Characteristic functions. Thermodynamics of chemical equilibrium Plan 1. Criterion of the Process’s Direction. 2. Gibbs Helmholtz equation and thermodynamics gas’s functiion. 3. The third law of thermodynamics. Prepared by Kozachok S.S.

Definition of the process’s direction according to the caracteristic functions (internal energy) U is the function of the isochoric-isoentropic process: U dU = TdS – pdV dWmax = -dU For the random process: U0 nonspontaneous spontaneous direction

Definition of the process’s direction according to the enthalpy Н is the function of the isobaric-isoentropic process:: Н dН = TdS + Vdp dWmax = -dН For the random process: Н0 spontaneous nonspontaneous direction

Definition of the process’s direction according to the entropy S is the function of isolated system: S dWmax = TdS For the random process: S0 spontaneous nonspontaneous direction

Determination of a direction of a process using Helmholtz’ energy F is the function of isochoric-isothermal process: F dF = dU - TdS dWmax = -dF For random process: F0 Spontaneous Forced process Direction of a process

Determination of a direction of a process using Gibbs’ free energy G is the function of isobaric-isothermal process : G dG = dH- TdS dWmax = -dG For spontaneous process: G0 Spontaneous Forced process Direction of a process

Helmholtz’ equation: F = U - TS Gibbs’ equation: G = H - TS

Thermodynamic functions of the ideal gases F = kF - RTlnV, where kF is the constant, which depends from temperature (kF = U – TkS) Gi = kG,I + RTlnPi For real gases: G = G0 + RTlnf, where f - a fugacity; f = γ · P; γ is a coefficient of a fugacity; γ = P/Pideal.

Nernst’ heat theorem: E Н Near Т = 0: G = Н - TS = H TS G T

Ludwig Boltzmann’ equation: THIRD LAW OF THERMODYNAMICS: the entropy of a perfectly pure crystal at absolute zero T=273 K is zero. Ludwig Boltzmann’ equation: S = klnW, where k is Boltzmann’s constant k= R/Na k=1.38 *10-23 J/K. At Т→0: W = 1; S = 0.

Calculation of a standard and an absolute meaning of Entropy Cp ∫ ln T , if S0 = 0

Chemical equilibrium Plan Chemical potential. Calculation of the chemical equilibrium. Phase equilibrium. Gibb’s phase rule.

The calculation of the chemical potential For ideal gas : For real gas: For ideal solution: For real solution :

CHEMICAL EQUILIBRIUM The state reached when the concentrations of reactants and products remain constant over time A mixture of reactants and products in the equilibrium state is called an equilibrium mixture.

According to the balanced equation, 2 According to the balanced equation, 2.0 mol of NO2 forms for each mole of N2O4 that disappears, so the concentration of N2O4 at any time equals the initial concentration of N2O4 minus half the concentration of NO2. As time passes, the concentration of N2O4 decreases and the concentration of NO2 increases until both concentrations level off at constant, equilibrium values:

The Equilibrium Constant Kc

Calculation of the equilibrium constant The equilibrium constant for a reaction at a particular temperature always has the same value. аА + bВ = сС + dD

Pi = CiRT, that Kp = Kc (RT)n, хi = CiRT/Ptotal, that where n is the change of moles of gases

The physical content of the equilibrium constants If n = 0 that Kp=Kc=Kx

N.B. This equations are true for ideal gases or solutions. For the real systems the equilibrium constant is expressed by using activity and is named thermodynamic equilibrium constant

Heterogeneous Equilibria Thus far we’ve been discussing homogeneous equilibria, in which all reactants and products are in a single phase, usually either gaseous or solution. Heterogeneous equilibria, by contrast, are those in which reactants and products are present in more than one phase.

Because both CaO and CaCO3 are pure solids, their molar “concentrations” are constants. In general, the concentration of any pure solid (or pure liquid) is independent of its amount because its concentration is the ratio of its amount (in moles) to its volume (in liters). If, for example, you double the amount of CaCO3 you also double its volume, but the ratio of the two (the concentration) remains constant. Rearranging the equilibrium equation for the decomposition of CaCO3 to combine the constants [CaCO3], [CaO], and “Kc”, we obtain

N.B. As a general rule, the concentrations of pure solids and pure liquids are not included when writing an equilibrium equation because their concentrations are constants that are incorporated into the value of the equilibrium constant. We include only the concentrations of gases and the concentrations of solutes in solutions because only those concentrations can be varied.

Judging the Extent of Reaction

Predicting the Direction of Reaction The reaction quotient Qc is defined in the same way as the equilibrium constant Kc except that the concentrations in are not necessarily equilibrium values.

Altering an Equilibrium Mixture: Changes in Concentration In general, when an equilibrium is disturbed by the addition or removal of any reactant or product, Le Châtelier’s principle predicts that • The concentration stress of an added reactant or product is relieved by net reaction in the direction that consumes the added substance. • The concentration stress of a removed reactant or product is relieved by net reaction in the direction that replenishes the removed substance.

If these rules are applied to the equilibrium then the yield of ammonia is increased by an increase in the N2 or H2 concentration or by a decrease in the NH3 concentration

Altering an Equilibrium Mixture: Changes in Pressure and Volume

Altering an Equilibrium Mixture: Changes in number of mokes If n < 0 at increasing pressure ↑ p → ↑ increasing in the equilibrium constant K → ↑ increasing in product’s quantity (products predominate over reactants) If n > 0 at ↑ p → ↓ K → ↓ decreasing in product’s quantity (reactants predominate over reactants) If n = 0 pressure doesn’t influence on the the equilibrium constant K

Altering an Equilibrium Mixture: Changes in Temperature

Van't Hoff's isotherm equation G = -RT ln K G = G0 + RT ln K Isobar equation Isochor equation

Van't Hoff's isotherm equation G = G0 + RT ln K G = RT ln - RT lnKp Predicting the Direction of Reaction according to isotherm equation G < 0, when < lnKp, the spontaneous process of net reaction goes from left to right G > 0, when > lnKp, the spontaneous process of net reaction goes from right to left G = 0 that is equilibrium state

Thanks for attention