Refractive Index

Name: Beatriz Marie A. Cerdeňa Date performed: September 13, 2011

Sec: 3ChED Group No.: 3 Date Submitted: September 20, 2011 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 refractiveindexand 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.

Refractiveindexof 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 refractiveindices (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 solution Temp (oC) Index of refraction Density (g/mL) 0% 7.3267 25.6 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 Mass of solution Temp (oC) Index of refraction Density (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

Figure 1 Specific refractvity vs mol fraction methanol 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 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0 0.2 0.4 0.6 0.8

Specific refractivity

Molar refractivity

Figure 2 Specific refractvity vs mol fraction toluene 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.

0.31 0.32 0.33 0.34 0.35 0.36 0 0.1 0.2 0.3

Specific refractivity

Molar refractivity

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 refractiveindexto mass density and self-consistency 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).

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