Partition Coefficient Formula

Partition coefficient is defined as a chemical’s concentration ratio between two mediums at equilibrium. In another way, a partition coefficient is the ratio of a substance’s concentration in one medium or phase to its concentration in a second medium or phase when the two concentrations are at equilibrium. Gases such as air, liquids such as water or olive oil, or complex mixes such as blood or other tissues can be used as media. However, in general, the partition coefficients of an uncharged solute in two separate two-phase systems with similar are uneven.

Formula

The formula for partition coefficient equals the ratio of solute’s concentration when it is stationary to the solute’s concentration when it shows mobility. It is directly proportional to the amount of stable solute but inversely proportional to the moving solute. It is denoted by the symbol K_d and is a unitless quantity as it is the ratio of two same quantities.

K_d = C_s/C_m

where,

K_d is the partition coefficient,

C_s is the concentration of solute in stationary mode,

C_m is the concentration of solute in mobility mode,

Sample Problems

Problem 1. Calculate the partition coefficient if the concentration of solute in the stationary phase is 9 M and 5 M in the mobile phase.

Solution:

We have,

C_s = 9

C_m = 5

Using the formula we get,

K_d = C_s/C_m

= 9/5

= 1.8

Problem 2. Calculate the partition coefficient if the concentration of solute in the stationary phase is 12 M and 8 M in the mobile phase.

Solution:

We have,

C_s = 12

C_m = 8

Using the formula we get,

K_d = C_s/C_m

= 12/8

= 1.5

Problem 3. Calculate the partition coefficient if the concentration of solute in the stationary phase is 20 M and 17 M in the mobile phase.

Solution:

We have,

C_s = 20

C_m = 17

Using the formula we get,

K_d = C_s/C_m

= 20/17

= 1.17

Problem 4. Calculate the concentration of solute in the stationary phase if the partition coefficient is 2.5 and the concentration in the mobile phase is 10 M.

Solution:

We have,

K_d = 2.5

C_m = 10

Using the formula we get,

K_d = C_s/C_m

=> C_s = K_d C_m

= 2.5 (10)

= 25 M

Problem 5. Calculate the concentration of solute in the stationary phase if the partition coefficient is 1.6 and the concentration in the mobile phase is 7 M.

Solution:

We have,

K_d = 1.6

C_m = 7

Using the formula we get,

K_d = C_s/C_m

=> C_s = K_d C_m

= 1.6 (7)

= 11.2 M

Problem 6. Calculate the concentration of solute in the mobile phase if the partition coefficient is 3.75 and the concentration in the stationary phase is 12 M.

Solution:

We have,

K_d = 3.75

C_m = 12

Using the formula we get,

K_d = C_s/C_m

=> C_m = C_s/K_d

= 12/3.75

= 3.2 M

Problem 7. Calculate the concentration of solute in the mobile phase if the partition coefficient is 1.9 and the concentration in the stationary phase is 5 M.

Solution:

We have,

K_d = 1.9

C_m = 5

Using the formula we get,

K_d = C_s/C_m

=> C_m = C_s/K_d

= 5/1.9

= 2.63 M