molecules moving from the aqueous layer to the organic layer

CH₃NH₂(aq) ⇌ CH₃NH₂(organic solvent)

• The value of its equilibrium constant is also called the partition coefficient

The partition coefficient is the ratio of methylamine molecules in the organic and aqueous layer once equilibrium has been established

• The partition coefficient (K_pc) for a system in which the solute is in the same physical state in the two solvents can be calculated using the equilibrium expression

Worked example: Calculating the partition coefficient

Answer

• Step 1: Write down the equilibrium equation

CH₃NH₂(aq) ⇌ CH₃NH₂(organic solvent)

• Step 2: Write down the equilibrium expression 

• Step 3: Determine how many moles of CH₃NH₂ has reacted with HCl at the end-point

At the end-point, all CH₃NH₂ (aq) has been neutralised by HCl (aq)

CH₃NH₂ (aq) + HCl (aq) → CH₃NH₃Cl (aq)

CH₃NH₂ and HCl react in a ratio of 1:1

Mol (HCl) = mol (CH₃NH₂) = 0.225 x 0.0141

= 3.18 x 10^-3 mol

• Step 4: Determine the number of moles of CH₃NH₂ present in the aqueous layer

Only 50.0 cm³ of the aqueous layer was used to titrate against HCl

Thus, 3.18 x 10^-3 mol of CH₃NH₂ was present in only 50.0 cm³ of the aqueous layer

The number of moles of CH₃NH₂ in 100 cm³ aqueous layer is, therefore:

Mol (CH₃NH₂ aqueous layer) = 3.18 x 10^-3 x 2 = 6.34 x 10^-3 mol

• Step 5: Determine the number of moles of CH₃NH₂ in the organic layer

Mol CH₃NH₂ (organic layer) = mol CH₃NH₂ (total) – mol CH₃NH₂(aqueous layer)

Mol CH₃NH₂ (total) = 0.100 x 0.150 = 0.015 mol

Mol CH₃NH₂ (organic layer) = 0.015 – 6.34 x 10^-3 = 8.67 x 10^-3 mol

• Step 6: Change the number of moles into concentrations

= 0.063 mol dm^-3

= 0.116 mol dm^-3

• Step 7: Substitute the values into the K_pc expression

= 1.83

Since the value of K_pc is larger than 1, methylamine is more soluble in the organic solvent than in water

• The partition coefficient (K_cp) depends on the solubilities of the solute in the two solvents
• The degree of solubility of a solute is determined by how strong the intermolecular bonds between solute and solvent  are
• The strength of these intermolecular bonds, in turn, depends on the polarity of the solute and solvent molecules
• For example, ammonia is more soluble in water than in an organic solvent such as carbon tetrachloride (CCl₄)
  • Ammonia and water are both polar molecules that form hydrogen bonds with each other
  • Ammonia forms permanent dipole-induced dipole forces with the non-polar CCl₄ molecules
  • Since these forces are much weaker than hydrogen bonding, ammonia is less soluble in CCl₄
• When K_pc is < 1 the solute is more soluble in water than the organic solvent
• When K_pc is > 1 the solute is more soluble in the organic solvent than the water