Refractive Index

Name: Beatriz Marie A. Cerdeňa

Date performed: September 13, 2011

Sec: 3ChED

Date Submitted: September 20, 2011

Group No.: 3

Instructor: Mr. Virgilio Agbayani

Experiment no. 2 REFRACTIVE INDEX

Abstract

The experiment focused on determining the indices of refraction of the different proportions of liquid in a binary mixture. It also aimed to determine the specific and molecular refractivities of each proportion of liquids in a binary mixture as well as to compare the observed molecular refractions with calculated values.

The index of refraction of toluene and methanol at different mol fractions were determined. The indices of refraction of these solutions were determined by reading them in the abbe refractometer. The index of refraction of the solution with 0%methanol is 1.337, 1.349 for 10% methanol, and 1.384 for 20% methanol, 1.404 for 30% methanol, 1.413 for 40% methanol and 1.428 for 50% methanol. The index of refraction is 1.502 for the solution with 0%toluene, 1.498 for 10%toluene, 1.462 for 20%toluene, 1.446 for 30% toluene, 1.431 for 40%toluene and 1.428 for 50%toluene.

INTRODUCTION A refractometer measures the extent to which light is bent or refracted when it moves from air into a sample and is typically used to determine the index of refraction of a liquid sample. The refractive index is a unitless number, between 1.3000 and 1.7000 for most compounds, and is normally determined to five digit precision. Since the index of

refraction depends on both the temperature of the sample and the wavelength of light used these are both indicated when reporting the refractive index. The refractive index is commonly determined as part of the characterization of liquid samples, in much the same way that melting points are routinely obtained to characterize solid compounds. The specific refraction of a substance is calculated through the electromagnetic theory presented by Lorenz and Lorentz: ( ) Where: Rs = the specific refraction of the substance = the index of refraction ρ = the density of the substance at a given temperature Molecular refraction, Rm is obtained by multiplying the specific refraction of the substance with its molecular weight, M:

( )

II. REVIEW OF RELATED LITERATURE Relationship of refractive index to mass density and self-consistency of mixing rules for multicomponent mixtures like ambient aerosols Yangang Liu , Peter H. Daum Abstract This paper focuses on two important yet poorly addressed aspects of ambient aerosols: relationship of refractive index

to mass density (index–density relationship) and

consistency of the mixing rules used to calculate these two quantities of a multicomponent mixture like ambient aerosols with the index–density relationship.

Combined empirical and theoretical analyses show that a denser material generally tends to have a larger refraction index because the applied electric field induces a greater number of electric dipoles, and that the index–density relationship can be described reasonably well by the Lorentz–Lorenz relation. It is shown that the commonly used volume–mean mixing rule for calculating the effective mass density, the Lorentz– Lorenz mixing rule and the molar refraction mixing rule for calculating effective refractive index form a set of mixing rules that are consistent with the Lorentz–Lorenz relation. The molar fraction mixing rule and the Lorentz–Lorenz mixing rule are shown to be equivalent for the Lorentz–Lorenz mixture while the linear volume-mixing rule is an approximation of the Lorentz–Lorenz mixing rule for quasi-homogeneous mixtures wherein the refractive indices of the constituents do not differ much. The results highlight the need for consistency of

the mixing rules for calculating the

effective refractive index and mass density with the index–density relationship, which not only provides a theoretical guide for judiciously choosing the mixing rules to calculate effective properties of ambient aerosols but also poses new challenges to develop an effective medium theory that applies to more than one quantity. An empirical power-law expression is obtained from the published data that relates the effective specific refractive index to the effective mass density of aerosol particles. Refractive index of standard oils as a function of wavelength and temperature Soraya A Khodier Abstract The refractive indices

(n) of eight standard oils from Physikalisch Technische

Bundesanstalt, Germany were determined with an accuracy of ±1×10−4 by using Abbe Refractometer. The measurements were performed at temperature 20°C in the spectral range 0.4–

. The experimental data were fitted to the simple Cauchy dispersion

formula and the results were found to be consistent within the limits of experimental error. In all cases, the refractive index

decreased monotonically with increasing

wavelength. The refractive indices (n) of these oils have been measured as a function of the temperature

up to 50°C) at

and were found to have linear

temperature dependencies. The refractive indices of the studied oils and the uncertainty in their values are calculated at λ=0.589. The Lorentz–Lorenz (L–L) formula has been

tested and it was found to be valid with a maximum deviation of 0.4% and was used to calculate the molecular polarizability θ. Density and Comparative Refractive Index Study on Mixing Properties of Binary Liquid Mixtures of Eucalyptol with Hydrocarbons at 303.15, 308.15 and 313.15K by Sangita Sharma, P B Patel, R S Patel, J J Vora Abstract Density and refractive index have been experimentally determined for binary liquid mixtures of eucalyptol with hydrocarbons (o-xylene, m-xylene and toluene) at 303.15K, 308.15K and 313.15K. A comparative study of Lorentz-Lorenz (L-L), Weiner (W), Heller (H), Gladstone-Dale (G- D), Arago-Biot (A-B), Eykman (Eyk), Newton (Nw), Eyring-John (E-J) and Oster (Os) relations for determining the refractive index of a liquid has been carried out to test their validity for the three binaries over the entire mole fraction range of eucalyptol at 303.15K, 308.15K and 313.15K. Comparison of various mixing rules has been expressed in terms of average deviation. From the experimentally measured values, refractive index deviations at different temperatures have been computed and fitted to the Redlich-Kister polynomial equation to derive the binary coefficients and standard deviations.

III. EXPERIMENT, DATA AND RESULTS The refractive indices of each solution were determined using the abbe refractometer. The reading is taken when the demarcation line between light and dark fields seen through the eyepiece is distinct and that it intersects the cross hairs. As shown in table 1, in the first set of solutions with methanol percentages range from 0 to 50%, the index of refraction increases as the methanol in the solution increases. Table 1. Refractive indices of Solutions with Different Concentrations of Methanol

Methanol

Mass of

Temp (oC)

solution 0%

7.3267

25.6

Index of

Density

refraction

(g/mL)

1.337

0.776

10%

7.4931

25.6

1.349

0.793

20%

7.5874

25.6

1.384

0.803

30%

7.6458

25.6

1.404

0.809

40%

7.6634

25.6

1.413

0.8111

50%

7.7572

25.6

1.428

0.821

For the second set of solutions, with toluene percentage range from 0 to 50%, as the percentage of toluene or amount of toluene in the solution increases, the index of refraction decreases. This relationship is shown in table 2. Table 2. Refractive indices of Solutions with Different Concentrations of Toluene

Toluene

Temp (oC)

Mass of solution

Index of

Density

refraction

(g/mL)

0%

8.0416

27.4

1.502

0.851

10%

7.9370

27.4

1.498

0.841

20%

7.8647

27.4

1.462

0.833

30%

7.8287

27.4

1.446

0.829

40%

7.7676

27.4

1.431

0.822

50%

7.7212

27.4

1.428

0.817

The specific refractivity and molar refractivity of each solution was also determined.

Specific

refractivity

is

obtained

by

using

the

formula

while the molar refractivity is obtained by multiplying the specific refractivity by the average of the molecular weights of the two compounds in the solution. The effect of mole fraction to these values was observed. As shown in table 3, for the first set of solutions, as the mole fraction of methanol increases, the specific refractivity also increases. The relationship between specific refractivity and mole fraction is shown in figure 1. For the solutions (1st set) where there is a mixture of methanol and ethanol, as the mole fraction of methanol increases, the molar refractivity also increases. The molar refractivity of pure toluene (0% methanol) is the highest among the first set of solutions.

Table 3 Specific Refractivity and Molar Refractivity

Methanol

Mole fraction

Rs

Rm

0%

0

0.2680

24.69

10%

0.2599

0.2706

16.796

20%

0.4412

0.2912

18.07

30%

0.5747

0.3023

18.76

40%

0.6784

0.3075

19.09

50%

0.7595

0.3134

19.45

30

Specific refractivity 0.32 0.31 0.3 0.29 0.28 0.27 0.26

Molar refractivity

20 10 0 0

0.2

0.4

0.6

0.8

Figure 1 Specific refractvity vs mol fraction methanol

0

0.2

0.4

0.6

0.8

Figure 2 Molar refractvity vs mol fraction methanol

As shown in table 4, as the molar fraction of toluene (in the second set of solutions) increases, the specific refractivity and molar refractivity decreases. The molar refractivity of pure methanol (0%toluene) is the smallest among the second set of solutions. Table 4. Specific Refractivity and Molar Refractivity

Toluene

Mole fraction

Rs

Rm

0%

0

0.3468

11.1

10%

0.0340

0.3485

21.63

20%

0.0734

0.3300

20.48

30%

0.1194

0.3217

19.97

40%

0.1746

0.3149

19.55

50%

0.2405

0.314903

19.55

Specific refractivity

Molar refractivity

0.36 0.35 0.34 0.33 0.32 0.31

30 20 10 0 0

0.1

0.2

0.3

Figure 2 Specific refractvity vs mol fraction toluene

0

0.1

0.2

0.3

Figure 2 Molar refractvity vs mol fraction toluene

IV. CONCLUSION The indices of refraction of different substances vary. When the substances are mixed, the index of refraction is affected. For pure methanol at 27.4 degrees centigrade, the index of refraction is 1.502 while for pure toluene at 25.6 degrees centigrade, the index of refraction is 1.337. For the different concentrations of methanol in methanol toluene solution, the percentage of methanol is directly proportional to the index of refraction. The mole fraction of methanol in methanol toluene solution is directly proportional to the specific refractivity and molar refractivity. For the different concentrations of toluene in methanol toluene solution, the percentage of toluene is inversely proportional to the index of refraction. The mole fraction of toluene in methanol toluene solution is inversely proportional to the specific refractivity and molar refractivity. It can be directly stated that toluene is more capable of refracting light than methanol even if the temperature in which the readings are taken differ because specific refractivity is an independent value.

REFERENCES Khodier S. (2002) Refractive index of standard oils as a function of wavelength and temperature. Optics and laser technology. vol. 34, no2, pp. 125-128 Liu Y. & Daum P (2008). Relationship of refractive index to mass density and selfconsistency of mixing rules for multicomponent mixtures like ambient aerosols. Journal of Aerosol Science. Volume: 39, Issue: 11, Publisher: Elsevier, Pages: 974-986.

Sharma S et al. (2007). Density and Comparative Refractive Index Study on Mixing Properties of Binary Liquid Mixtures of Eucalyptol with Hydrocarbons at 303.15, 308.15 and 313.15K. Engineering Journal Chem. Volume: 4, Issue: 3,

Pages: 343-349. Refractometry.Available:http://www2.ups.edu/faculty/hanson/labtechniques/refractometr y. Date visited September 15, 2011.

APPENDIX Computation of specific refractivity ( )

( Molar refractivity: Rm=Rs(MW ave solution) Meth1(0%meth) : Rm=0.2680 x 92.14 Toluene (0%toluene) : Rm = 0.3468 x 32 = 11.1 10%meth Rm= 0.2706 x 62.07 = 16.796 10%toluene Rm= 0.3485 x 62.07 = 21.63

Density = mass salution / volume solution Density methanol @ 27.4 oC = 8.0416/9.45 = 0.851 Density toluene @ 25.6 oC = 7.3267/9.45 = 0.776

)