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Introduction: Background Material
Published in Nassir H. Sabah, Neuromuscular Fundamentals, 2020
At equilibrium, r = 0, kf[A]e[B]e = kr[C]e[D]e, where the subscript e refers to the equilibrium state. The equilibrium constant is:
Thermodynamics Entropy and Free Energy
Published in Patrick E. McMahon, Rosemary F. McMahon, Bohdan B. Khomtchouk, Survival Guide to General Chemistry, 2019
Patrick E. McMahon, Rosemary F. McMahon, Bohdan B. Khomtchouk
Any mixture of exactly 1 Molar reactants and products for a reversible reaction will proceed in the spontaneous direction given by the standard enthalpy and entropy, expressed as a value for ΔG°T. The reaction will continue until the concentration of products in the spontaneous direction build up to the point where the concentration entropy exactly cancels the ΔG°T: this is the point of equilibrium. The equilibrium constant defines the corresponding concentrations.
Simple Receptor-Ligand Interactions
Published in John C. Matthews, Fundamentals of Receptor, Enzyme, and Transport Kinetics, 2017
We can now introduce a new term, the equilibrium constant. The equilibrium constant (K) is defined as equal to the ratio of the rate constants. We can see from Equation 6 that K is also equal to the ratio of product and reactant concentrations at equilibrium.
Application of crosslinked chitosan-nanoclay composite beads for efficient removal of Ponceau S azo dye from aqueous medium
Published in Toxin Reviews, 2023
Seda Çınar, Ayşe Dinçer, Ahmet Eser, Tülin Aydemir
The adsorption dynamics can be evaluated by thermodynamic studies. To understand the adsorptive behavior of Ponceau S on crosslinked CS/NC composite beads, thermodynamic parameters were calculated. The free energy change (ΔG°, kJ/mol), enthalpy change (ΔH°, kJ/mol K) and entropy change (ΔS°, kJ/mol K) for the adsorption of dye was calculated using the following equations (3) and (4): Kc is the adsorption equilibrium constant. Enthalpy (ΔH°) and entropy (ΔS°) were calculated from the slope and intercept from the plot of ln Kc versus 1/T. Where Kc = (CA/Ce) is the adsorption equilibrium constant, CA is the amount of Ponceau S dye adsorbed on the CS/NC composite beads at equilibrium (mg/L); Ce is the equilibrium concentration of the Ponceau S dye in the solution (mg/L). T (K) is the absolute temperature; R is the gas constant (Cheruiyot et al.2019, Banisheykholeslami et al.2021, Priyadarshini et al.2021, Sultana et al.2022). ln KC-1/T graphics and the calculated thermodynamic parameters were given in Figure 5 and Table 3.
Mercury(II) decontamination using a newly synthesized poly(acrylonitrile-acrylic acid)/ammonium molybdophosphate composite exchanger
Published in Toxin Reviews, 2022
Adel A. El-Zahhar, Abubakr M. Idris
The Van’t Hoff plot, lnkd against the reciprocal of absolute temperature (1/T), is shown in Figure 3(d). The results show that the amount of Hg(II) adsorbed on either P(AN-AA)/AMP or P(AN-AA) resins increased as reaction temperature increased. This finding could be attributed to that Hg(II) ions become more mobile at high temperatures and have sufficient energy to interact with the resin active sites. Furthermore, the resins could be highly swelled at high temperatures, which facilitate ions to penetrate within the resin particles resulting in adsorption increase (Doğan and Alkan 2003). The reaction thermodynamics, that is, free energy (ΔG°) (kJ/mol), enthalpy (ΔH°) (kJ/mol), and entropy (ΔS°) (J/mol.K) changes, were determined using Equations (9), (10), and (11); where kd is the equilibrium constant, T (K) is the absolute temperature, R is the gas constant (8.314 J/mol.K), ΔG° is standard free energy changes (J); R is the universal gas constant, 8.314 J/mol K, and T is the absolute temperature (K).
Equilibria, kinetics and mechanism for the degradation of the cytotoxic compound L-NG-nitroarginine
Published in Drug Development and Industrial Pharmacy, 2018
Pham Van Quyet, Bernice Mei Jin Tan, Celine Valeria Liew, Lai Wah Chan, Quan Sing Ng, Paul Wan Sia Heng
The kinetic and equilibrium constants are useful for determining and evaluating the stability of compounds under different conditions [17–20]. It was previously shown that LNNA is highly stable in acidic solutions. Therefore, a practical approach would be to prepare a concentrated solution of LNNA at low pH. Prior to use, this solution can be diluted with slightly basic media to achieve an acceptable pH for injection/infusion. A stable injectable LNNA solution with high drug load of 60 mg/ml was desired. In the following example, the concentration of a 5 ml HCl solution that can completely dissolve 300 mg LNNA was determined. The known parameters are substituted into Equation (14):