• 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 cm^3?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 CH₃NH_2?(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_pc)?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