Chemical Equilibrium

2021 ◽  
pp. 254-275
Author(s):  
Christopher O. Oriakhi
Keyword(s):  
Equilibrium Constant ◽  
Chemical Reaction ◽  
Chemical Equilibrium ◽  
Equilibrium Position ◽  
Dynamic Equilibrium ◽  
Reaction Conditions ◽  
The Relationship ◽  
Equilibrium Calculations

Chemical Equilibrium reviews the principles of equilibrium in systems of gases and liquids, starting with the concepts of reversible and irreversible reactions and dynamic equilibrium. The equilibrium constant (K) and reaction quotient (Q) are described, and comparison of K and Q is used to determine the direction in which a reaction must proceed to reach equilibrium. Calculations involving K in terms of concentration and pressure are presented. The relationship between the magnitude of K, the equilibrium position and the concentrations of reactants and products is discussed for both homogeneous and heterogeneous equilibria. The chapter ends with a qualitative treatment of equilibrium based on Le Chatelier’s principle, as well as how changes in reaction conditions can disturb a chemical equilibrium and how the chemical reaction responds to those changes.

Chemical Equilibrium

2009 ◽  
Author(s):  
Christopher O. Oriakhi
Keyword(s):  
Equilibrium Constant ◽  
Chemical Equilibrium ◽  
Cold Water ◽  
Reverse Reaction ◽  
Mass Action ◽  
Forward Reaction ◽  
Chemical Equilibria ◽  
Partial Pressures ◽  
The Relationship ◽  
Dynamic Equilibria

Many chemical reactions go to completion; i.e., all the reactants are converted to products. A good example is the reaction of calcium with cold water. . . Ca(s)+2 H2O(l) → Ca(OH)2(s)+ H2(g) . . . There is no evidence that the reverse reaction occurs. Such reactions are said to be irreversible. On the other hand, many reactions are reversible: the process can be made to go in the opposite direction. This means that both the reactants and products will be present at any given time. A reversible reaction is defined as one in which the products formed can react to give the original reactants. A double arrow is used to indicate that the reaction is reversible, as illustrated by the general equation:. . . aA+bB ⇌ cC +dD. . . At the start of the reaction, the reactants convert more quickly to products than products turn back to reactants because the reactants are present in much greater amount. Eventually the concentration of products is sufficient for the reverse reaction to become significant. The reaction is said to reach equilibrium when the net change in the products and reactants is zero, i.e., the rate of forward reaction equals the rate of reverse reaction. Chemical equilibria are dynamic equilibria because, although nothing appears to be happening, opposing reactions are occurring at the same rate. Figure 17-1 illustrates that for a reaction in chemical equilibrium, the rate of forward reaction equals the rate of reverse reaction. When a chemical reaction is at equilibrium, the concentrations of reactants and products are constant. The relationship between the concentrations of reactants and products is given by the equilibrium expression, also known as the law of mass action. For the general reaction:. . . aA+bB cC +dD. . . at a constant temperature, the equilibrium constant expression is written as: Kc = [C]c[D]d/[A]a[B]b where [A], [B], [C], and [D] are the molar concentrations or partial pressures of A,B,C, and D at equilibrium. The exponents a,b, c, and d in the equilibrium expression are the coefficients in the balanced equation; Kc is the equilibrium constant and is not given units. The subscript c shows that K is in terms of concentration. The numerical value for Kc is usually determined experimentally.

scholarly journals Measuring and Modeling the Solubility of Hydrogen Sulfide in rFeCl3/[bmim]Cl

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 652
Author(s):  
Huanong Cheng ◽  
Na Li ◽  
Rui Zhang ◽  
Ning Wang ◽  
Yuanyuan Yang ◽  
...  
Keyword(s):  
Ionic Liquid ◽  
Hydrogen Sulfide ◽  
Equilibrium Constant ◽  
Chemical Reaction ◽  
Chemical Equilibrium ◽  
Thermodynamic Model ◽  
Equilibrium Thermodynamic ◽  
Mean Relative Error ◽  
The Mean ◽  
Reaction Equilibrium

The solubility of hydrogen sulfide in different mole ratios of ferric chloride and 1-butyl-3-methylimidazolium chloride ionic liquid (rFeCl3/[bmim]Cl, r = 0.6, 0.8, 1.0, 1.2, 1.4) at temperatures of 303.15 to 348.15 K and pressures of 100 to 1000 kPa was determined. The total solubility increased with the increase of pressure and the decrease of temperature. The solubility data were fitted using the reaction equilibrium thermodynamic model (RETM). The mean relative error between the predicted value and the measured value was less than 4%. Henry’s coefficient and the equilibrium constant of chemical reaction at each temperature were calculated. Henry’s coefficient first decreased and then increased with the increase of mole ratio, and increased with the increase of temperature. The equilibrium constant of the chemical reaction followed the same law as Henry’s coefficient. The chemical solubility was related to both Henry’s coefficient and the chemical equilibrium constant. H2S had the highest chemical solubility in FeCl3/[bmim]Cl at a mole ratio of 0.6 and a temperature of 333.15 K. The chemical solubility increased with the increase of pressure.

Complete monotonicity of entropy production in chemical reaction

1981 ◽  
Vol 46 (2) ◽  
pp. 452-456
Author(s):  
Milan Šolc
Keyword(s):  
Entropy Production ◽  
Equilibrium Constant ◽  
Chemical Reaction ◽  
Relative Entropy ◽  
Order Reaction ◽  
Complete Monotonicity ◽  
First Order Reaction ◽  
First Order ◽  
Completely Monotonic ◽  
Derivatives Of

The successive time derivatives of relative entropy and entropy production for a system with a reversible first-order reaction alternate in sign. It is proved that the relative entropy for reactions with an equilibrium constant smaller than or equal to one is completely monotonic in the whole definition interval, and for reactions with an equilibrium constant larger than one this function is completely monotonic at the beginning of the reaction and near to equilibrium.

Chemical equilibrium and chemical kinetics

2018 ◽  
Author(s):  
Dennis Sherwood ◽  
Paul Dalby
Keyword(s):  
Free Energy ◽  
Equilibrium Constant ◽  
Gibbs Free Energy ◽  
Chemical Kinetics ◽  
Chemical Equilibrium ◽  
First Principles ◽  
Effect Of Temperature ◽  
Total System ◽  
Free Energies

Building on the previous chapter, this chapter examines gas phase chemical equilibrium, and the equilibrium constant. This chapter takes a rigorous, yet very clear, ‘first principles’ approach, expressing the total Gibbs free energy of a reaction mixture at any time as the sum of the instantaneous Gibbs free energies of each component, as expressed in terms of the extent-of-reaction. The equilibrium reaction mixture is then defined as the point at which the total system Gibbs free energy is a minimum, from which concepts such as the equilibrium constant emerge. The chapter also explores the temperature dependence of equilibrium, this being one example of Le Chatelier’s principle. Finally, the chapter links thermodynamics to chemical kinetics by showing how the equilibrium constant is the ratio of the forward and backward rate constants. We also introduce the Arrhenius equation, closing with a discussion of the overall effect of temperature on chemical equilibrium.

scholarly journals MUC1 and MUC5AC Acting on Helicobacter pylori-Related Deficiency and Solid Syndrome of Spleen and Stomach

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Ling Hu ◽  
Wanqun Chen ◽  
Ming Cheng ◽  
Ting Zhang ◽  
Shaoyang Lan ◽  
...  
Keyword(s):  
Helicobacter Pylori ◽  
Dynamic Equilibrium ◽  
Deficiency Syndrome ◽  
Blue Staining ◽  
Significant Difference ◽  
Tai Ji ◽  
Hematoxylin And Eosin ◽  
Relationship Of ◽  
Heat Syndrome ◽  
The Relationship

To investigate the relationship of MUC1, MUC5AC, and the syndrome of spleen and stomach, 109 subjects (34 peptic ulcer (PU), 62 chronic gastritis (CG), and 13 healthy volunteers (CON)) were included. All the subjects included were surveyed with questionnaire to classify them into damp-heat syndrome of spleen and stomach (DHSS), spleen-qi deficiency syndrome (SQD), and CON, examined by gastric endoscope, and biopsied. Rapid urease and methylene blue staining (MBS) were performed on every subject to diagnose for Helicobacter pylori (Hp) infection, and both were defined as Hp-positive. Hematoxylin and eosin (HE) staining was performed on every specimen to explore the histomorphology, inflammatory degree, and inflammatory activity of different groups; then Elivision™ plus kit was used to test the expression of MUC1 and MUC5AC. All the results of digital images were reviewed by two experts blindly. The inflammatory degree with Hp infection was higher than those uninfected or CON, but no significant difference was found between DHSS and SQD. And the expressions of MUC5AC with positive Hp was higher than those with negative Hp or CON regardless of the deficiency and solid syndrome of spleen-stomach but not for MUC1. We speculate that the deficiency and solid syndrome of spleen-stomach is a condition like Tai Ji symbol of dynamic equilibrium, showing the higher expression of MUC5AC but no change of MUC1 in the circumstance of Hp infection.

scholarly journals Kinetics and optimization on discoloration of dyeing wastewater by schorl-catalyzed fenton-like reaction

2014 ◽  
Vol 79 (3) ◽  
pp. 361-377 ◽  
Author(s):  
Huan-Yan Xu ◽  
Wei-Chao Liu ◽  
Shu-Yan Qi ◽  
Yan Li ◽  
Yuan Zhao ◽  
...  
Keyword(s):  
Response Surface ◽  
Reaction Rate Constant ◽  
Second Order ◽  
Order Kinetic ◽  
Reaction Conditions ◽  
Design And Optimization ◽  
Order Kinetic Model ◽  
Kinetic Investigations ◽  
The Relationship ◽  
Experimental Design And Optimization

Kinetics and optimization on the discoloration of an active commercial dye, Argazol Blue BFBR (ABB) by heterogeneous Fenton-like reaction catalyzed by natural schorl were investigated in this study. Kinetic investigations revealed that the first-order kinetic model was more favorable to describe the discoloration of ABB at different reaction conditions than the second-order and Behnajady-Modirshahla-Ghanbery models. The relationship between the reaction rate constant k and reaction temperature T followed the Arrhenius equation, with the apparent activation energy Ea of 51.31kJ?mol-1. The central composite design under the response surface methodology was employed for the experimental design and optimization of the ABB discoloration process. The significance of a second order polynomial model for predicting the optimal values of ABB discoloration was evaluated by the analysis of variance and 3D response surface plots for the interactions between two variables were constructed. Then, the optimum conditions were determined.

Dynamic Stability of Hovercraft in Heave

1970 ◽  
Vol 37 (4) ◽  
pp. 895-900 ◽  
Author(s):  
H. J. Davies ◽  
G. A. Poland
Keyword(s):  
Mathematical Model ◽  
Dynamic Behavior ◽  
Dynamic Stability ◽  
Equilibrium Position ◽  
Forced Oscillation ◽  
Dynamic Equilibrium ◽  
Forced Oscillations ◽  
Two Dimensional ◽  
Oscillation Characteristics ◽  
Nonlinear Nature

The regimes of flow governing the dynamic behavior of a two-dimensional mathematical model of an edge-jet Hovercraft in heaving motion are described and the equations associated with such regimes derived. Both the free and forced-oscillation characteristics are studied. The nonlinear nature of the system manifests itself, in the case of the forced oscillations, as a shift in the dynamic equilibrium position resulting in a loss of mean hoverheight.

scholarly journals Full characterization of GPCR monomer–dimer dynamic equilibrium by single molecule imaging

2011 ◽  
Vol 192 (3) ◽  
pp. 463-480 ◽  
Author(s):  
Rinshi S. Kasai ◽  
Kenichi G. N. Suzuki ◽  
Eric R. Prossnitz ◽  
Ikuko Koyama-Honda ◽  
Chieko Nakada ◽  
...  
Keyword(s):  
Equilibrium Constant ◽  
Single Molecule ◽  
Dynamic Equilibrium ◽  
Dissociation Rate ◽  
Formyl Peptide Receptor ◽  
Live Cells ◽  
Imaging Method ◽  
Full Characterization ◽  
Before And After ◽  
Dissociation Rate Constants

Receptor dimerization is important for many signaling pathways. However, the monomer–dimer equilibrium has never been fully characterized for any receptor with a 2D equilibrium constant as well as association/dissociation rate constants (termed super-quantification). Here, we determined the dynamic equilibrium for the N-formyl peptide receptor (FPR), a chemoattractant G protein–coupled receptor (GPCR), in live cells at 37°C by developing a single fluorescent-molecule imaging method. Both before and after liganding, the dimer–monomer 2D equilibrium is unchanged, giving an equilibrium constant of 3.6 copies/µm2, with a dissociation and 2D association rate constant of 11.0 s−1 and 3.1 copies/µm2s−1, respectively. At physiological expression levels of ∼2.1 receptor copies/µm2 (∼6,000 copies/cell), monomers continually convert into dimers every 150 ms, dimers dissociate into monomers in 91 ms, and at any moment, 2,500 and 3,500 receptor molecules participate in transient dimers and monomers, respectively. Not only do FPR dimers fall apart rapidly, but FPR monomers also convert into dimers very quickly.

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