Thiele Modulus calculation

In our porous system, the comparison between adsorption and diffusion rates was realized using the Thiele modulus[1]. Its expression is:

(1)

In equation (1) h is the Thiele modulus, VP is the particle volume, SP is the external surface of the particle, and Deff is the effective diffusion coefficient in the porous media for the Cr(VI). In order to represent the adsorption rate, a first kinetic order was choice according to Cao et. al. [2], with a kinetic constant k = 1.510-4s-1

For our spherical particles,VP/SPis equal to DP/6. ADPvalue of 467nmwas used.

The Cr(VI) effective diffusion coefficient was calculated according to Bosanquet [1]:

Deff = DMP /  (2)

The molecular diffusion coefficient of Cr(VI), DM, was estimated following the suggestions of Reid et. al. [3]for the calculus of electrolytes diffusion coefficients, obtaining a DM10-10m2/s.The porosity for a MCM-41 with our structural properties is P = 9x10-2, and it was adopted atortuosity,  1, bearing in mind the straight channels of this mesoporous material. Using these values in equation (2) aDeff910-12m2/s was obtained.

Replacing in equation (1) the values of VP/SP, k y Deff mentioned above, a h2 10-7 was obtained for our system. This value of h2 means that the diffusion rate exceeds in seven orders of magnitude the adsorption rate.It can be concluded that the Cr(VI) concentration is uniform into the porous media since, the influence of the diffusion velocity over the adsorption velocity is negligible.This result can be attributed to the nanometric length and the straightnessof the channels.

Colorimetric method for determination of hexavalent chromium in water [4]

The colorimetric method is useful for the determination of hexavalent chromium in water in the range from 0.1 to 1 ppm. This range can be extended byappropriate sample dilution or concentration and/or use of longer cell paths.

Principle

The hexavalentchromium is determined colorimetrically by reaction with diphenylcarbazide in acid solution. Ared-violet colored complex of unknown composition is produced. The reaction is very sensitive,the molar absorptivity based on chromium,is about 40000 L.g–1.cm–1 at 540 nm.

Procedure

a.Preparation of calibration curve: the first step is to obtain a calibration curve using standard solutions of Cr(VI) in a concentration range appropriate for the sample under study.

b.Color development and measurements: transfer a known aliquot of the Cr(VI) sample to volumetric flask, use 0.2N H2SO4and a pH meter to adjust the pH solution to 1.0 ± 0.3, dilute with water, and mix. Add adiphenylcarbazidesolution, mix, and let stand 5 to 10 min for fullcolor development. Transfer an appropriate portion to a 1-cm absorption cell and measure itsabsorbance at 540 nm, using distilled water as reference.

References

[1] R. Aris, Introduction to the Analysis of Chemical Reactors (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, USA, 1965 ).

[2] J. Cao, Y. Wub, Y. Jin, P. Yilihan, W. Huang, J. Taiwan Inst. Chem. Eng. 45 (2014) 860–868.

[3] R. C. Reid, J. M. Prausnitz, B. E. Poling, The Properties of Gases & Liquids ( McGraw-Hill Inc., 4th Edition, New York, USA, 1987 ).

[4] APHA, 1985. Standard methods for the examination of water and wastewater, 16th ed., Washington, DC.