All chemical reactions are to some extent reversible, ie. along with direct response (the interaction of the original substances) flows and reverse reaction (the interaction of the reaction products). As the consumption of starting materials the velocity of the forward reaction decreases, and the speed return - increases. When both speeds become equal, condition comes dynamic equilibrium: the concentrations of all substances, participating in the reaction (the starting materials and products), cease to change with time under constant external conditions. This state is called chemical equilibrium.

Chemical equilibrium is movably. The changing external environment, for example temperature, shifts the equilibrium in one direction or another, ie. it is already under different equilibrium concentrations of the reactants. Thus an infinitesimal change in external conditions causes an infinitesimal displacement of the equilibrium. That is chemical reactions near equilibrium States can occur as thermodynamically equilibrium processes and can apply the General conditions of thermodynamic equilibrium.

Get expression for the change in the Isobaric potential of the reaction:

aA+bB dD+eE (3.1)

at constant P and T. Applicable to this reaction equation (2.69):

dG_P,T= ,

where m_i - the chemical potential of the component; n_i - the number of moles of the component.

For the reaction (3.1) the equation (2.69) will look:

dG_P,T=m_Edn_E+m_Ddn_D -m_Adn_A -m_Bdn_B (3.2)

Substances react is proportional to the stoichiometric coefficients,b,d,e. The amount of the reactant dn_i, attributed to its stoichiometric coefficient in the reaction equation n_i, characterizes the completeness of the reaction and is called the chemical variable - x (Zeta):

dx= dn_i/n_i (3.3)

Taking into account (3.3) the equation (2.69):

dG_P,T = S[(n_i m_i)dx]_P,T (3.4)

For a single run of the chemical reaction of variable x changes from 0 to 1. Therefore the integration of the equations (3.4) from the initial to final state leads to the expression:

DG_P,T=S(n_i m_i)_cont - S(n_i m_i)_Ref (3.5)

or specifically to a chemical reaction (3.1):

DG_P,T = em_E + dm_D - am_A - bm_B (3.6)

Suppose, all reagents - ideal gases with initial relativenon-equilibrium partial pressures of the components _A, _B, _D, _E . Substituting in the equation (3.6) the values of chemical potentials of the components of an ideal gas mixture (2.78):

m_i=m⁰_i+RT ln _i ,

get:

DG_P,T = (em⁰_E+dm⁰_D-am⁰_A-bm⁰_B) + RT ln (3.7)

It should be noted, in the equation (3.7) and further under the sign of logarithm of dimensionless are, the relative partial pressure of the components (cm. paragraph 2.9). In chemical equilibrium DG_P,T=0, and pressure of all components become equilibrium (without stroke). Then from the equation (3.7) in terms of balance get:

em⁰_E + dm⁰_D - am⁰_A- bm⁰_B = -RT ln (3.8)

The left part of the equation (3.8) at constant P and T is a constant, Δμº reaction. Therefore, and in the right part of the expression under logarithm is a constant value under these conditions. Let's denote it :

= (3.9)

called standard constant of chemical equilibrium. In thermodynamic calculations is often used is the empirical equilibrium constant For_P, expressed in absolute values of partial pressures:

To_P = (3.10)

Remember, that numerical coincidence of the constants, calculated according to the equations (3.9) and (3.10) possible only in two cases: for standard when the partial pressure components of pressure are equal 1 ATM and then the numerical values of the relative and absolute partial pressures of the same, or, if Δν reaction [cm. the equation (3.22)] zero. In the General case they are related by:

To_P = (3.11)

Equation (3.9) and (3.10) Express the law of mass action. This law was first formulated quantitatively by mass action and the Waag (1867 g).

The constant of chemical equilibrium, expressed in partial pressures of the components (To_P and ) - depends only on the temperature. It does not depend on the mechanism, the kinetics of the process, the total pressure in the system and the initial partial pressures of components. However, this does not mean, that the chemical composition at equilibrium will not change with pressure. Below this effect will be considered in the description of other ways of expressing equilibrium constants (To_N, K_C).

Taking into account the adopted notation (3.9) and equations (3.8), from the equation (3.7) get:

DG_P,T = - RT ln + RT ln (3.12)

The equation (3.12) called the equation of the isotherm of chemical reaction Van ' t Hoff.

The equation (3.12) can be written in the form:

, (3.13)

where

(3.14)

Under standard conditions, ie. if =1, it =1, then (3.13):

DG⁰_P,T = - RT ln (3.15)

The equation (3.15) called uravnoveshennoi isotherms, and DG⁰_P,T - standard Isobaric capacity reactions.

The constant of chemical equilibrium - the most important characteristic of the reaction. It can be determined experimentally according to chemical analysis or be calculated theoretically by the equation:

(3.16)

reaction is calculated by the equation:

= - T , (3.17)

where - standard heat of reaction at temperature T; - standard entropy of reaction at temperature T.

The heat of reaction at a given temperature calculated using equation Kirchhoff [(1.63) or (1.64)].

The entropy change of the reaction at a given temperature T calculated according to equation:

(3.18)

determine standard values of absolute entropies of the reaction products and initial substances (the equation 2.9).

We have considered the derivation of the isotherm equation for the reaction, occurring in an ideal gas mixture, expressing the equilibrium constant using partial pressures of the components. Consider other ways of expressing equilibrium constants.

The partial pressure of component P_i related to their molar fractions N_i and total system pressure P by the relation P_i = PN_i .

The molar proportion of the component:

N_i = n_i/Sn_i = P_i/P (3.19)

As for “n” moles of a component i by equation Chaperonemediated P_iV = n_iRT, it

P_i = n_iRT/V = C_iRT , (3.20)

where C_i - the concentration of the component in mol/l.

Express To_P using mole fractions of N_i and molar concentrations of components With_i :

To_P= (3.21)

where Dn = S(n_i)_cont. - S(n_i)_Ref. , (3.22)

ν_i - the stoichiometric coefficients in the reaction equation. Entering into the equation (3.21) corresponding designations of the equilibrium constants, expressed in N_i and C_i , get the ratio of the constants:

To_P = _N×P^Dn = K_C×(RT)^Dn (3.23)

If the reaction, proceeding in the gas phase, not accompanied by changes in the number of moles, then Dn=0 and

To_P = _N = K_C (3.24)

For real gas systems the equilibrium constant expressed in terms of the fugacity f_i and refer To_f, as for the reactions in real solutions - through the activity and_i components, To_and. In ideal solutions apply the expression To_N or K_C. It should be remembered, in thermodynamic calculations, and in these cases apply a standard equilibrium constants, expressing them through the relative values of the relevant parameters, as stated above (cm. paragraph 2.9).

Most real gases to pressures of the order of 50 ATM obey the Clapeyron equation - Mendeleyev and to them it is lawful to use in the calculations of constants To_P, ie. constants, expressed in partial pressures, instead of fugacity.