Fraction of solute in two layers

[Godislove]

Derive the following equation for the fraction of a solute in layer 1 of the 2 layers formed by two immiscible liquids;

Fraction of solute in layer 1 = (K_D*V₁)/((K_D*V₁)+V₂)

where K_D=Distribution coefficient for the solute between chemical in V₁ and chemical in V₂
V₁=Volume of liquid in layer 1
V₂=Volume of liquid in layer 2

I understand that to find the fraction of A in the total A+B you simply divide A by A+B. But how does the distribution coefficient fit into this?

 

[Borek]

Distribution coefficient is a ratio of concentrations.

 

[Godislove]

yes i have that information, I am having trouble understanding how to incorporate it into the expression for the fraction of solute in each of the layers of liquid at equilibrium. Essentially i want to know where this equation comes from. Any ideas/ answers would be greatly appreciated

 

[Borek]

Write equations describing your system. Definitions of fractions won't hurt either.

 

[Querious]

Using the definition of K_D being ratio of concentrations in the 2 layers, try writing K_D in terms of solute present in the 2 layers, A & B and the volumes V₁ & V₂

With the equation that you've made and A/(A+B) you should be able to slove this quite neatly