Relationship between Refractive Index and Molar Concentration of Multi-Component Solutions Zhu Xingyu 1, a, Mai Tiancheng 2, b and Zhao Zilong 2, c

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1 Advances n Computer Scence Research, volume 71 4th Internatonal Conference on Machnery, Materals and Informaton Technology Applcatons (ICMMITA 2016) Relatonshp between Refractve Index and Molar Concentraton of Mult-Component Solutons Zhu Xngyu 1, a, Ma Tancheng 2, b and Zhao Zlong 2, c 1 The Hgh School Afflated to Renmn Unversty, Bejng , Chna; 2 The Hgh School Afflated to Renmn Unversty, Bejng , Chna; 3 The Hgh School Afflated to Renmn Unversty, Bejng , Chna. a jupter_zhu_007@126.com Keywords: Physcal optcs; Mult-component soluton; Refractve ndex; Molar concentraton; Lnear relatonshp. Abstract. Varatons n molar denstes and solute propertes, whch together form a soluton s basc ndex, can cause changes n the soluton s refractve ndex. The lnear relatonshp between the ternary system s refractve ndex soluton and each solute s molar concentraton can be determned through ternary system soluton analyss on lght passng through the soluton. Experments were conducted on a CuSO4-aCl-H2O soluton s refractve ndex n ths study. The model utlzed here can be further appled to mult-component solutons, as the soluton s refractve ndex has a lnear relatonshp wth the propertes of each solute. A new refractve ndex model can be derved accordngly to further enhance the results. Introducton The refractve ndex s a fundamental property of a soluton whch can vary wth temperature, composton, concentraton [1], and ncdent lght wavelength [2]. The relatonshp between the soluton concentraton and refractve ndex has many applcatons such as measurng sea salt concentraton [3] and beer qualty assessment [4]. Glover et al. [5] nvestgated the relatonshp between sucrose soluton concentraton, mass concentraton, and the refractve ndex to establsh an ndex characterzed by the tme t taes a beam of lght to pass through a unt volume of a gven soluton. Zhang et al. [6] proposed a lnear correlaton to a bnary soluton s refractve ndex ( δ An B ) based on Lorentz's electroncs theory, Lambert's law, and Beer's law. Zhu et al. [7] expermentally nvestgated the relatonshp between a ternary norganc soluton s molar concentraton and ts refractve ndex, whch s also lnear. Accordng to the electron cloud nductor model, Zhang [8]suggested that a soluton s refractve ndex can be expressed as n 1 ( ρ m Dm ). Ths study was carred out based on the refractve ndex correlaton of Snell's law. The nfluence of varatons n a molar soluton concentraton on ts refractve ndex was nvestgated by analyzng lght passng through solutons wth dfferent molar concentratons. The mult-component soluton refractve ndex vared lnearly wth each solute s molar concentraton under the nteracton condtons between solute ons and varous volumes after controllng for dssoluton. The Model of Ternary System Soluton As Snell's law suggests, the refractve ndex of a medum s the rato of the ncdent angle s sne to the refracted angle s sne consderng the lght ncdence from the vacuum nto the medum,.e.: c sn θ1 n (1) v sn θ 2 Where c s the speed of lght n a vacuum, v s the speed of lght n the medum, and θ 1 and θ 2 are the ncdent and refracted angles, respectvely. Copyrght 2017, the Authors. Publshed by Atlants Press. Ths s an open access artcle under the CC BY-C lcense ( 442

2 Advances n Computer Scence Research, volume 71 V2 V3 lqud1 lqud2 lqud3 Fg. 1 Schematc dagram of lght path through ternary system soluton As shown n Fg. 1, the soluton volume s wea because the sold solute dssolves n a solvent. The ternary system soluton (two solutes dssolved n a solvent) can also be regarded as a trple-lqud combnaton wth constant molar concentraton and refractve ndex. Lquds 1 and 2 are solutons wth constant molar concentraton and refractve ndex whch combne wthsolutesx 1 andx 2, respectvely. Lquds 1 and 2 molar concentratons are mol/l and lqud 3 s the solvent (the remanng solvent after removng the solvents combned n lquds 1 and 2) wth constant molar concentraton and refractve ndex. Lght speed n a vacuum s c and lght speed n the soluton s v, so the lght speedsarev 1, v 2, andv 3 n the lquds, respectvely. The molar concentratons of solutesx 1 and X 2 are p 1 mol/l and p 2 mol/l. For the ternary system soluton unt volume, t s assumed here that the lqud volume wth nown molar concentraton, nown refractve ndex, and unque solute X 1 s V 1. The lqud volume wth nown molar concentraton, nown refractve ndex, and unque solute X 2 s V 2, and the rest of the solute volume s V 3. The total dstance of lght passng through the soluton s Land the total tme s T. The dstances n lqud 1, lqud2, and lqud3, are L 1, L 2, andl 3 and the tmes are T 1, T 2, and T 3, respectvely. The qualtes of solute X 1 andx 2 n the soluton are the same as those n lquds 1and2, so: p1 ( V2 V3 ) p2 ( V2 V3 ) V2 p1 V2 V3 p2 V2 V2 V3 Lp1 L1 L V2 V3 L2 L3 Lp2 L (1 p1 p2 ) (2) (3) (4) (5) (6) (7) (8) Lp1 v1 Lp t2 2 v2 L(1 p1 p2 ) t3 v3 L[ p1v2v3 p2v1v3 (1 p1 p2 )v1v2 ] T v1v2v3 t1 (9) (10) (11) (12) 443

3 Advances n Computer Scence Research, volume 71 v L v1v2v3 T p1v2v3 p2v1v3 (1 p1 p2 )v1v2 (13) As for the refractve ndex n, c c [ p1v2 v3 p2 v1v3 (1 p1 p2 )v1v2 ] ( cv cv1 ) ( cv3 cv2 ) c p1 3 n p2 (14) v1v3 v2 v3 v3 v v1v2 v3 As shown n Eq.(14), the refractve ndex vares lnearly wth molar concentratons n the ternary system soluton. The soluton s refractve ndex change rate, whch s a result of changes n the molar concentratons of the two solutes, depends on the soluton propertes: amely, the speed of lght n the soluton (mol/l). Expermental Verfcaton Expermental Methods and Data Collecton The refractve ndex of the ternary system soluton contanng two typcal solutes (CuSO 4 -acl-h 2 O) was measured to verfy the model dscussed above. There were sx soluton groups (CuSO 4 -acl-h 2 O) wth 36 nds of molar concentratons under analyss. TheCuSO 4 and acl samples were analytcally pure ( 99.9%). CuSO 4 and acl molar concentratons vared from mol/l at change rate of 0.1 mol /L. The temperature was18.5 (±0.5 ), and a 589nm sodum lght served as the lght source. A 2W Abbe refracttometer (Shangha Optcal Instrument Factory) was used to measure the refractve ndex of the sx soluton groups (CuSO 4 -acl-h 2 O) wth 36 molar concentratons. The measurement results are shown n Table 1. CuSO 4 (mol/l) Table 1 Refractve ndexes of CuSO 4 -acl-h 2 O wth dfferent molar concentratons acl(mol/l) Data Analyss The relatonshp between the mxed lqud refractve ndex and thecuso 4 and acl molar concentratons determned by processng the above data va lnear regresson s llustrated n Fg. 2. Coeffcent R2above was consdered to ndcate a close lnear ft. Regardless of changes ncuso 4 or acl molar concentraton, the refractve ndex of CuSO 4 -acl-h 2 O soluton vared lnearly. In addton, these changes had no sgnfcant effect on the refractve ndex n accordance wth the proposed model. TheCuSO 4 -acl-h 2 O soluton contaned acl soluton (1 mol/l)and CuSO 4 soluton (1 mol/l);lquds 1and 2were selected wth nown molar concentratons and a nown refractve ndex. The actual refractve ndex of the acl soluton (1 mol/l), CuSO4 soluton (1 mol/l), and deonzed water comprsed the benchmar. The refractve ndexes of the ternary system solutons wth dfferent molar concentratons were calculated accordngly. The calculated and expermental results were n accordance, wth a mean relatve error of Thsconfrms the feasblty and effectveness of the proposed equvalent analyss and mathematcal modelng technque for ternary system soluton refractve ndexes. 444

4 Advances n Computer Scence Research, volume 71 Fg. 2 Relatonshp between refractve ndex of CuSO 4 -acl-h 2 O and molar concentraton of CuSO 4 Refractve Index Mult component Soluton Analyss The relatonshp between the -ary soluton s refractve ndex and each solute s molar concentraton was analyzed based on assessment of the ternary system soluton s refractve ndex and subsequent expermental verfcaton. The -ary soluton was regarded as a combnaton of nds of lquds wth constant molar concentratons and refractve ndexes. Lqud 1, lqud 2, and lqud (-1)were consdered to be solutons wth constant molar concentratons and refractve ndexes whch combne ntosolutesx 1, andx 2, respectvely. The molar concentraton of lqud m (m [1, -1]) s mol/l. Lqud s a solvent wth constant molar concentraton and refractve ndex (the remanng solvent after removng what was combned n lqud 1, lqud 2, and lqud (-1)). Lght speed n a vacuum s c, lght speed n the soluton s v, lght speed n lqud m s v m, and the solute s molar concentraton X m s p m mol/l. For a unt volume n -ary soluton, t s assumed that the lqud volume wth nown refractve ndex and molar concentraton s V m and the remanng solvent volume s V. The dstance of lght passng through the soluton s Land the total tme s T; the dstance of lght passng through the lqud m s L m and the tme s t m. The qualty of solute X m n the soluton s the same as that n lqud m, thus: pmv Vm Vm pm Lm L tm t (15) (16) V Lpm (17) L 1 p 1 (18) Lpm (19) vm L 1 p 1 (20) v Lp T L 1 p 1 v 1 v (21) 445

5 Advances n Computer Scence Research, volume 71 c 1 p c (v v ) c Tc cp c n 1 p (22) v L v v v v v The refractve ndex s lnearly related to the molar concentratons of (-1) solutes for -ary soluton. The molar concentraton change rate s dependent on the lght speeds n (-1) lquds v m (m [1, 1]). The above equaton can also be wrttenas follows: ` cp cv vv ( c v ) V (c v ) 1 n (23) v v V v V v V p v where c s lght speed n a vacuum, p s the solute s molar concentraton X m, v s lght speed n the solute wth constant molar concentraton of mol/l and constant refractve ndex, v s lght speed n the soluton, and s the lqud molar concentraton wth constant molar concentraton and refractve ndex. 1 1 Concluson In ths study, a mult-component soluton was modeled and deduced accordng to the tme necessary for monochromatc lght to pass through the medum. The mult component system refractve ndex was found to be lnearly related to each solute s molar concentraton. A detaled correlaton model of the mult-component soluton refractve ndex was proposed, and the model was verfed by a ternary system soluton experment. It s mportant to note that the model was establshed wthout consderng the nteracton between solute ons, and thus would not wor well for a soluton n whch volume s sgnfcantly reduced after dssoluton (e.g., water and ethanol). Further research s needed to mae the necessary volume change correcton. References [1] Jm enezrob oo R J, Phlpp M, Ramos M A et al. Concentraton and Temperature Dependence of the Refractve Index of Ethanol-Water Mxtures: Influence of Intermolecular Interactons[J]. The European Physcal Journal E. 2009,30(10): [2] Yahya M, Saghr M Z. Predcton and Expermental Measurement of Refractve Index n Ternary Hydrocarbon Mxtures[J]. Journal of Chemcal & Engneerng Data, 2015, 60 (8): [3] Ma Xaochun, Dong Junlang, Lang Fang et al. A Fber Optc Salnty Measurement Method Based on the Fresnel Prncple[J]. Laser Technology, 2010, 34(3): [4] Zhao Dewe. A ovel Fast Detectng Devce for Beer Qualty[J]. Global Alcohol Industry Informaton. 2015(1): [5] Glover F A, Goulden J D S, Relatonshp Between Refractve Index and Concentraton of Solutons[J]. ature, 1963, 200(4912): [6] Zhang Zhwe, Yn Wefeng, Wen Tngdun et al. Study on Relatonal Expresson of Soluton Concentraton and Its Refractve Index[J]. Journal of orth Unversty of Chna (atural Scence Edton), 2009, 30(3): [7] Zhu Mn, XnDuqang, XeYanle et al. A method to calculate the refractve ndex of ternary norganc soluton[j]. Journal of Bejng ormal Unversty (atural Scence), 2006, 42(2): [8] Zhang Tao. Refracton of lght n medum[j]. Scence n Chna (Physcs, Mechancs & Astronomy), 2007, 37(2):