Activity Coefficients of RbF in UreaâWater and FormamideâWater

Article pubs.acs.org/jced

Activity Coefficients of RbF in Urea−Water and Formamide−Water Mixtures from Potentiometric Measurements Xiuhua Hao, Shuni Li,* Quanguo Zhai, Yucheng Jiang, and Mancheng Hu* Key Laboratory of Macromolecular Science of Shaanxi Province, School of Chemistry and Chemical Engineering, Shaanxi Normal University, Xi’an, Shaanxi 710062, P. R. China S Supporting Information *

ABSTRACT: The potentiometric method was used to obtain mean activity coefficients of RbF in urea/formamide−water mixed solvents at 298.2 K. The weight fractions of amide were varied from 0 to 40 %. The Pitzer, modified Pitzer and extended Debye−Hückel equations were used for representing the mean activity coefficients and other related thermodynamic properties of the systems. Furthermore, corresponding parameters of the thermodynamic models mentioned herein before were also obtained.

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INTRODUCTION Aqueous electrolyte solutions are of great importance in chemical, biological, and environment systems. Thermodynamic properties are essential for a great deal of applications in chemical process industries, such as water treatment, separation, and electrochemistry. Amide is extensively used as organic solvent and raw material in laboratory and industry. Among them, urea is widely used in industries involving medicine, agriculture, commerce, and cosmetic applications. Moreover, urea and formamide have similar structures, and the cosolvent of urea−water and formamide−water are both εincreasing systems. Therefore, probing into the nature of interactions between amides and electrolytes is important for the design of suitable processes for its application. For example, Hernández-Luis et al. carried out a series of systematic studies of electrolyte NaF/NaCl/NaBr in formamide−water mixtures.1−3 In recent years, our research group investigated the thermodynamic properties of heavy alkaline metal chlorides and fluorides in organic−water with ε-increasing and εdecreasing cosolvents such as alcohol−water, amino acid− water, and amide−water et al.4−6 The solution properties of aqueous mixtures of formamide−water and urea−water have received considerable attention in the literature.7,8 The results showed that the dielectric constants (ε-increasing and εdecreasing cosolvents) of the mixed solvents had a great effect on the thermodynamic properties of the systems. In this work, the potentiometric method was used to determine the thermodynamic properties of RbF in urea−water © XXXX American Chemical Society

and formamide−water mixtures. The experimental data were modeled by Pitzer, modified Pitzer, and extended Debye− Hückel equations.

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EXPERIMENTAL SECTION The chemical RbF was supplied by Shanghai China Lithium Industrial Co., Ltd. Urea and formamide were supplied by Sinopharm Chemical Reagent Co., Ltd. Details of the chemicals used in this study are summarized in Table 1. The water for this research was doubly distilled and deionized. The Rb-ISE was a PVC membrane type filled with 0.1 mol· L−1 RbF solution as the working electrode. F-ISE was a kind of crystal membrane electrode as the reference electrode. Both electrodes were activated and calibrated before measuring the potential difference of the cells: Rb‐ISE|RbF(m),

water|F‐ISE

Rb‐ISE|RbF(m),

urea/formamide(w),

water(1 − w)|F‐ISE

(A)

(B)

where w is the mass fraction of urea in (urea + water) mixed solvents, or formamide in (formamide + water) mixed solvents. w = 0.00, 0.10, 0.20, 0.30, and 0.40 in this paper. m represents Received: June 11, 2015 Accepted: November 2, 2015

A

DOI: 10.1021/acs.jced.5b00484 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Description of Chemical Samples Used in This Study chemical name

mass purity

specification

source

purification method

RbF urea formamide

> 99.5 % > 99.5 % > 99.0 %

A.R. A.R. A.R.

Shanghai China Lithium Industrial Co., Ltd. Sinopharm Chemical Reagent Co., Ltd. Sinopharm Chemical Reagent Co., Ltd.

dried in vacuum at 403 K for 36 h and stored in a desiccator before use none none

and b = 1.2 kg1/2·mol−1/2. β(0) (kg·mol−1), β(1) (kg·mol−1), and Cφ (kg·mol−1)2 are the variables of the Pitzer equation. Aφ is the Debye−Hückel coefficient for the osmotic function expressed as

the molality of RbF. Each set of solutions was obtained gravimetrically by the use of an analytical balance whose standard uncertainty was 0.1 mg. The density (ρ/g·cm−3) and the relative permittivity (ε) of the mixtures were obtained from the literature,1,9 and the values are listed in Table S1 in the Supporting Information. The cell and the solution were temperature-controlled in a doublewalled glass vessel maintained at 298.2 K (standard uncertainty of 0.2 K) with circulating water, the working solution in the vessel was stirred constantly by a magnetic stirrer to minimize the concentration gradient. Each set of experiments was performed at fixed mass fraction of urea or formamide. A pH/mV meter (Orion-868, America) with resolution 0.1 mV was used for the electrochemical measurements, and the voltage readings were taken when they were stable to within 0.1 mV. The whole experiment process was performed within 1.5 h avoiding fatigue of the electrodes.

Aφ = 1.4006 ·106ρ1/2 (εT )3/2 kg1/2·mol−1/2

where ρ and ε are the mean density and relative permittivity of the electrolyte, respectively. Aφ has a definite value in pure water of 0.3921 kg1/2·mol−1/2 at 298.2 K. Modified Pitzer Model. For single-component electrolyte aqueous solution, the modified Pitzer equation proposed by Pérez-Villaseńor and co-workers contains only three adjustable parameters.12 The mean activity coefficient (γ±) and osmotic coefficient (Φ) can be described by the modified Pitzer model in the following form:

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ln γ± = −Aφ[I1/2/(1 + bMX I1/2) + (2/bMX )

THERMODYNAMICS MODEL In this work, the Pitzer,10,11 modified Pitzer,12,13 and extended Debye−Hückel14,15 models were used to process the electrochemical measurements in order to describe the interactions between amides and inorganic salts in solution. The Pitzer Model. According to the Pitzer equation, the mean-ion activity coefficient (γ±) for the 1−1 type electrolytes was determined in terms of the following equations:11 ln γ± = f γ + mBγ + m2C γ

ln(1 + bMX I1/2)] + 2mBMX + 3m2CMX

(6)

Extended Debye−Hü ckel Equation. On the basis of probing into the Debye−Hückel theory which is the basis of the theory of electrolyte solution, the extended Debye−Hückel equation is obtained:14,15 log γ± = −Am1/2 /(1 + Bam1/2) + cm + dm2

with

− log(1 + 0.002mM )

f γ = −Aφ[I1/2/(1 + bI1/2) + (2/b) ln(1 + bI1/2)]

M = MA XA + M w (1 − XA )

Bγ = 2β (0) + 2β (1){[1 − exp(−αI1/2)(1 + αI1/2

(1c)

The osmotic coefficient (Φ) is calculated from the following formula: (2)

where f

φ

= − A φ (I

1/2

/(1 + bI

1/2

))

(2a)

Bφ = β (0) + β (1)exp( −αI1/2)

(2b)

A = 1.8247·106ρ1/2 /(εT )3/2 kg1/2·mol−1/2

(7b)

B = 50.2901ρ1/2 /(εT )1/2 kg1/2·mol−1/2·Å−1

(7c)

All the equation parameters have the common meaning. The values of M, A, B and Debye−Hückel osmotic coefficient parameter (Aφ) for the mixed solvents and pure water are also shown in Table S1.

The excess Gibbs free energy (GE) used to measure how well an actual process fits the ideal process in the course of mixing the solution, can be written as follows: GE = 2RTI(1 − Φ + ln γ±)

(7a)

where a is the ion size parameter in Å. c and d symbolize the ion-interaction parameters. M represents the average molecular mass of the mixed solvent. MA stands for the molecular masses of amides and Mw stands for that of pure water, XA denotes the mole fraction of amides in amide−water mixtures. The Debye− Hückel constants A and B for each solvent composition are given by

(1b)

Φ − 1 = f φ + mBφ + m2C φ

(7)

with

(1a)

C γ = 1.5C φ

(5)

Φ − 1 = −AφI1/2/(1 + bMX I1/2) + mBMX + 2m2CMX

(1)

− α 2I /2)]/(α 2I )}

(4)

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RESULTS AND DISCUSSION Calibration of the Electrode Pair Rb-ISE and F-ISE. The potentials E of the electrochemical cell (A) is related to the mean activity coefficient γ± of the electrolyte by the Nernst equation:

(3)

In the above equations, I is the ionic strength on a molarity basis, m is the molalitiy of electrolyte (mol·kg−1), for 1−1 type electrolytes; I and m have the same value. α = 2.0 kg1/2·mol−1/2, B



Article

Table 2. Experimental Potential Difference E, Mean Activity Coefficients γ±, Osmotic Coefficients Φ, and Excess Gibbs Free Energy GE for RbF in Urea/Formamide + H2O at T = 298.2 K and p = 0.1 MPaa m/(mol·kg−1)

E/mV

γ±

Φ

0.0026 0.0061 0.0109 0.0170 0.0230 0.0297 0.0406 0.0472 0.0579 0.0713 0.0808 0.0935

−187.7 −144.1 −116.1 −94.8 −79.8 −67.7 −52.6 −45.2 −35.7 −25.7 −19.9 −13.1

0.9462 0.9210 0.8997 0.8802 0.8657 0.8528 0.8358 0.8274 0.8157 0.8037 0.7964 0.7878

0.9822 0.9741 0.9674 0.9614 0.9571 0.9534 0.9487 0.9465 0.9435 0.9407 0.9390 0.9373

0.0033 0.0068 0.0102 0.0137 0.0172 0.0246 0.0325 0.0399 0.0460 0.0576 0.0708 0.0831

−179.1 −143.7 −123.6 −109.5 −98.5 −81.0 −67.2 −57.4 −50.5 −39.8 −29.8 −22.3

0.9452 0.9256 0.9121 0.9011 0.8921 0.8771 0.8645 0.8548 0.8479 0.8368 0.8264 0.8183

0.9821 0.9760 0.9719 0.9687 0.9661 0.9618 0.9585 0.9560 0.9543 0.9517 0.9494 0.9477

0.0022 0.0050 0.0080 0.0105 0.0137 0.0198 0.0273 0.0344 0.0427 0.0547 0.0660 0.0778

−193.3 −152.6 −128.9 −116.1 −102.5 −84.4 −68.7 −57.7 −47.1 −35.1 −26.0 −18.0

0.9573 0.9387 0.9253 0.9168 0.9075 0.8938 0.8809 0.8711 0.8617 0.8506 0.8420 0.8344

0.9860 0.9802 0.9762 0.9736 0.9709 0.9671 0.9637 0.9612 0.9590 0.9565 0.9547 0.9532

0.0034 0.0062 0.0092 0.0129 0.0160 0.0229 0.0298 0.0373 0.0452 0.0565 0.0678 0.0795

−160.9 −130.9 −111.5 −95.1 −84.6 −66.8 −54.0 −42.7 −33.4 −22.5 −13.8 −5.7

0.9513 0.9372 0.9264 0.9165 0.9095 0.8973 0.8879 0.8796 0.8724 0.8640 0.8571 0.8511

0.9843 0.9801 0.9770 0.9743 0.9724 0.9694 0.9672 0.9654 0.9640 0.9625 0.9615 0.9607

0.0028 0.0056 0.0084 0.0110 0.0133 0.0198

−157.0 −121.9 −101.6 −88.1 −78.3 −59.3

0.9578 0.9434 0.9333 0.9257 0.9202 0.9080

0.9864 0.9821 0.9792 0.9770 0.9755 0.9724

m/(mol·kg−1)

GE/(RT)

RbF+ Urea + H2O w = 0.00 −0.0002 0.1138 −0.0007 0.1361 −0.0016 0.1690 −0.0030 0.2002 −0.0047 0.2461 −0.0067 0.2892 −0.0104 0.3435 −0.0129 0.3997 −0.0171 0.4744 −0.0227 0.5454 −0.0270 0.6116 −0.0329 w = 0.10 −0.0003 0.1029 −0.0007 0.1249 −0.0013 0.1548 −0.0020 0.1884 −0.0028 0.2305 −0.0046 0.2759 −0.0068 0.3332 −0.0090 0.3902 −0.0110 0.4653 −0.0149 0.5378 −0.0198 0.6054 −0.0246 w = 0.20 −0.0001 0.0973 −0.0004 0.1154 −0.0009 0.1471 −0.0013 0.1780 −0.0019 0.2213 −0.0031 0.2652 −0.0049 0.3222 −0.0068 0.3780 −0.0092 0.4580 −0.0129 0.5313 −0.0167 0.6035 −0.0209 w = 0.30 −0.0002 0.0993 −0.0006 0.1177 −0.0010 0.1488 −0.0016 0.1795 −0.0022 0.2248 −0.0036 0.2723 −0.0051 0.3288 −0.0070 0.3866 −0.0091 0.4716 −0.0123 0.5428 −0.0157 0.6160 −0.0194 w = 0.40 −0.0002 0.0889 −0.0005 0.1052 −0.0008 0.1317 −0.0012 0.1621 −0.0016 0.1980 −0.0027 0.2355 C

E/mV

γ±

Φ

GE/(RT)

−3.7 4.3 14.5 22.3 32.0 39.8 48.0 55.5 63.8 70.5 76.5

0.7763 0.7660 0.7539 0.7448 0.7343 0.7266 0.7191 0.7133 0.7076 0.7038 0.7013

0.9352 0.9336 0.9321 0.9315 0.9314 0.9320 0.9333 0.9351 0.9379 0.9410 0.9440

−0.0429 −0.0545 −0.0725 −0.0906 −0.1183 −0.1454 −0.1807 −0.2182 −0.2693 −0.3188 −0.3656

−12.0 −2.8 7.2 16.5 26.0 34.6 43.6 51.1 59.5 66.5 72.3

0.8073 0.7973 0.7863 0.7762 0.7660 0.7570 0.7476 0.7397 0.7311 0.7240 0.7182

0.9457 0.9439 0.9422 0.9408 0.9396 0.9387 0.9378 0.9372 0.9366 0.9360 0.9356

−0.0329 −0.0426 −0.0565 −0.0732 −0.0951 −0.1198 −0.1525 −0.1863 −0.2325 −0.2786 −0.3228

−7.3 0.7 12.2 21.4 31.7 40.4 49.8 57.5 66.7 74.0 80.2

0.8241 0.8161 0.8050 0.7962 0.7864 0.7783 0.7696 0.7625 0.7541 0.7475 0.7418

0.9514 0.9501 0.9486 0.9476 0.9467 0.9460 0.9454 0.9450 0.9444 0.9439 0.9434

−0.0282 −0.0354 −0.0487 −0.0625 −0.0828 −0.1043 −0.1336 −0.1633 −0.2076 −0.2497 −0.2923

4.7 13.2 24.5 33.5 44.4 53.9 63.0 70.8 80.7 87.7 93.7

0.8429 0.8367 0.8283 0.8217 0.8140 0.8076 0.8012 0.7956 0.7886 0.7833 0.7783

0.9598 0.9593 0.9588 0.9586 0.9585 0.9585 0.9584 0.9582 0.9576 0.9570 0.9561

−0.0260 −0.0324 −0.0438 −0.0556 −0.0739 −0.0938 −0.1184 −0.1444 −0.1841 −0.2184 −0.2546

14.4 22.4 33.3 43.3 53.1 61.6

0.8560 0.8503 0.8427 0.8360 0.8297 0.8243

0.9630 0.9625 0.9621 0.9619 0.9620 0.9621

−0.0211 −0.0262 −0.0351 −0.0457 −0.0589 −0.0731



Article

Table 2. continued m/(mol·kg−1)

E/mV

γ±

Φ

0.0262 0.0329 0.0399 0.0502 0.0609 0.0715

−45.6 −34.6 −24.9 −13.5 −4.5 3.8

0.8987 0.8910 0.8842 0.8761 0.8693 0.8636

0.9702 0.9685 0.9672 0.9657 0.9646 0.9638

0.0044 0.0095 0.0145 0.0197 0.0226 0.0332 0.0442 0.0542 0.0612 0.0746 0.0861

−174.8 −138.5 −117.7 −103.3 −96.6 −79.4 −65.5 −55.9 −50.3 −41.1 −34.5

0.9313 0.9053 0.8874 0.8734 0.8665 0.8468 0.8311 0.8195 0.8126 0.8010 0.7926

0.9774 0.9692 0.9636 0.9594 0.9574 0.9517 0.9474 0.9445 0.9428 0.9401 0.9383

0.0034 0.0072 0.0105 0.0140 0.0185 0.0263 0.0337 0.0412 0.0486 0.0603 0.0722 0.0842

−157.5 −121.0 −102.8 −88.8 −75.7 −58.9 −47.3 −37.6 −29.7 −19.6 −11.2 −3.9

0.9442 0.9228 0.9099 0.8988 0.8876 0.8719 0.8604 0.8505 0.8420 0.8309 0.8214 0.8131

0.9818 0.9750 0.9711 0.9678 0.9645 0.9600 0.9569 0.9543 0.9521 0.9494 0.9472 0.9453

0.0032 0.0067 0.0102 0.0140 0.0217 0.0291 0.0369 0.0442 0.0518 0.0629 0.0742 0.0888

−154.4 −118.6 −97.8 −82.9 −62.7 −48.0 −36.5 −27.9 −20.4 −11.1 −3.6 4.9

0.9489 0.9297 0.9163 0.9049 0.8875 0.8745 0.8637 0.8549 0.8472 0.8373 0.8287 0.8192

0.9833 0.9773 0.9731 0.9697 0.9646 0.9610 0.9580 0.9557 0.9537 0.9512 0.9491 0.9469

0.0029 0.0057 0.0089 0.0120 0.0190 0.0259 0.0328 0.0399 0.0502 0.0607 0.0714 0.0855

−148.1 −114.2 −92.8 −78.4 −56.0 −41.1 −29.8 −20.3 −9.0 −0.1 7.3 15.9

0.9552 0.9397 0.9278 0.9189 0.9034 0.8921 0.8832 0.8755 0.8661 0.8582 0.8513 0.8436

0.9855 0.9808 0.9772 0.9747 0.9704 0.9675 0.9653 0.9635 0.9614 0.9597 0.9583 0.9568

m/(mol·kg−1)

GE/(RT)

w = 0.40 −0.0040 −0.0055 −0.0072 −0.0098 −0.0128 −0.0158 RbF+ Formamide w = 0.00 −0.0004 −0.0013 −0.0024 −0.0037 −0.0046 −0.0078 −0.0117 −0.0156 −0.0184 −0.0242 −0.0294 w = 0.10 −0.0003 −0.0008 −0.0014 −0.0021 −0.0031 −0.0051 −0.0072 −0.0096 −0.0121 −0.0163 −0.0208 −0.0256 w = 0.20 −0.0002 −0.0007 −0.0012 −0.0019 −0.0036 −0.0055 −0.0077 −0.0099 −0.0124 −0.0162 −0.0204 −0.0260 w = 0.30 −0.0002 −0.0005 −0.0009 −0.0014 −0.0027 −0.0042 −0.0059 −0.0077 −0.0106 −0.0137 −0.0170 −0.0217

D

E/mV

γ±

Φ

GE/(RT)

0.2851 0.3309 0.4105 0.4790 0.5463 0.6065 + H2O

71.4 78.6 89.2 96.4 103.0 108.3

0.8185 0.8141 0.8075 0.8027 0.7984 0.7948

0.9623 0.9624 0.9624 0.9622 0.9618 0.9614

−0.0927 −0.1112 −0.1447 −0.1744 −0.2043 −0.2317

0.0993 0.1201 0.1411 0.1709 0.1972 0.2474 0.2962 0.3670 0.4347 0.5187 0.5989

−28.1 −19.3 −11.9 −2.9 3.8 14.2 23.1 33.2 41.3 49.9 56.9

0.7843 0.7732 0.7640 0.7533 0.7456 0.7340 0.7255 0.7165 0.7103 0.7050 0.7017

0.9366 0.9346 0.9333 0.9321 0.9316 0.9315 0.9321 0.9340 0.9363 0.9398 0.9434

−0.0357 −0.0461 −0.0571 −0.0736 −0.0888 −0.1191 −0.1499 −0.1963 −0.2420 −0.3001 −0.3566

0.1042 0.1243 0.1555 0.1876 0.2358 0.2845 0.3472 0.4090 0.4865 0.5592 0.6312

5.9 14.0 24.5 33.2 43.8 52.5 61.7 69.3 77.3 83.7 89.3

0.8015 0.7918 0.7794 0.7689 0.7561 0.7455 0.7342 0.7249 0.7148 0.7066 0.6994

0.9429 0.9409 0.9386 0.9368 0.9347 0.9330 0.9313 0.9298 0.9282 0.9268 0.9255

−0.0342 −0.0433 −0.0584 −0.0749 −0.1010 −0.1290 −0.1668 −0.2058 −0.2568 −0.3064 −0.3572

0.1049 0.1260 0.1555 0.1872 0.2330 0.2820 0.3421 0.4024 0.4780 0.5506 0.6195

12.4 21.0 30.8 39.3 49.4 58.5 67.3 74.8 82.7 89.2 94.5

0.8102 0.8001 0.7884 0.7780 0.7654 0.7543 0.7428 0.7330 0.7223 0.7132 0.7055

0.9449 0.9427 0.9403 0.9382 0.9357 0.9336 0.9313 0.9293 0.9269 0.9248 0.9229

−0.0326 −0.0417 −0.0554 −0.0709 −0.0946 −0.1216 −0.1564 −0.1931 −0.2412 −0.2894 −0.3367

0.1041 0.1218 0.1499 0.1843 0.2268 0.2764 0.3362 0.3984 0.4708 0.5397 0.6095

25.3 32.6 42.4 52.2 62.0 71.2 80.4 88.3 96.0 102.2 107.7

0.8350 0.8280 0.8187 0.8091 0.7991 0.7890 0.7785 0.7686 0.7580 0.7486 0.7395

0.9552 0.9540 0.9523 0.9506 0.9486 0.9464 0.9436 0.9406 0.9370 0.9334 0.9295

−0.0282 −0.0348 −0.0457 −0.0599 −0.0784 −0.1013 −0.1305 −0.1624 −0.2016 −0.2406 −0.2819



Article

Table 2. continued m/(mol·kg−1)

E/mV

γ±

Φ

0.0031 0.0066 0.0099 0.0130 0.0199 0.0274 0.0350 0.0425 0.0538 0.0655 0.0756 0.0900

−131.8 −94.5 −75.0 −61.7 −40.9 −25.1 −13.5 −4.0 7.0 16.5 23.3 31.8

0.9571 0.9409 0.9307 0.9232 0.9106 0.9003 0.8922 0.8856 0.8775 0.8705 0.8655 0.8593

0.9863 0.9815 0.9786 0.9766 0.9734 0.9710 0.9692 0.9679 0.9664 0.9652 0.9644 0.9635

m/(mol·kg−1)

GE/(RT)

w = 0.40 −0.0002 −0.0006 −0.0010 −0.0015 −0.0027 −0.0042 −0.0058 −0.0076 −0.0104 −0.0136 −0.0165 −0.0207

0.1120 0.1298 0.1589 0.1942 0.2420 0.2925 0.3549 0.4184 0.4891 0.5626 0.6359

E/mV

γ±

Φ

GE/(RT)

42.2 49.2 59.0 68.5 78.8 87.7 96.8 104.8 112.0 118.5 123.5

0.8514 0.8460 0.8384 0.8306 0.8214 0.8128 0.8031 0.7937 0.7837 0.7735 0.7636

0.9624 0.9616 0.9605 0.9592 0.9573 0.9551 0.9520 0.9484 0.9441 0.9392 0.9341

−0.0276 −0.0335 −0.0435 −0.0563 −0.0745 −0.0949 −0.1216 −0.1502 −0.1837 −0.2206 −0.2591

a

w = murea/(murea+ mH2O) for RbF + urea + H2O system and w = mformamide/(mformamide + mH2O) for RbF + formamide + H2O system. m is the molality of RbF in pure water or mixtures. Standard uncertainties u are u(m) = 0.0001 mol·kg−1; u(E) = 0.1 mV; u(γ±) = 0.01; u(T) = 0.2 K; u(P) = 3 kPa.

Table 3. Summary of Mass Fraction w, Standard Potential E0, and Parameter Values Obtained from the Pitzer and the Modified Pitzer Equations of RbF in Urea or Formamide + Water Mixtures at T = 298.2 K and p = 0.1 MPa Pitzer β w

β

(0) −1

kg· mol

Modified Pitzer

(1)

0

E −1

kg· mol

bMX

mV

0.10 0.20 0.30 0.40

0.0338 0.0286 0.0143 0.0171

0.4666 0.4872 0.6023 0.5705

114.5 120.9 131.1 145.3

0.10 0.20 0.30 0.40

0.0230 0.0116 −0.0286 −0.0517

0.4511 0.4084 0.5819 0.6801

130.2 135.9 147.6 159.9

BMX −1/2

SD

−2

kg · mol 2

kg· mol

RbF + Urea + H2O 0.18 3.9432 0.18 4.3056 0.16 4.7455 0.24 4.3548 RbF + Formamide + H2O 0.08 2.8790 0.23 3.0142 0.13 4.0299 0.19 4.8855

E0

CMX −1

kg ·mol 1/2

mV

SD

−0.0326 −0.0339 0.0097 0.0344

0.0398 0.0412 0.0100 −0.0045

114.2 120.6 130.7 145.1

0.13 0.11 0.11 0.22

0.0359 0.0048 0.0006 0.0067

−0.0111 0.0006 −0.0127 −0.0251

130.1 135.8 147.4 159.6

0.08 0.22 0.10 0.16

Table 4. Values of E0 and the Debye-Hückel Parameters for RbF in the Urea or Formamide + Water Mixtures at T = 298.2 K and p = 0.1 MPa a w

Å

0.10 0.20 0.30 0.40

6.1382 6.6817 8.3833 8.4367

E = E 0 + 2k ln(mγ±)

E0

c −1

kg· mol

a

mV

RbF + Urea + H2O 0.0178 114.4 0.0191 120.8 0.0202 130.9 0.0264 145.1

SD

Å

0.16 0.15 0.12 0.22

5.9154 5.9246 8.2903 10.6408

c −1

kg· mol

E0

.

mV

SD

RbF + Formamide + H2O 0.0086 130.1 0.0007 135.9 −0.0170 147.4 −0.0231 159.6

0.07 0.22 0.10 0.17

For the RbF + formamide + water system, the values of E0, k, and R2 are 100.0 mV, 25.0, and 1.0. From the Nernst slope k and the correlation coefficients values, it can be concluded that the electrode pairs were satisfactory for this work. The Nernst response results for RbF in RbF + urea + water and RbF + formamide + water systems can be seen directly from Figure S2, and the values of E and ln(mγ±) for the above two systems are shown in Table S2. Calculation of Thermodynamic Properties. The activity coefficient is an equilibrium thermodynamic property that gives insight into the deviation of a system from ideal behavior and is a reflection of the interactions between the components in the solution. In this work the mean activity coefficient was measured at T = 298.2 K with pressure p = 0.1 MPa, and for solutions of electrolytes the standard state is chosen on molality

(8)

where E0 is the experimental standard potential, k = RT/F, is the Nernst theoretical slope, R and T represent the universal gas constant and the thermodynamic temperature, respectively. F indicates the Faraday constant. The k can be calculated from linear regression of values of E versus ln(mγ±). By combining eqs 1 and 8, the mean activity coefficients of RbF in pure water were obtained and the relevant parameters were taken from the literature.11 The experimental results for RbF in pure water including m, E, and γ± are shown in Table 2. The comparison of the activity coefficient of RbF in water in this work and the reference16 is shown in Figure S1. The values of E0, k, and R2 for the RbF + urea + water system are 119.5 mV, 25.5 (theoretical value is 25.69 mV at 298.2 K) and 1.0. E



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scales. The mean activity coefficients, osmotic coefficients, together with excess Gibbs free energy were calculated by the Pitzer equation and listed in Table 2. The Pitzer, modified Pitzer, and extended Debye−Hückel equations provide a satisfactory fit for the systems studied and the E0 values coincide well with each other. The three sets of model parameters, the values of E0 and the fitting standard deviation are shown in Tables 3 and 4. As is known to all, the term Cφ in Pitzer and d in extended Debye−Hückel equations are insignificant at low concentrations of the electrolyte.2,11 The concentration of RbF is less than 1 mol·kg−1 in this work, so it is proper to define the value of Cφ and d as zero. Figure 1 shows the mean activity coefficients γ± against the molality of RbF m in urea + H2O cosolvent systems. γ± clearly

Figure 2. Comparison of the mean activity coefficients γ± or the excess Gibbs free energy GE of RbF in urea/formamide + H2O (w = 0.10) mixed solvents at T = 298.2 K.

Figure 1. Mean activity coefficients for RbF versus the molality in urea + H2O system containing (0.00, 0.10, 0.20, 0.30, and 0.40) mass fraction of amide at T = 298.2 K.

decreases with the increase of m at a certain mass fraction of amide. The result is caused by two kinds of short-range interactions in electrolyte solutions:14,17 ion-pair association between cations and ions, solvation interactions between ion and solvent.17,18 Also, the mean activity coefficients of RbF increase when the amide weight percentage increases. For RbF + formamide + water, γ± has a similar tendency as depicted in Figure S3. Because urea−water and formamide−water are both an ε-increasing cosolvent system, the interactions between Rb+ and F− are reduced by the solvents. Moreover, the Pitzer equation parameter β(1) for the studied systems show an upward tendency along with the variation of 1/ε approximately, while β(0) has an opposite trend in this work. The positive values for β(1) indicate the existence of a net repulsive force in short-range interactions. Comparison of the mean activity coefficients of RbF in (urea + water) and (formamide + water) mixtures at wamide = 0.10 were plotted in Figure 2. The mean activity coefficient of RbF in (urea + water) is larger than that in (formamide + water). The result may be caused by the dielectric constant of the mixed solvent. The excess Gibbs free energy (GE) represents the nonideal behaviors of real systems and can reflect the different interactions in the solution.19,20 Figure 3 plotted the excess Gibbs free energy versus the concentration of RbF in urea + H2O system. GE increases when the amides mass fraction

Figure 3. Variation of excess Gibbs free energy with molality of RbF in urea + H2O system containing (0.00, 0.10, 0.20, 0.30, and 0.40) mass fraction of amide at T = 298.2 K.

increases showing a similar trend as that of activity coefficients. GE for RbF + formamide + water system is plotted in Figure S4. The standard Gibbs energy of transfer is the difference of the standard Gibbs free energy for electrolyte in pure water (reference solvent) and in mixed solvents.21 The model has the form as follows:22 ΔGt 0 = F(Em 0 − Ew 0) + 2RT ln(ρw /ρm )

(9)

where the subscript “m” and “w” represent the mixed solvent and water. The meaning of the other symbols was detailed above. The values of ΔGt0 are given in Table 5. It should be noted that E0* in Table 5 were the average of that obtained from the Pitzer, modified Pitzer, and the extended Debye− F



Article

Table 5. Values of Mass Fraction w, Average Standard Potential E0* for the Three Models, Standard Gibbs Free Energy of Transfer ΔGt0 of RbF from Water to the (Amides + Water) Mixtures at T = 298.2 K and p = 0.1 MPa E0* w

mV

0.00 0.10 0.20 0.30 0.40

ΔGt0 kJ·mol

−1

RbF + Urea + H2O 119.5 0.0000 114.3 −0.6494 120.8 −0.1417 130.9 0.7096 145.2 1.9193

E0*

ΔGt0

mV

kJ·mol−1

increase of amide content in the mixed solvent. However, the curves of ΔGt0 for RbF + formamide + H2O and RbF + urea + H2O systems are much different because of the different amino groups in the structure of amide.

■

ASSOCIATED CONTENT

S Supporting Information *

RbF + Formamide + H2O 100.0 0.0000 130.1 2.8411 135.9 3.3271 147.4 4.3777 159.7 5.4964

. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.5b00484. Values of average molecular mass M, dielectric constant ε, density ρ, Debye−Hückel constants A, B, and Aφ for different amide−water mixtures at T = 298.2 K and p = 0.1 MPa; values of molality m, experimental potential difference E, mean activity coefficients γ± and natural logarithm of the activity ln (mγ±) of RbF in pure water using electrode pairs in RbF + urea + water and RbF + formamide + water systems at T = 298.2 K and p = 0.1 MPa; the comparison of the activity coefficient of RbF in water in this work and the reference for RbF + urea + H2O and RbF + formamide + H2O systems at 298.2 K; response of the Rb-ISE and F-ISE electrode pair for RbF + urea + H2O (a) and RbF + formamide + H2O (b) systems at 298.2 K; mean activity coefficients for RbF versus the molality in formamide + H2O system containing (0.00, 0.10, 0.20, 0.30, and 0.40) mass fraction of amide at 298.2 K; variation of excess Gibbs free energy with molality of RbF in formamide + H2O system containing (0.00, 0.10, 0.20, 0.30, and 0.40) mass fraction of amide at 298.2 K (PDF)

Hückel equations. Figure 4 shows the standard Gibbs energy of transfer for RbF in different compositions of amides at 298.2 K.

■

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Tel.: +86-29-81530767. Fax: +86-29-81530727. *E-mail: [email protected].

Figure 4. Standard Gibbs energy of transfer for RbF vs the mass fraction of urea/formamide at T = 298.2 K (■, urea; ●, formamide).

Funding

This work was supported by the National Natural Science Foundation of China (nos. 21171111 and 21301114), Natural Science Foundation of Shaanxi Province (no. 2013JQ2009).

ΔGt0

in the amide + water cosolvent system increases First, with the concentration of the cosolvent, and the ΔGt0 for the RbF + formamide + H2O system is larger than that for the RbF + urea + H2O system. It may suggest that RbF is more easily solvated in urea−water mixtures than in formamide−water. Second, ΔGt0 are positive for the RbF + formamide + H2O system, suggesting a nonspontaneous transfer for RbF from water to the mixed solvent. On the other hand, ΔGt0 is negative at wurea = 0.1 and 0.2, then it eventually becomes positive at w = 0.3 and 0.4 in urea−water mixtures. It may be caused by the structure of urea with two amino groups.

Notes

The authors declare no competing financial interest.

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REFERENCES

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■

CONCLUSION This study presents data on mean ionic activity coefficients, excess Gibbs free energy and the standard Gibbs free energy of transfer of the RbF + urea + water and RbF + formamide + water systems at 298.2 K. The experimental data were correlated using the Pitzer, modified Pitzer, and the extended Debye−Hückel models. The mean activity coefficients of RbF decrease with the increase of the concentration of electrolyte, and increase with the increase of amide percentage in the mixed solvent, and γ± of RbF in the (urea + water) mixture is greater than that in the (formamide + water) mixture. The results can be explained by the dielectric constant of the solvent. The standard Gibbs energy of transfer, ΔGt0, increases with the G



Article

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Activity Coefficients of RbF in UreaâWater and FormamideâWater

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