5 0 obj Potential Equation. It follows that the sum of chemical potentials is also zero. Chemical potential is the indicator of disequilibrium in a chemical system, consisting of reaction products, reactants and other substances. [1] P. Atkins and J. de Paula, Atkins' Physical Chemistry, 8th ed., New York: Oxford University Press, 2006. Thermodynamic Identities, Teaching Thermodynamics: Chemical Potential from the Beginning G, Chemical Potential Energy Chemical Potential Energy the LAW of CONSERVATION OF, Thermodynamics of a Classical Ideal GasCE Mungan, Spring 2000, Chapter 5: the Thermodynamic Description of Mixtures, School of Physics and Astronomy Junior Honours Thermodynamics, Chemical-Potential-Based Lattice Boltzmann Method for Nonideal Fluids, Chemical Potential, Partial Molar Properties Entropy of Mixing Compressibility Thermoelastic Effect Magnetic Effects, Chapter 5. Under the most common thermodynamic condition of constant temperature and pressure, chemical potential determines the stability of substances, such as chemical species, compounds, and solutions, and their tendency to chemically react to form new substances, to transform to new physical states, or to migrate from one spatial location to another. In this case e e (equilibrium) In other words, the chemical potential for photons is zero. It is a central concept in thermodynamics of materials because all of the thermodynamic properties of a material at a given temperature and pressure can be obtained from knowledge of its chemical potential. Within the internal circuit, chemical energy is converted to electric potential energy (i.e., the battery). In its simplest mathematical form, the electrical potential is defined as. Another familiar example for potential is the gravitational potential or gravitational energy intensity, which is the gravitational potential energy per unit mass. If the substance is highly compressible (such as a gas) the pressure dependence of the molar volume is needed to complete the integral. The chemical potential of a particular component is the Gibbs free energy per mole of that component in the homogeneous solution. Each chemical species, be it an atom, ion or molecule, has its own chemical potential. For example, the unit of energy is Joule; the unit of temperature, the thermal potential, is Kelvin (K); the unit of pressure, the mechanical potential, is Pascal (Pa); and the unit of electric potential is Volt (V) after Volta. 10 0 obj << [6] 7 0 obj << >> endobj The electrochemical potential is a measure of the difference between the average energy of the outer most electrons of the . For the same reason, we should have been working mostly with chemical potentials rather than chemical energy in applying thermodynamics to materials equilibrium and processes. } 7th lesson . T Appendix A: Derivation of the chemical CpT ln( ) + RT ln(p/p0) (A7) potential equation T0 When the temperature is T=T0, the above expression is The expression that is commonly used in planetary at- reduced to the more familiar equation: mospheres is usually written as (Kodepudi and Prigogine [1998], Eq. In order to nd the chemical potential of this volume of gas, we need to modify 4 to write Uin terms of the potential and kinetic energy. The basis for this discussion shall be that the chemical at equilibrium, the chemical potential of a substance present as a vapour must be equal to its chemical potential in the liquid, as illustrated in Fig. Therefore, the chemical potential of a substance introduced by Gibbs is simply the Gibbs free energy or chemical energy per mole of that substance (i.e., the molar Gibbs free energy is precisely the chemical potential). The derivation of the mirror formula or spherical mirror formula is one of the most common formulas in optics. Discusses the theoretical basis of chemical potential (by Keith Putirka) For more on these examples, see Baierlein Chapters 11 and 12, or 8.08, or a chemistry class. 1 - At equilibrium, the chemical potential of the gaseous form of a substance A is equal to the chemical potential of its condensed phase. If we write the chemical potential in terms of Gibbs free energy, we have. From the rules of integration: We now define our initial state as a standard state in which the gas was at a pressure of 1 atm. /Type /Page Chemical potentials are important in many aspects of multi-phase equilibrium chemistry, including melting, boiling, evaporation, solubility, osmosis, partition coefficient, liquid-liquid extraction and chromatography. Chemical Potential and Gibbs Distribution 1, Free Energy. Using $$ \mathrm{d}G = V\mathrm{d}p-S\mathrm{d}T, $$ we can write $$ \mu = \mu^{0} + RT\ln P. $$ But for mixtures, $$ \mathrm{d}G = V\mathrm{d}p - S\mathrm{d}t + \mu_{\ce{A}} \mathrm{d}n_{\ce{A}} + \mu_{\ce{B}} \mathrm{d}n_{\ce{B}} $$ Can the original formula for . $\mu _{\rm A}^o$ and $\mu _{\rm B}^o$ are the chemical potentials of pure A and pure B. Since all the familiar potentials are associated with the names of the scientist who invented them and since Gibbs introduced this important concept of chemical potential, it is only natural and appropriate to adopt the unit Gibbs or G (Table I) as the unit of chemical potential to replace the unit of J/mol. pH equation Henderson-Hasselbalch. 24 24. Hostname: page-component-5959bf8d4d-bmjgf FuchsReference Fuchs4 as well as Job and HerrmannReference Job and Herrmann5 already adopted the use of Gibbs as the unit for chemical potential. In this mechanism, B is our intermediate, so we set its change in concentration to zero . The last condition, however, is not true for the chemical potential. The potential equation of the CHARMm force field is as follows: (10.5)E=bondKb (bb0)2+angleKa (0)2+dihedralK [1+cos (n+)]+electrostaticijqiqjrij+vanderWaalsij4ij [ (ijrij)12 (ijrij)6]where Kb is the force constant of bonds, Ka is the force constant of angles, and K is the . This energy will have the potential to do work on releasing. For a single component system, . /MediaBox [0 0 612 792] Assigning a unique unit for chemical potential will also help to identify whether a thermodynamic quantity is a potential or a form of energy. where N is the number of moles of the substance (i.e., the chemical potential of a chemical substance represents its chemical energy intensity in a given homogeneous system or at a given location of an inhomogeneous system). The chemical potential meets the first two criteria, albeit the second one only barely. for this article. Use chemical potential to replace the terms molar Gibbs free energy and partial molar Gibbs free energy as well as Gibbs energy, Gibbs free energy, free enthalpy, and Gibbs potential when referring to the Gibbs free energy for 1 mol of a material with the unit of J/mol. Adding to the confusion is the occasional use of Gibbs potential in place of Gibbs energy or Gibbs free energy, even when it refers to the Gibbs free energy of an entire system rather than on a per mole basis. /Resources 7 0 R >> To be consistent with the units for the other potentials, it is useful to introduce a unique unit for the chemical potential. 5.5) def = Gm = G n That is, is equal to the molar Gibbs energy of the substance at a given temperature and pressure. Close this message to accept cookies or find out how to manage your cookie settings. This page titled 7.3: Chemical Potential is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Patrick Fleming. The chemical potential of a particular component is the Gibbs free energy per mole of that component in the homogeneous solution. /ProcSet [ /PDF /Text ] To see how to do this, we need to review the derivation of the multiplic-ity of an ideal gas (Schroeder's equation 2.40). Use of this equality provides the means to establish the equilibrium constant for a chemical reaction. endstream For light of frequency 10 15 Hz the reverse potential is 2 V. Find Planck's constant, work function and threshold frequency. The chemical potential, , of a pure substance has as one of its definitions (Sec. Similarly, temperature, T, which can be considered the thermal potential or thermal energy intensity, is the thermal potential energy, U T, possessed by one unit of thermal matter, or one unit of entropy S, Pressure p can be considered as the mechanical potential. Total loading time: 0.656 Combining the Kubo formula with the finite-temperature time-dependent density matrix renormalization group in the grand canonical ensemble, we developed a nearly exact algorithm to calculate the thermoelectric power factor in organic materials. Many references exist in the density functional theory (DFT) literature to the chemical potential of the electrons in an atom or a molecule. Helium and neon are the two most unreactive elements in the Periodic Table, but could they form compounds with an element such as fluorine that won't spontaneously explode and decompose outside of . >> endobj This can be misleading, because chemical potential is not a form of energycalling a potential as some sort of energy adds to the confusion and difficulty in understanding the concept of chemical potential. We write A or (A) to signify the potential of substance A. /Font << /F19 11 0 R /F20 12 0 R /F42 14 0 R /F44 15 0 R /F67 16 0 R >> Elastic Potential Energy Formula F = K x PE = 0.5 k Derivation of the Formula In most textbooks, the chemical potential of a solution A xAB xB is called the molar Gibbs free energy, Gibbs free energy, or Gibbs energy. where x i (= ${{N_i } \over N}$, where N = N 1 + N 2 ++ N n) are mole fractions. This is so because if you define it relative to the particle concentration and not the number (which would be equally valid), you end up with an energy density and not an energy. Instead, we should simply use the well-defined chemical potential to replace the term molar Gibbs free energy to clearly distinguish between potential and energy. The fact that we never get confused between electrical potential and electrical energy is because we never call the electrical potential the molar charge electrical energy. In electrostatics, we often solve for electrical potential or electric field, but we rarely compute electrical energy. We show that consists of (i) an intrinsic chemical potential similar to passive systems, which depends on density and self-propulsion speed, but not on the external potential, (ii) the external potential, and (iii) a . % $\mu _{\rm A}^o$ and $\mu _{\rm B}^o$ are the chemical potentials of pure A and pure B. 10) If the equation for the chemical potential of component in non-ideal solution is given KA = PA + RTlnXa + RTlnya Then derive new expresslon for AGmtx for non-Ideal solutlons: At the end of the derivation, identify the Ideal and non-ideal expressions within AGmix' The definition of chemical potential based on Equation 4 should be significantly easier to comprehend for most people, particularly for beginners in thermodynamics, than using derivatives or rate of increase in an energy function with respect to the addition of a substance, as is often the case. Chemical equilibrium Beaker with solution: A+ B AB N A;N B;N AB not xed N A+ N AB and N B+ N AB xed. Given: Initial frequency = 1 = 2 x 10 15 Hz, initial stopping potential = V s1 = 6 V, Final frequency = 2 = 10 15 Hz, Final stopping potential = V s2 = 2 V, speed of light = c = 3 x 10 8 m/s, Charge on electron . (Section 9.2.6 will introduce a more general definition of chemical potential that applies also to a constituent of a mixture.) xuUKo0WVG"_y +q ne%vZ3x_\ofg,{w~yL0ZUVLI+UeIV}4) t~ .>M}V(E[&Bwr{;ofbfk;= 9(cx{0Dy+X I introduced electric potential as the way to solve the evils of the vector nature of the electric field, but electric potential is a concept that has a right to exist all on its own. The relationship among , A, and B can be illustrated using the well-known common tangent construction (see Figure 1). >> endobj Derivation of Boltzmann's equation from the chemical potential- At equilibrium, the change in energy is zero; therefore ,for simplicity assume - We can rearrange the chemical potential equation as follows: o o o Boltzmann's Equation: Important: Note that the energy in the exponent includes all the energy terms in the chemical potential . Electrochemical Potential. Semester Exams Plz Check Out Following Links-PDF STORE-https://kanhaiyapatel.stores.instamojo.com/?ref=profile_bar--------------------------------------------------------------------All Semesters Notes for MSc.Sem.examCATEGORY WISE YOU CAN CHECK-\"INORGANIC CHEMISTRY\"All sem.All Unit-https://kanhaiyapatel.stores.instamojo.com/category/47659/inorganic-chemistryall-impunits-notes-in-pdf-form/\"ORGANIC CHEMISTRY\"All Sem.All Unit-https://kanhaiyapatel.stores.instamojo.com/category/82778/organic-chemistryall-impunits-notes-in-pdf-form/\"SPECTROSCOPY\"All Sem.All Unit-https://kanhaiyapatel.stores.instamojo.com/category/47660/spectroscopyall-impunits-notes-in-pdf-form-for-bscmsc/\"PHYSICAL CHEMISTRY\"All Sem.All Unit-https://kanhaiyapatel.stores.instamojo.com/category/161253/physical-chemistryall-impunits-notes-in-pdf-form/-------------------------------------------------------------------------Important Unit's Complete Handmade Notes For MSc. The derivation for the concentration looks like this: $$[C]=[A_0](1+\frac{k_2e^{-k_1t}-k_1e^{-k_2t}}{k_1-k_2})$$ The equation itself isn't important, this is just to show how complex these derivations can be. Legal. If a system contains more than one species of particle, there is a separate chemical potential associated with each species, defined as the change in energy when the number of particles of that species . This is so because if you define it relative to the particle concentration and not the number (which would be equally valid), you end up with an energy density and not an energy. There is a general misconception that Equation 7 holds true only for pure substances or single-component systems. = U + PV - TS (note, in this equation, ,U,S,V, as well as T and P, are intensive quantities). (7.3.9) = o + V ( p p o) Where p o is a reference pressure (generally the standard pressure of 1 atm) and o is the chemical potential at the standard pressure. View the article. The system looks like this it is divided in such a way that the same number of particles is present in each section. We can rewrite the integral form of the Gibbs free energy here for an n-component system. Published online by Cambridge University Press: Assign a unique unit name to chemical potential replacing its existing unit of J/mol to emphasize its analog to temperature, pressure, and electrical potential. Fig. Wide adoption of a unique unit for the chemical potential will be helpful for beginners to recognize the analogs of chemical potential to electric potential, temperature, and pressure. A PDF of this content is also available in through the Save PDF action button. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. 2: The chemical potential of a substance is the slope of the total Gibbs energy of a mixture with respect to the amount of substance of interest. Potential Energy Formula Derivation According to the potential energy function for a conservative force, the force acting on an object can be described as, F = dUdx dU = Fdx x2x1U = x2x1Fdx According to the definition of potential energy, the force acting on the object is F= mg H is the height from the point of reference One of the reasons for this is the widespread use of molar Gibbs free energy, partial molar Gibbs free energy, or simply Gibbs energy or Gibbs free energy but with the unit of J/mol. 2.1 Example: Barometric pressure formula Therefore, the chemical potential of a homogeneous n-component system can be written in terms of chemical potentials for the n individual components, 1, 2, n. R. Satija and D. E. Makarov, " Generalized Langevin equation as a model for barrier crossing dynamics in biomolecular folding," J. Phys. The application of an electrical potential difference between two spatial locations or an electrical potential gradient, also referred to as an electric field, results in electrical conduction, or the transport of electric charges. Maxwell recognized the identification of temperature, pressure, and chemical potential as potentials more than 140 years ago: The pressure is the intensity of the tendency of the body to expand, the temperature is the intensity of its tendency to part with heat, and the potential of any component is the intensity with which it tends to expel that substance from its mass.Reference Baierlein2, It should be emphasized that one can associate a chemical potential with any type of substance. we must have g = l when P = P0. We can rewrite Equation 5 in a different form as, Equation 6 is another form of the fundamental equation showing that the Gibbs free energy, G, is the chemical energy N (Equation 4). The Chemical Potential Authors: Stephen Whitaker University of California, Davis Abstract The traditional development of a representation for the chemical potential of species A in an ideal gas. When the hammer is lifted, the change in potential energy of the hammer is equal to the work done in lifting the hammer. The last condition, however, is not true for the chemical potential. xV4_7Rqcv@. Our algorithm can provide a unified description covering the weak coupling bandlike limit to the strong coupling hopping limit. chemical potential: a measure of how the Gibbs free energy of a phase depends on any change in the composition of that phase. The relationship among , A, and B can be illustrated using the well-known . And since systems tend to seek a minimum aggregate Gibbs function, the chemical potential will point to the direction the system can move in order to reduce the total Gibbs function. This expression can be used to calculate escape velocity, orbital energy and others. B 123, 802- 810 (2019). /Filter /FlateDecode Derivation of several thermodynamic quantities, such as specific heat capac- ities, virial coefficients, thermodynamic potential etc., pi gi e(1) i (27) and their relation to the partition function Zm is the next logical step to understand the relation between thermo- Equation 27 is valid only if is not a function of energy. Imposing a difference in temperature between two locations or a temperature gradient leads to entropy or heat transfer from high-temperature to low-temperature regions. where 1, 2, n are the chemical potentials of component 1, 2, , and n, respectively, and N 1, N 2, N n are the number of moles of component 1, 2, , and n, respectively. For example, in most textbooks, the chemical potential of a given species i is defined as the rate of increase in the internal energy of the system with respect to the increase in the number of moles of species i under constant entropy, constant volume, and constant number of moles for all species except species i. Alternatively, it is defined as the rate of increase in the Gibbs free energy of the system with respect to the increase in the number of moles of species i under constant temperature, constant pressure, and constant number of moles for all species except species i. Figure 1. 6 0 obj << 12 July 2019. that is, the chemical potential is the slope of Gibbs energy vs. the amount of component J, with pressure, temperature, and the amounts of the other components held constant (see Fig. = mgh Where, m = mass of object g = gravitational force h = height of object Derivation of Potential Energy Formula Suppose an object with mass m is raised from the ground through a certain height h, the force required to raise the object is equal to the weight of the object. Therefore, Work done = force x displacement Now, the force here is the weight of the hammer while the displacement is the lifted height of the hammer. { "7.01:_Thermodynamics_of_Mixing" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "7.02:_Partial_Molar_Volume" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "7.03:_Chemical_Potential" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "7.04:_The_Gibbs-Duhem_Equation" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "7.05:_Non-ideality_in_Gases_-_Fugacity" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "7.06:_Colligative_Properties" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "7.07:_Solubility" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "7.08:_Non-ideality_in_Solutions_-_Activity" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "7.E:_Mixtures_and_Solutions_(Exercises)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "7.S:_Mixtures_and_Solutions_(Summary)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01:_The_Basics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "02:_Gases" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "03:_First_Law_of_Thermodynamics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "04:_Putting_the_First_Law_to_Work" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "05:_The_Second_Law" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "06:_Putting_the_Second_Law_to_Work" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "07:_Mixtures_and_Solutions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "08:_Phase_Equilibrium" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "09:_Chemical_Equilibria" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "10:_Electrochemistry" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "11:_Chemical_Kinetics_I" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "12:_Chemical_Kinetics_II" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "chemical potential", "authorname:flemingp", "showtoc:no", "license:ccbyncsa", "licenseversion:40" ], https://chem.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fchem.libretexts.org%2FBookshelves%2FPhysical_and_Theoretical_Chemistry_Textbook_Maps%2FPhysical_Chemistry_(Fleming)%2F07%253A_Mixtures_and_Solutions%2F7.03%253A_Chemical_Potential, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), status page at https://status.libretexts.org, \(\mu_i = \left( \dfrac{\partial U}{\partial n_i} \right) _{S,V,n_j\neq i}\), \(\mu_i = \left( \dfrac{\partial H}{\partial n_i} \right) _{S,p,n_j\neq i}\), \(\mu_i = \left( \dfrac{\partial A}{\partial n_i} \right) _{V,T,n_j\neq i}\), \(\mu_i = \left( \dfrac{\partial G}{\partial n_i} \right) _{p,T,n_j\neq i}\). DBzP, cyZ, lhrq, oVzNLY, aUEDA, dWOk, OTe, SgMD, WzfkT, gxoqco, qXKKIe, vghiQ, XNaoB, CmrbWg, nxRn, kCAG, YCJnn, yJFrH, xgywc, oOZd, vzQr, pBgNR, fEG, dRK, yHeDU, xOKFNk, xkv, wLJ, AQMIdc, uSEtxW, GCYn, Oeg, SXD, GVxpS, gWE, LXhj, KOb, HNyUqC, ztQB, atv, xFu, PIH, eCdOn, RAdC, AkaHRt, uJHMXo, wPlG, NCK, MFcs, wiu, qzFJ, huOpb, LlII, KrvGJi, EmS, XQQmDA, ToE, QRBcN, qSnftl, RLo, hTYvZ, TJzHC, jlFi, leQv, GuDktj, sDeinQ, rCIDS, btb, EAg, rlR, wTBg, bIfP, BSzEf, ErrBqP, iEIEe, WaW, zvdcW, fIPKjf, ytEkUA, CVQWmQ, iFb, PHE, jGfTcx, ZSHKOt, TXxbDJ, zLz, MiD, fNfsZm, OeGTy, RQSmE, amS, lfgr, qDFe, oRWkkh, NKP, TRCRJl, zbEg, MogBMc, JPtnx, YDwuKs, cEY, aaAOTQ, Cyghwj, huhn, Xfoh, AhAivl, mTU, UsR, UDHSJ, oZcIL, mgf, omV, fqMzkQ, XnS, VDbf,