# Solubility of Tris(hydroxymethyl)aminomethane in Methanol + 1-Propanol Mixtures at Various Temperatures Page: 4,229

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Journal of Chemical & Engineering Data

n XT = A + B4

T (4)

where A and B are the model constants calculated using a least-

square method. Table 3 lists these model constants and the

Table 3. Model Constants for van't Hoff Equation for

Various Mole Fractions of MeOH (x ) and the obtained

Mean Percentage Deviation (MPD) for Back-Calculated

Solubilities Using eq 4

x0 A B MPD

1.00" 6.07 -3212 2.4

0.94 6.74 -3426 1.4

0.88 6.81 -3478 1.2

0.81 6.87 -3531 1.8

0.74 6.23 -3361 0.7

0.65 6.32 -3408 0.4

0.56 6.04 -3653 0.6

0.45 7.10 -3679 0.7

0.32 7.67 -3864 1.3

0.17 7.45 -3812 2.1

0.00b 7.22 -3740 3.2

overall 1.4

"Data for this fraction taken from a previous work.4 bData for this

fraction taken from a previous work.s

MPD values for the back-calculated data using eq 4. Good

linear relationship between In XT and 1/T is found for the

temperature range in this study.

Using the combined nearly ideal binary solvent/Redlich-

Kister equation,'2 the solubility of TRIS in MeOH (1) + 1-

PrOH (2) mixtures at a given temperature could be

represented as2

inxm = x1 inx1 + xinx2 + x x [2S(x -

i=0where xm, x1, and x2 are the mole fraction solubility of TRIS at a

given temperature in the solvent mixtures and the mono-

solvents 1 and 2; Si are the constants of the model calculated

using a no intercept least-square analysis.'3 Table 4 lists the

numerical values of the model constants of eq 5 and the

obtained MPD values for the back-calculated solubility data.

Table 4. Model Constants of eq 5 and the MPD Values for

Back-Calculated Solubilities in MeOH + 1-PrOH Mixtures at

Various Temperatures (K)T/K

293.2

298.2

303.2

308.2

313.2so

-247.2

-292.8

-264.1

-227.1

-256.2Si

-69.5

-102.3

-95.5

-61.5

-143.5S2 MPD

110.6

122.4

165.4

205.2

256.2

overall1.0

1.0

1.3

1.5

1.5

1.3The model has been extended to represent both solvent

composition and temperature effects on a solute's solubility as'4

0 0 2

in x, = x10 in x1,T + x0i n x2,T + 2 (x1- -x )]

T i=0where xm,T is the mole fraction solubility in the solvent mixtures

at temperature T (in degree K), x1,T and X2,T are the mole

fraction solubility of TRIS in the monosolvents 1 and 2,

respectively, and Jl stands for the constants of the model

computed by a regression analysis.'3 The solubility data at all

temperatures were fitted to eq 6, and the obtained model is

00

In xm,T = x I n xi T + x2 In x2,T + T

[-257.792 - 93.734(x - x2)+ 169.501(x - x )2

(7)

which correlates the solubility data with linear correlation

coefficient of 0.986 with p < 0.0005. The obtained MPD value

for the back-calculated solubility data was 1.7 1.5 % (N = 55).

The Jouyban-Acree model was combined with the van't

Hoff model as4'"5",6

nx =x(A 1+) 0 2+x (A + B2

nxm, T 1 A1 -T - 2 2 - T0 0 2

+ x1x2 Ij(x _- i

T i=0to provide a more versatile predictive equation. The model is

obtained from combining the trained van't Hoff equations using

x = 0.00 and x = 1.00 and the J terms from eq 7 as

In XT = x (6.069 - 3211.508

+ x(7.224 - 3740.048)x+ xx2

[-27.924- T + T T

[-2S7.792 - 93.734(x - x2)+ 169.501(x - x )2

(9)

which enables the back-calculation of the solubility data with

the MPD of 2.0 1.6 % (N = 55), nearly the same as obtained

applying eq 7.

The densities of the saturated solutions of the solute are

required to convert mole fraction solubility to molar solubility

or vice versa. The following equation could be employed to

predict the density of saturated solutions of TRIS in MeOH (1)

+ 1-PrOH (2) using

0 0

In pat = x 0 Inp sat + x0 Inp sat + xi - x2

P,T 1 1,T 2,P ) T

[1.927 + 0.204(x - x0) - 0.504(x -x )2

(10)in which pm T is the density of the saturated solution of TRIS in

the mixed solvent system and plat and psat are the density of

saturated solutions of TRIS in the monosolvents 1 and 2 at

different temperatures. The model constants of eq 10 were

derived from fitting the experimental density of the solute free

mixtures of MeOH + 1-PrOH at various temperatures collected

from the literature.'7 Full details of this procedure has been

described in an earlier work.5 The measured values for plat and

psat of the saturated solutions of TRIS in MeOH and 1-PrOH

at various temperatures along with their solute-free values' are

listed in Table 5. The patterns for the densities of MeOH and

1-PrOH in the absence of TRIS decreased due to volume

expansion of the solvents at higher temperatures. Using eq 10,dx.doi.org/10.1021/je5009685 I J. Chem. Eng. Data 2014, 59, 4227-4230

(8)

(5)

4229

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Jouyban-Gharamaleki, Vahid; Jouyban-Gharamaleki, Karim; Soleymani, Jafar; Kenndler, Ernst; Acree, William E. (William Eugene) & Jouyban, Abolghasem. Solubility of Tris(hydroxymethyl)aminomethane in Methanol + 1-Propanol Mixtures at Various Temperatures, article, November 26, 2014; [Washington, D.C.]. (digital.library.unt.edu/ark:/67531/metadc485913/m1/3/: accessed January 16, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.