Hi,

is R2 0.02? It is incredibly low. It may happen by two reasons: (1) all three points  (lnK) show against 1/K a scatter even not approaching to linear trend;  (2) all three points show good linear dependence with a slope approaching zero, i.e.,  no effect of temperature, or formally the enthalpy change, within the model, close to zero; and it is Ok!.

If the latter is the case, you might want to check also how the Langmuir maximal capacity changes (or not) with temperature. Very often, when looking at lnK (Langmuir) vs 1/T, the changes in maximal coverage is not examined. and it is pity. Since K is obtained from a model, one should check also if all the model assumptions are Ok, and the independence of Langmuir maximal capacity on the temperature is one of them.

or...just overimpose all three isotherms determined at three temperatures? do they coincide?

Now, I would suggest to do also something else than using the Langmuir model  (the use of which may lead some poorly recognizable difficulties): since isotherms are measured at three temperatures, try to determine isosteric heat, i.e, plotting ln C(solution) at a constant sorbed concentration vs 1/T. This procedure made for different loadings might help to check whether sorption heat depends on a specific sorbhend concentration.

Are three temperature sufficient? Difficult question. It depends on the range of temperatures, and data accuracy, and whether a non-linearity of Vant-Hoff plot is statistically detectable.

Hi Mikhail Borisover,

Thank you so much for your response. I willlook at the other plots you recommended and see if that helps my data. I too had wondered if the slope was too small and meant it was approaching zero. ( it is -85). I appreciate all your help! Thanks!

Hi Bobbi,

If Langmuir isotherm is fitting well to your process, then I would suggest you try one another method for estimation of change in enthalpy and entropy. The values of Langmuir constant i.e. b obtained from the linear plot of isotherms multiply that value with the molecular weight of binding molecule then b will be in units L/mmol. If you have plotted isotherms at three temperatures then you will get three values of b. use these values to calculate Gibbs free energy dG=-RTlnb. The values of b can be used in Vant-toff eq. to estimate dH by taking modified eq. ln(b2/b1)= -dh/R*(Ti-T2/T1T2). Now after getting the values of dG and dH put in eq dG=dH-Tds rearrange the equation and you will get the value of dS. 

I hope this will be helpful.

Regards 

Sumit

Hello Bobbi: To answer, I would like to know if you have solid particles in an aqueous solution. If so, I would have to write a whole article as an answer. Instead here is a list of publications. There are too many key points for me to cover them here.

Selected References

1. M. T. Lam, D. S. Gamble, C. L. Chakrabarti and A. L. Ismaily. On - line micro extraction of Zn(II) and Cd(II) in soil slurries: A chemical speciation method. Intern. J. Environ. Anal. Chem. 64, 217 - 231 (1996).

57. C. M. Monreal, H. Dinel, M. Schnitzer and D. S. Gamble. Impact of carbon sequestration on indicators of soil quality as influenced by management in sustainable agriculture. Advances in Soil Sci. (1996).

58. Jinhe Li, Cooper H. Langford and Donald S. Gamble. Atrazine sorption by a mineral soil: Processes of labile and nonlabile uptake. J. Agric. Food Chem. 44, 3672 - 3679 (1996).

59. Jinhe Li, Cooper H. Langford and Donald S. Gamble. Atrazine sorption by a mineral soil: The effects of size fractions and temperature. J. Agric. Food Chem. 44, 3680 - 3684 (1996).

60. Donald W. Gutzman, Donald S. Gamble and Jacques Millette. Thermodynamic and kinetic behaviour of free and bound toxins: Atrazine and metolachlor interactions with aquatic sediments. Proceedings, Exotox Workshop. Winnipeg, Manitoba. June 16 - 19. (1996).

61. Luis E. Sojo, Donald S. Gamble, and Donald W. Gutzman. Sorption and bound residue formation of linuron, methylparathion, and metolachlor by carrot tissues: Kinstics by on - line microextraction. J. Agric. Food Chem. 45, 3634 - 3641 (1997).

62 Donald S. Gamble. Pesticide - soil interaction research for the behavior of chlorothalonil and its metabolite SDS - 3701 in soil. Final Report, submitted to Ricerca Inc. of Painesville Ohio September 15, 1998.

63 Li, J. S.O. Prasher. R.S. Clemente, W.D. Reynolds, W.N. Smith, D.S. Gamble, E. Topp,

C.H. Langford, and F. Salehi. Modeling the sorption behavior of atrazine on intact soilcolumns. Journal of Irrigation and Drainage Engineering. 125(4), 212 - 222 (1999).

64 Donald S. Gamble, Aldo G. Bruccoleri, Elspeth Lindesay, Gregory A. Leyes and Cooper H. Langford. Chlorothalonil in a quartz sand soil: Speciation and kinetics. Environ. Sci. Technol. 34, 120 - 124 (2000).

65 Donald S. Gamble, Aldo Bruccoleri, Elspeth Lindsay, Cooper H. Langford and Gregory A. Leyes. Chlorothalonil in a quartz sand soil: Wetting effects on sorption capacity and bound residue. Environ. Sci. Technol. 34, 125 - 129 (2000).

66 R. Sha’ato, E. Buncel, D. S. Gamble and G. W. vanLoon. Kinetics and equilibria of Metribuzin sorption on model soil components. Can. J. Soil Sci. 80: 301–307 (2000).

67 Donald S. Gamble, Elspeth Lindsay, Aldo G. Bruccoleri, cooper H. Langford, and Gregory A. Leyes. Chlorothalonil And Its 4-Hydroxy Derivative In Simple Quartz Sand Soils: A Comparison Of Sorption Processes. Environ. Sci. Technol. 35, 2375 - 2380 (2001).

68 Donald S. Gamble, Cooper H. Langford, and Aldo G. Bruccoleri. Chemical stoichiometry and molecular level mechanisms as support for future predictive engineering. Chapter 6 In, Eds. I. V. Perminova, N. Herkorn, and P. Baveye. Use of humic substances to remediate polluted environments: From theory to practice. NATO Science Series. Kluwer Academic Publisher. Dordrecht. (2005).

69 Donald S. Gamble and Marc Lamoureux. Analytical chemical methods for determining reaction mechanisms in soils and sediments. Department of Chemistry, Saint Mary’s University. Halifax Nova Scotia B3H 3C3. Refereed proceedings, EnviroAnalysis 2006, The 6th Biennial Conference on Monitoring and Measurement of the Environment Toronto, Canada from May 15-17, (2006).

70 Donald S. Gamble. Atrazine Sorption kinetics in a characterized soil: Predictive calculations. Environ. Sci. Technol. 42, 1537 - 1541 (2008).

71 Donald S. Gamble. Herbicide sorption by immersed soils: Stoichiometry and the law of mass action in support of predictive kinetics. Environ. Sci. Technol. 43(6), 1930 - 1934 (2009).

72 D. S. Gamble, G. R. Barrie Webster, Marc Lamoureux, Quantitative Prediction Of Atrazine Sorption In A Manitoba Soil Using Conventional Chemical Kinetics Instead Of Empirical Parameters. J. Phys. Chem. C 2010, 114, 20055-20061. Internet.

73 Donald S. Gamble, G. R. Barrie Webster, and Marc Lamoureux. Pesticide reaction mechanism in soil: an interactive spreadsheet model based on conventional chemical kinetics. J. Environ. Monit., 2012, 14 (4), 1166 - 1172. Advance Article DOI: 10.1039/C2EM10366D

74 Donald S. Gamble. Discoveries Leading To Conventional Chemical Kinetics For Pesticides In Soils: A Review. Chapter 6. In, Donald L. Sparks, Ed. Advances In Agronomy Volume 120, June 2013.

75 Heather A. Gamble1, Donald S. Gamble2. A Quantitative LC-MS/MS Study of the

Partitioning, Transport, and Fate of Pesticide Residues on Soil. Journal of Environmental Protection, 2016, 7, 331-340. http://dx.doi.org/10.4236/jep.2016.73029 .

76 Donald S. Gamble and Aldo G. Bruccoleri. Pesticide regulations for agriculture: Chemically flawed regulatory practice. Journal of Environmental Science and Health, Part B. 2016, Vol. 0, No. 0, 1–7. http://dx.doi.org/10.1080/03601234.2016.1171646.

cations.

Do you require some else other than Prof. Kumar to answer this question?

Entropy: A concept that is not a physical quantity

https://www.researchgate.net/publication/230554936_Entropy_A_concept_that_is_not_a_physical_quantity