*2.5. Determining Distribution Coe*ffi*cient and Crystal Yield*

In order to conduct the layer and suspension crystallization experiments, the freezing points of two DBNH[OAc] aqueous solutions were determined in the jacketed crystallizer fitted with a scraper. Upon seeding, ice crystallization commenced and as a result of the heat of crystallization, the solution temperature increased until a constant value was attained, which remained for the duration of crystallization. This temperature was taken as the freezing point and was measured with a thermocouple with a standard uncertainty of 0.01 ◦C (expanded uncertainty of 0.02 ◦C).

The ice crystal yield and the distribution coefficient were the main parameters used to assess the efficiency of freeze crystallization as a separation method.

Ice crystal yield was determined based on the mass of a pure ice sample as calculated by Equation (4)

$$Y = \frac{\mathbf{m}\_{\text{ice}}}{\mathbf{m}\_{\text{water},\text{sol}}} \cdot 100 \,, \tag{4}$$

where

mice mass of the pure ice (kg),

mwater,sol mass of the water in initial solution (kg).

The mass of the ice samples produced by layer freeze crystallization was determined by weighing, whereas the mass of ice samples crystallized in the suspension crystallizer was calculated based on the concentration difference of [DBNH][OAc] in the mother liquor at the end of crystallization and the initial solution.

The distribution coefficient, K, is expressed as the ratio of the impurity in the ice to the initial impurity in the solution:

$$\mathbf{K} = \frac{\mathbf{C}\_{\text{imp}}}{\mathbf{C}\_0},\tag{5}$$

where

Cimp concentration of ionic liquid in ice (kg [DBNH][OAc]/kg ice),

C0 initial concentration of ionic liquid in solution (kg [DBNH][OAc]/kg solution).

Purity of the ice samples —which is determined from the concentration of [DBNH][OAc] present in the ice crystals—was analyzed by the measurement of melted ice and mother liquor sample electrical conductivities with a Consort C3050 electrical conductivity meter. To obtain a correlation between electrical conductivity and concentration, the electrical conductivities of six solutions (0, 2, 4, 6, 8, and 10 wt.% [DBNH][OAc](aq)) were measured and are shown in Figure 4.

**Figure 4.** Electrical conductivity of aqueous solutions as a function of ionic liquid concentration.
