Discussed in the dilution unit, an iterative mixing process can be used to successively dilute a solution. However the dilution technique explored there is really a special case of generalized iterative mixing. While dilution would require the mass of solute in container #1 to be zero and would cause the resulting solution to become successively more dilute, the mass in container #1 could, in fact, be set to any amount causing the resulting solution to approach the concentration in container #1.
The equation which predicts the resulting concentration in container #3 after 'n' mixing iterations is shown below. It can be derived similarly to the way in which the equation for dilution can be derived. Please look at the derivation page before continuing. As an alternate, try the new separation exercise on for size.
Notice that the equation for dilution, a special case of iterative mixing, can be reduced from the above equation by imposing the restriction that m1 (and therefore C1) be equal to zero, as shown below.