# Хемијска равнотежа

Хемијска равжнотежа је стање у реакционом систему при којем се концентрације реактаната и продуката не мењају током времена.[1] До равнотеже обично долази када се код повратних хемијских реакција брзине ракција у оба смера изједначе. То не значи да су брзине једнаке нули него да су, ма колике биле, брзине хемијских реакција у оба смера изједначене.[2]

Општи пример би изгледао овако:

${\displaystyle mA+nB\leftrightarrow pC+qD}$

На основу закона о дејству маса и чињенице да су, по постизању равнотеже, брзине реакције улево и удесно једнаке може се написати следеће:

${\displaystyle K_{eq}\equiv {\frac {k_{AB}}{k_{CD}}}={\frac {\left[C\right]^{p}\left[D\right]^{q}}{\left[A\right]^{m}\left[B\right]^{n}}}}$

Знајући константу равнотеже (Keq) на основу равнотежних концентрација осталих учесника могуће је израчунати непознату равнотежну концентрацију преосталог учесника у реакцији.

Далеко занимљивији и важнији су утицаји промене фактора под којима се реакција одвија (температура, притисак, концентрације...) на равнотежу реакције.[3][1] Претпоставке у вези са овим даје Ле Шатељеов принцип. Он има велике практичне импликације.

## Историјски увод

The concept of chemical equilibrium was developed in 1803, after Berthollet found that some chemical reactions are reversible.[4] For any reaction mixture to exist at equilibrium, the rates of the forward and backward (reverse) reactions must be equal. In the following chemical equation, arrows point both ways to indicate equilibrium.[5] A and B are reactant chemical species, S and T are product species, and α, β, σ, and τ are the stoichiometric coefficients of the respective reactants and products:

α A + β B ⇌ σ S + τ T

The equilibrium concentration position of a reaction is said to lie "far to the right" if, at equilibrium, nearly all the reactants are consumed. Conversely the equilibrium position is said to be "far to the left" if hardly any product is formed from the reactants.

Guldberg and Waage (1865), building on Berthollet's ideas, proposed the law of mass action:

{\displaystyle {\begin{aligned}{\text{forward reaction rate}}&=k_{+}{\ce {A}}^{\alpha }{\ce {B}}^{\beta }\\{\text{backward reaction rate}}&=k_{-}{\ce {S}}^{\sigma }{\ce {T}}^{\tau }\end{aligned}}}

where A, B, S and T are active masses and k+ and k are rate constants. Since at equilibrium forward and backward rates are equal:

${\displaystyle k_{+}\left\{{\ce {A}}\right\}^{\alpha }\left\{{\ce {B}}\right\}^{\beta }=k_{-}\left\{{\ce {S}}\right\}^{\sigma }\left\{{\ce {T}}\right\}^{\tau }}$

and the ratio of the rate constants is also a constant, now known as an equilibrium constant.

${\displaystyle K_{c}={\frac {k_{+}}{k_{-}}}={\frac {\{{\ce {S}}\}^{\sigma }\{{\ce {T}}\}^{\tau }}{\{{\ce {A}}\}^{\alpha }\{{\ce {B}}\}^{\beta }}}}$

By convention, the products form the numerator. However, the law of mass action is valid only for concerted one-step reactions that proceed through a single transition state and is not valid in general because rate equations do not, in general, follow the stoichiometry of the reaction as Guldberg and Waage had proposed (see, for example, nucleophilic aliphatic substitution by SN1 or reaction of hydrogen and bromine to form hydrogen bromide). Equality of forward and backward reaction rates, however, is a necessary condition for chemical equilibrium, though it is not sufficient to explain why equilibrium occurs.

Despite the failure of this derivation, the equilibrium constant for a reaction is indeed a constant, independent of the activities of the various species involved, though it does depend on temperature as observed by the van 't Hoff equation. Adding a catalyst will affect both the forward reaction and the reverse reaction in the same way and will not have an effect on the equilibrium constant. The catalyst will speed up both reactions thereby increasing the speed at which equilibrium is reached.[6][7]

Although the macroscopic equilibrium concentrations are constant in time, reactions do occur at the molecular level. For example, in the case of acetic acid dissolved in water and forming acetate and hydronium ions,

CH3CO2H + H2O ⇌ CH
3
CO
2
+ H3O+

a proton may hop from one molecule of acetic acid onto a water molecule and then onto an acetate anion to form another molecule of acetic acid and leaving the number of acetic acid molecules unchanged. This is an example of dynamic equilibrium. Equilibria, like the rest of thermodynamics, are statistical phenomena, averages of microscopic behavior.

Ле Шатељеов принцип (1884) predicts the behavior of an equilibrium system when changes to its reaction conditions occur. If a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to partially reverse the change. For example, adding more S from the outside will cause an excess of products, and the system will try to counteract this by increasing the reverse reaction and pushing the equilibrium point backward (though the equilibrium constant will stay the same).

If mineral acid is added to the acetic acid mixture, increasing the concentration of hydronium ion, the amount of dissociation must decrease as the reaction is driven to the left in accordance with this principle. This can also be deduced from the equilibrium constant expression for the reaction:

${\displaystyle K={\frac {\{{\ce {CH3CO2-}}\}\{{\ce {H3O+}}\}}{{\ce {\{CH3CO2H\}}}}}}$

If {H3O+} increases {CH3CO2H} must increase and CH
3
CO
2
must decrease. The H2O is left out, as it is the solvent and its concentration remains high and nearly constant.

A quantitative version is given by the reaction quotient.

J. W. Gibbs suggested in 1873 that equilibrium is attained when the Gibbs free energy of the system is at its minimum value (assuming the reaction is carried out at a constant temperature and pressure). What this means is that the derivative of the Gibbs energy with respect to reaction coordinate (a measure of the extent of reaction that has occurred, ranging from zero for all reactants to a maximum for all products) vanishes, signaling a stationary point. This derivative is called the reaction Gibbs energy (or energy change) and corresponds to the difference between the chemical potentials of reactants and products at the composition of the reaction mixture.[1] This criterion is both necessary and sufficient. If a mixture is not at equilibrium, the liberation of the excess Gibbs energy (or Helmholtz energy at constant volume reactions) is the "driving force" for the composition of the mixture to change until equilibrium is reached. The equilibrium constant can be related to the standard Gibbs free energy change for the reaction by the equation

${\displaystyle \Delta _{r}G^{\ominus }=-RT\ln K_{\mathrm {eq} }}$

where R is the universal gas constant and T the temperature.

When the reactants are dissolved in a medium of high ionic strength the quotient of activity coefficients may be taken to be constant. In that case the concentration quotient, Kc,

${\displaystyle K_{\ce {c}}={\frac {[{\ce {S}}]^{\sigma }[{\ce {T}}]^{\tau }}{[{\ce {A}}]^{\alpha }[{\ce {B}}]^{\beta }}}}$

where [A] is the concentration of A, etc., is independent of the analytical concentration of the reactants. For this reason, equilibrium constants for solutions are usually determined in media of high ionic strength. Kc varies with ionic strength, temperature and pressure (or volume). Likewise Kp for gases depends on partial pressure. These constants are easier to measure and encountered in high-school chemistry courses.

## Термодинамика

At constant temperature and pressure, one must consider the Gibbs free energy, G, while at constant temperature and volume, one must consider the Helmholtz free energy, A, for the reaction; and at constant internal energy and volume, one must consider the entropy, S, for the reaction.

The constant volume case is important in geochemistry and atmospheric chemistry where pressure variations are significant. Note that, if reactants and products were in standard state (completely pure), then there would be no reversibility and no equilibrium. Indeed, they would necessarily occupy disjoint volumes of space. The mixing of the products and reactants contributes a large entropy (known as entropy of mixing) to states containing equal mixture of products and reactants. The standard Gibbs energy change, together with the Gibbs energy of mixing, determine the equilibrium state.[8][9]

In this article only the constant pressure case is considered. The relation between the Gibbs free energy and the equilibrium constant can be found by considering chemical potentials.[1]

At constant temperature and pressure, the Gibbs free energy, G, for the reaction depends only on the extent of reaction: ξ (Greek letter xi), and can only decrease according to the second law of thermodynamics. It means that the derivative of G with ξ must be negative if the reaction happens; at the equilibrium the derivative being equal to zero.

${\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=0~}$:     equilibrium

In order to meet the thermodynamic condition for equilibrium, the Gibbs energy must be stationary, meaning that the derivative of G with respect to the extent of reaction: ξ, must be zero. It can be shown that in this case, the sum of chemical potentials of the products is equal to the sum of those corresponding to the reactants. Therefore, the sum of the Gibbs energies of the reactants must be the equal to the sum of the Gibbs energies of the products.

${\displaystyle \alpha \mu _{\mathrm {A} }+\beta \mu _{\mathrm {B} }=\sigma \mu _{\mathrm {S} }+\tau \mu _{\mathrm {T} }\,}$

where μ is in this case a partial molar Gibbs energy, a chemical potential. The chemical potential of a reagent A is a function of the activity, {A} of that reagent.

${\displaystyle \mu _{\mathrm {A} }=\mu _{A}^{\ominus }+RT\ln\{\mathrm {A} \}\,}$

(where μo
A
is the standard chemical potential).

The definition of the Gibbs energy equation interacts with the fundamental thermodynamic relation to produce

${\displaystyle dG=Vdp-SdT+\sum _{i=1}^{k}\mu _{i}dN_{i}}$.

Inserting dNi = νi dξ into the above equation gives a Stoichiometric coefficient (${\displaystyle \nu _{i}~}$) and a differential that denotes the reaction occurring once (). At constant pressure and temperature the above equations can be written as

${\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\sum _{i=1}^{k}\mu _{i}\nu _{i}=\Delta _{\mathrm {r} }G_{T,p}}$ which is the "Gibbs free energy change for the reaction .

This results in:

${\displaystyle \Delta _{\mathrm {r} }G_{T,p}=\sigma \mu _{\mathrm {S} }+\tau \mu _{\mathrm {T} }-\alpha \mu _{\mathrm {A} }-\beta \mu _{\mathrm {B} }\,}$.

By substituting the chemical potentials:

${\displaystyle \Delta _{\mathrm {r} }G_{T,p}=(\sigma \mu _{\mathrm {S} }^{\ominus }+\tau \mu _{\mathrm {T} }^{\ominus })-(\alpha \mu _{\mathrm {A} }^{\ominus }+\beta \mu _{\mathrm {B} }^{\ominus })+(\sigma RT\ln\{\mathrm {S} \}+\tau RT\ln\{\mathrm {T} \})-(\alpha RT\ln\{\mathrm {A} \}+\beta RT\ln\{\mathrm {B} \})}$,

the relationship becomes:

${\displaystyle \Delta _{\mathrm {r} }G_{T,p}=\sum _{i=1}^{k}\mu _{i}^{\ominus }\nu _{i}+RT\ln {\frac {\{\mathrm {S} \}^{\sigma }\{\mathrm {T} \}^{\tau }}{\{\mathrm {A} \}^{\alpha }\{\mathrm {B} \}^{\beta }}}}$
${\displaystyle \sum _{i=1}^{k}\mu _{i}^{\ominus }\nu _{i}=\Delta _{\mathrm {r} }G^{\ominus }}$:

which is the standard Gibbs energy change for the reaction that can be calculated using thermodynamical tables. The reaction quotient is defined as:

${\displaystyle Q_{\mathrm {r} }={\frac {\{\mathrm {S} \}^{\sigma }\{\mathrm {T} \}^{\tau }}{\{\mathrm {A} \}^{\alpha }\{\mathrm {B} \}^{\beta }}}}$

Therefore,

${\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\Delta _{\mathrm {r} }G_{T,p}=\Delta _{\mathrm {r} }G^{\ominus }+RT\ln Q_{\mathrm {r} }}$

At equilibrium:

${\displaystyle \left({\frac {dG}{d\xi }}\right)_{T,p}=\Delta _{\mathrm {r} }G_{T,p}=0}$

${\displaystyle 0=\Delta _{\mathrm {r} }G^{\ominus }+RT\ln K_{\mathrm {eq} }}$

and

${\displaystyle \Delta _{\mathrm {r} }G^{\ominus }=-RT\ln K_{\mathrm {eq} }}$

Obtaining the value of the standard Gibbs energy change, allows the calculation of the equilibrium constant.

### Термодинамичка равнотежа

Хемијска равнотежа је део термодинамичке равнотеже.

Термодинамичка равнотежа обухвата механичку, термичку и хемијску равнотежу. Механичка равнотежа представља стање система у коме не постоји кретање унутар система. Термичка равнотежа представља стање система у коме је температура константна у свим деловима система, односно не постоји пренос топлоте. Хемијска равнотежа је стање у коме се састав система не мења, односно количине реактаната и продуката остају у константном односу неограничено време, уколико се спољашњи услови не промене.

## Услови хемијске равнотеже

Хемијска равнотежа је одређена општим термодинамичким условима за равнотежу система:

1. максимум ентропије при условима константне унутрашње енергије и температуре
${\displaystyle \Delta S_{U,T}=0}$
2. минимум унутрашње енергије при условима константне запремине и ентропије
${\displaystyle \Delta U_{V,S}=0}$
3. минимум енталпије при условима константног притиска и ентропије
${\displaystyle \Delta H_{p,S}=0}$
4. минимум Хелмхолцове функције при условима константе запремине и температуре
${\displaystyle \Delta A_{V,T}=0}$
5. минимум Гибсове функције при условима притиска и температуре
${\displaystyle \Delta G_{p,T}=0}$

## Референце

1. ^ а б в г Peter Atkins, Loretta Jones. Chemical Principles: The Quest for Insight (2nd изд.). ISBN 0716757010 неважећи ISBN.
2. ^
3. ^ James E. Brady, Fred Senese. Chemistry: Matter and Its Changes (4th изд.). ISBN 978-0-471-21517-2.
4. ^ Berthollet, C.L. (1803). Essai de statique chimique [Essay on chemical statics] (на језику: француски). Paris, France: Firmin Didot. On pp. 404–407, Berthellot mentions that when he accompanied Napoleon on his expedition to Egypt, he (Berthellot) visited Lake Natron and found sodium carbonate along its shores. He realized that this was a product of the reverse of the usual reaction Na2CO3 + CaCl2 → 2NaCl + CaCO3↓ and therefore that the final state of a reaction was a state of equilibrium between two opposing processes. From p. 405: " … la décomposition du muriate de soude continue donc jusqu'à ce qu'il se soit formé assez de muriate de chaux, parce que l'acide muriatique devant se partager entre les deux bases en raison de leur action, il arrive un terme où leurs forces se balancent." ( … the decomposition of the sodium chloride thus continues until enough calcium chloride is formed, because the hydrochloric acid must be shared between the two bases in the ratio of their action [i.e., capacity to react]; it reaches an end [point] at which their forces are balanced.)
5. ^ The notation ⇌ was proposed in 1884 by the Dutch chemist Jacobus Henricus van 't Hoff. See: van 't Hoff, J.H. (1884). Études de Dynamique Chemique [Studies of chemical dynamics] (на језику: француски). Amsterdam, Netherlands: Frederik Muller & Co. стр. 4—5. Van 't Hoff called reactions that didn't proceed to completion "limited reactions". From pp. 4–5: "Or M. Pfaundler a relié ces deux phénomênes … s'accomplit en même temps dans deux sens opposés." (Now Mr. Pfaundler has joined these two phenomena in a single concept by considering the observed limit as the result of two opposing reactions, driving the one in the example cited to the formation of sea salt [i.e., NaCl] and nitric acid, [and] the other to hydrochloric acid and sodium nitrate. This consideration, which experiment validates, justifies the expression "chemical equilibrium", which is used to characterize the final state of limited reactions. I would propose to translate this expression by the following symbol:
HCl + NO3 Na ⇌ NO3 H + Cl Na .
I thus replace, in this case, the = sign in the chemical equation by the sign ⇌, which in reality doesn't express just equality but shows also the direction of the reaction. This clearly expresses that a chemical action occurs simultaneously in two opposing directions.)
6. ^ Atkins, Peter W.; Jones, Loretta (2008). Chemical Principles: The Quest for Insight (2nd изд.). ISBN 978-0-7167-9903-0.
7. ^ Brady, James E. (2004-02-04). Chemistry: Matter and Its Changes (4th изд.). Fred Senese. ISBN 0-471-21517-1.
8. ^ Schultz, Mary Jane (1999). „Why Equilibrium? Understanding Entropy of Mixing”. Journal of Chemical Education. 76 (10): 1391. Bibcode:1999JChEd..76.1391S. doi:10.1021/ed076p1391.
9. ^ Clugston, Michael J. (1990). „A mathematical verification of the second law of thermodynamics from the entropy of mixing”. Journal of Chemical Education. 67 (3): 203. Bibcode:1990JChEd..67Q.203C. doi:10.1021/ed067p203.

## Литература

• Peter Atkins, Loretta Jones. Chemical Principles: The Quest for Insight (2nd изд.). ISBN 0716757010 неважећи ISBN.
• James E. Brady, Fred Senese. Chemistry: Matter and Its Changes (4th изд.). ISBN 978-0-471-21517-2.
• Van Zeggeren, F.; Storey, S. H. (1970). The Computation of Chemical Equilibria. Cambridge University Press. Mainly concerned with gas-phase equilibria.
• Leggett, D. J., ур. (1985). Computational Methods for the Determination of Formation Constants. Plenum Press.
• Martell, A. E.; Motekaitis, R. J. (1992). The Determination and Use of Stability Constants. Wiley-VCH.