Equilibrium constants, free energy changes, and coupled reactions: Concepts and misconcepts

1986 ◽  
Vol 14 (3) ◽  
pp. 137-141 ◽  
Author(s):  
Ann A McPartland ◽  
Irwin H Segel
Keyword(s):  
Free Energy ◽  
Equilibrium Constants ◽  
Coupled Reactions

Article

1999 ◽  
Vol 77 (5-6) ◽  
pp. 934-942
Author(s):  
J Peter Guthrie
Keyword(s):  
Carbon Dioxide ◽  
Free Energy ◽  
Equilibrium Constants ◽  
Marcus Theory ◽  
Energy Of Activation ◽  
Free Energies ◽  
Orbital Theory ◽  
Activation Free Energy ◽  
Free Energy Of Activation ◽  
Rms Error

Rate constants for hydration of carbon dioxide and ketene can be calculated by applying No Barrier Theory, which needs only equilibrium constants and distortion energies, the latter calculated using molecular orbital theory. The calculated free energies of activation are in satisfactory agreement with experiment: the rms error in free energy of activation is 2.38 kcal/mol. These compounds can also be described using Marcus Theory or Multidimensional Marcus Theory using the transferable intrinsic barrier appropriate to simple carbonyl compounds; in this case the rms error in free energy of activation is 2.19 kcal/mol. The two methods agree on preferred mechanistic path except for uncatalyzed hydration of ketene where Multidimensional Marcus Theory leads to a lower activation free energy for addition to the C=O, while No Barrier Theory leads to a lower free energy of activation for addition to the C=CH2. A rate constant for hydroxide ion catalyzed hydration of ketene can be calculated and is in accord with preliminary experimental results.Key words: ketene, carbon dioxide, hydration, Marcus Theory, No Barrier Theory.

Tautomeric equilibria and pKa values for 'sulfurous acid' in aqueous solution: a thermodynamic analysis

1979 ◽  
Vol 57 (4) ◽  
pp. 454-457 ◽  
Author(s):  
J. Peter Guthrie
Keyword(s):  
Aqueous Solution ◽  
Free Energy ◽  
Aqueous Solutions ◽  
Equilibrium Constants ◽  
Acid Solutions ◽  
Sulfurous Acid ◽  
Free Energy Of Formation ◽  
Dilute Aqueous Solutions ◽  
Sulfite Ion ◽  
Energy Of Formation

The free energy of formation of dimethyl sulfite in aqueous solution can be calculated as −91.45 ± 0.79 kcal/mol; this calculation required measurement of the solubility of dimethyl sulfite. From this value and the pKa of SO(OH)2, using previously reported methods, the free energy of formation of SO(OH)2 can be calculated to be −129.26 ± 0.89 kcal/mol. Comparison of this value with the value obtained from the free energy of formation of 'sulfurous acid' solutions, calculated from the free energy of formation of sulfite ion and the apparent pKa, values, permits evaluation of the free energy of covalent hydration of SO2 as 1.6 + 1.0 kcal/mol, in agreement with earlier qualitative spectroscopic observations. From the apparent pKa and the anticipated pKa values for the tautomers (SO(OH)2, pK1 = 2.3; HSO2(OH), pK1 = −2.6) it is possible to calculate the free energy change for tautomerization of SO(OH)2 to H—SO2(OH) as +4.5 ± 1.2 kcal/mol. All equilibrium constants required for Scheme 1, describing the species present in dilute aqueous solutions of SO2, have been calculated. In agreement with previous Raman studies the major tautomer of 'bisulfite ion' is calculated to be H—SO3−.

Free energy

2018 ◽  
Author(s):  
Dennis Sherwood ◽  
Paul Dalby
Keyword(s):  
Free Energy ◽  
Gibbs Free Energy ◽  
Helmholtz Free Energy ◽  
Chemical Potential ◽  
Free Energies ◽  
Central Concept ◽  
Mathematical Properties ◽  
Closed Systems ◽  
Coupled Reactions ◽  
Enthalpy And Entropy

A critical chapter, explaining how the principles of thermodynamics can be applied to real systems. The central concept is the Gibbs free energy, which is explored in depth, with many examples. Specific topics addressed are: Spontaneous changes in closed systems. Definitions and mathematical properties of Gibbs free energy and Helmholtz free energy. Enthalpy- and entropy-driven reactions. Maximum available work. Coupled reactions, and how to make non-spontaneous changes happen, with examples such as tidying a room, life, and global warming. Standard Gibbs free energies. Mixtures, partial molar quantities and the chemical potential.

Effect of Different Substituents on Uracil and its 2-Hydroxy-4-oxo Enol Tautomer – A Theoretical Study

2008 ◽  
Vol 63 (10-11) ◽  
pp. 693-702
Author(s):  
Hamzeh S. M. Al-Omari
Keyword(s):  
Free Energy ◽  
Gibbs Free Energy ◽  
Theoretical Study ◽  
Equilibrium Constants ◽  
Semiempirical Method ◽  
Forward Direction ◽  
Heat Of Formation ◽  
Geometrical Parameters ◽  
Homo And Lumo ◽  
Enol Tautomer

The uracil/2-hydroxy-4-oxo uracil tautomeric system was studied by employing the MNDO semiempirical method for the calculations. The uracil structure was found to be energetically favourable as indicated by the calculated heat of formation, the Gibbs free energy, the HOMO and LUMO energies, and charges. The substitution by F, OH, NH2, CH3, and BH2 at the carbon-6 position was found to affect the geometrical parameters of the substituted molecules. All of the substituents were found to shift the equilibrium in forward direction compared to the unsubstituted tautomeric pair as indicated by the calculated values for the equilibrium constants.

The Solubility of Metallic Selenium under Anoxic Conditions

2000 ◽  
Vol 663 ◽  
Author(s):  
Yoshihisa Iida ◽  
Tetsuji Yamaguchi ◽  
Shinichi Nakayama ◽  
Tomoko Nakajima ◽  
Yoshiaki Sakamoto
Keyword(s):  
Free Energy ◽  
Solid Phase ◽  
Equilibrium Constants ◽  
Absorption Spectrometry ◽  
X Ray Diffraction ◽  
Molar Free Energy ◽  
Anoxic Conditions ◽  
X Ray ◽  
Free Energy Of Formation ◽  
Energy Of Formation

ABSTRACTThe solubility of metallic selenium was measured in a mixture of 0.1M-NaCl and 0.05M-N2H4under anoxic conditions (O2 < 1 ppm) by both oversaturation and undersaturation methods. Equilibrium was attained in 40 days. The aqueous selenium species identified were HSe at pH between 5 and 8, and Se42at pH between 10 and 13, by UV-Vis absorption spectrometry. The solid phase was identified as Se (cr) by X-ray diffraction. The equilibrium constants ofSe(cr) + H+ + 2e- = HSe- logK0 = -6.5±0.5 and4Se(cr) + 2e- = Se42- logK0 = -16.8±0.5were determined. The standard molar free energy of formation of HSe- and Se42-was determined to be (37.1±2.9) and (95.9±2.9) kJ/mol, respectively.

scholarly journals Theory for rates, equilibrium constants, and Brønsted slopes in F1-ATPase single molecule imaging experiments

2015 ◽  
Vol 112 (46) ◽  
pp. 14230-14235 ◽  
Author(s):  
Sándor Volkán-Kacsó ◽  
Rudolph A. Marcus
Keyword(s):  
Ligand Binding ◽  
Single Molecule ◽  
Driving Forces ◽  
Equilibrium Constants ◽  
Reaction Rates ◽  
Exponential Dependence ◽  
Single Molecule Imaging ◽  
Free Energies ◽  
Coupled Reactions ◽  
Stall Angle

A theoretical model of elastically coupled reactions is proposed for single molecule imaging and rotor manipulation experiments on F1-ATPase. Stalling experiments are considered in which rates of individual ligand binding, ligand release, and chemical reaction steps have an exponential dependence on rotor angle. These data are treated in terms of the effect of thermodynamic driving forces on reaction rates, and lead to equations relating rate constants and free energies to the stalling angle. These relations, in turn, are modeled using a formalism originally developed to treat electron and other transfer reactions. During stalling the free energy profile of the enzymatic steps is altered by a work term due to elastic structural twisting. Using biochemical and single molecule data, the dependence of the rate constant and equilibrium constant on the stall angle, as well as the Børnsted slope are predicted and compared with experiment. Reasonable agreement is found with stalling experiments for ATP and GTP binding. The model can be applied to other torque-generating steps of reversible ligand binding, such as ADP and Pi release, when sufficient data become available.

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