A B C
ACHE CAD, PLASTICATING SCREWS CAF, COMPRESSED ASBESTOS FIBRE JOINTING CALANDRIA CALCIUM CALCULATING TIME CHARACTERISTICS OF IGNITION OF HYBRID GAS SUSPENSIONS CALDER HALL CALORIE CALORIFIC VALUE OF FUEL CALORIMETRY CANDU NUCLEAR POWER REACTORS CANONICAL PARTITION FUNCTION CAP BUBBLES CAPACATIVE HEAT EXCHANGERS CAPILLARITY Capillary action CAPILLARY CONVECTION CARBOLIC ACID CARBON CARBON ARC CARBON DIOXIDE CARBON DIOXIDE POLLUTION CARBON DIOXIDE, AS A POLLUTANT CARBON DISULFIDE COMBUSTION CARBON MONOXIDE CARBON STEELS CARBON SUBNITRIDE COMBUSTION CARBON THERMOMETERS CARBONACEOUS FUELS CARBONTETRACHLORIDE CARNOT CYCLE CARNOT, NLS CARRYUNDER CARTESIAN COORDINATES CASTING OF METALS CATALYSIS CATALYSTS CATALYTIC ACTIVITY CATALYTIC CONVERSION CATALYTIC CONVERTERS CATALYTIC CRACKING OF PALM OIL CATALYTIC RICH GAS PROCESS, CRG CATHODE CAUCHY SURFACE CAUCHY'S CONVEYENCE PRINCIPLE CAUCHY'S THEOREM CAUSTIC SODA CAVITATING FLOWS CAVITATION CAVITIES, FOR NUCLEATION CAVITY, SQUARE CEA CEC CELL GROWTH CELL POTENTIAL CELLULOSIC FIRES CELSIUS TEMPERATURE SCALE CENTIGRADE TEMPERATURE SCALE CENTRIFUGAL FILTERS CENTRIFUGAL FLOWMETERS CENTRIFUGAL FLUIDIZED BED CENTRIFUGAL SCRUBBER CENTRIFUGAL SEPARATORS CENTRIFUGES CENTRIPETAL BUOYANCY CENTRIPETAL FORCE CERAMIC CRUCIBLE PLASMA FURNACE CERAMICS CERENKOV RADIATION CERMETS CFCS, CHLOROFLUOROCARBON CFD CFD MODELS CHAIN REACTION CHANG-LIN TIEN CHANNEL CONTROL Channel Flow CHANNEL INSTABILITY CHANNEL IRREGULARLY HEATED CHANNELING EFFECT CHAOS CHAR CHARACTERISTIC DRYING CURVE CHARACTERISTIC EQUATIONS, FOR SUPERSONIC FLOW CHARACTERISTICS, METHOD OF CHARACTERISTICS, OF DIFFERENTIAL EQUATIONS CHARCOAL CHARGE CARRIERS CHARGE COUPLED DEVICES, CCD CHARLES LAW CHEBYSHEV EQUATION CHEBYSHEV POLYNOMIAL EXPANSION CHEBYSHEV POLYNOMIALS CHELATION CHEMICAL COMPLEXITY CHEMICAL EQUILIBRIUM CHEMICAL KINETICS CHEMICAL LASERS CHEMICAL POTENTIAL CHEMICAL REACTION CHEMICAL REACTION FOULING CHEMICAL THEORIES, FOR CATALYSIS CHEMICAL THERMODYNAMICS CHEMISORPTION CHEN CORRELATION CHEVRON SEPARATORS Chezy Formula CHF CORRELATIONS CHF, CRITICAL HEAT FLUX CHILTON-COLBURN ANALOGY CHIMNEY PLUMES CHIMNEYS CHLOR-ALKALI ELECTROLYSIS CHLORINE CHLOROFLUOROCARBON, CFC CHLOROFORM CHOKED FLOW CHROMATIC DISPERSION CHROMATOGRAPHY CHUGGING INSTABILITIES Churn Flow CIRCUIT BREAKER CIRCULATION RATIO CISE CORRELATIONS CLADDING CLAPEYRON EQUATION CLAPEYRON-CLAUSIUS EQUATION CLARIFICATION CLARIFIERS Classification of foam structures CLASSIFICATION OF HEAT EXCHANGERS CLASSIFIERS CLAUSIUS CLAUSIUS NUMBER CLAUSIUS-CLAPEYRON EQUATION CLAUSIUS-MOSOTTI EQUATION CLEANING TECHNIQUES, HEAT EXCHANGERS Climate study CLIMATIZATION CLIMBING FILM EVAPORATOR Closed cell foam CLOSED CYCLE GAS TURBINE CLOSED CYCLE MHD GENERATORS CLOSED SYSTEM CLOSURE LAWS CLOUD POINT SPECIFICATION CNEN CO-GENERATION SYSTEMS CO-ORDINATE TRANSFORMATION METHODS COAGULATION COAGULATION, OF AEROSOLS COAGULATION, OF DROPS COAL COAL BURNERS COAL CARBONIZATION COAL COMBUSTION COAL GAS COAL GASIFICATION COAL RESEARCH ESTABLISHMENT, CRE COAL SLURRY COALESCENCE Coanda Effect COARSE VARIABLES FOR DYNAMICS COARSE-GRAINED APPROXIMATION COATINGS COAXIAL TWISTING FLOW COEFFICIENT OF PERFORMANCE, COP COHERENCE FUNCTION COHERENCE STRICTURES, IN TURBULENT FLOW COHERENCE, OF RADIATION COHERENT SYSTEM OF UNITS COIL IN TANK COILED TUBE BOILERS Coiled Tube, Flow and Pressure Drop in Coiled Tubes, Heat Transfer in COILED WIRE INSERTS COKE COKE OVENS COKE-OVEN GAS COLBURN CORRELATION COLBURN FACTOR COLBURN HEAT TRANSFER FACTOR COLBURN J-FACTOR COLBURN, ALLAN PHILIP (1904-1955) COLBURN-CHILTON ANALOGY COLD ROD EFFECTS COLEBROOK-WHITE EQUATION, FOR FRICTION FACTOR COLEBROOK-WHITE FORMULA COLLECTION EFFICIENCY COLLIGATIVE PROPERTIES COLLIGEND COLLOCATION COLLOIDAL DISPERSIONS COLOR SEGREGATION IN METAL-HALIDE LAMPS COLUMN CHROMATOGRAPHY COLUMNS COMBINATORIAL MODELING COMBINED BRINKMAN-ELECTRIC BOUNDARY LAYER COMBINED CYCLES COMBINED HEAT AND MASS TRANSFER Combined heat transfer by radiation, conduction, and convection COMBINED RADIATION AND COMBUSTION COMBUSTION COMBUSTION CHAMBER COMBUSTION PRODUCTS COMFORT CONDITIONS COMITATO NAZIONALE PER LA RICERCA E PER LO SVILUPPO DELL'ENERGIA NUCLEARE E DELLE ENERGIE ALTERNATIVE, ENEA COMMERCIAL PLASMATRON COMMISSARIAT A L'ENERGIE ATOMIQUE, CEA COMMISSION OF THE EUROPEAN COMMUNITY, CEC COMMON MODE FAILURE COMMONWEALTH SCIENTIFIC AND INDUSTRIAL RESEARCH ORGANISATION, CSIRO COMPACT HEAT EXCHANGERS COMPILER COMPLEX COMPOUND CATALYSIS COMPLEXIFICATION COMPLEXING IONS COMPLEXITY COMPOSITE FLOW COMPOSITE MATERIALS COMPOSITE MATERIALS, ABLATION OF COMPOSITE MATERIALS, COMPUTATION OF COMPOSITE POROUS LAYER COMPOSITES, THERMAL CONDUCTIVITY OF COMPOUND AUGMENTATION COMPRESSED ASBESTOS FIBER JOINTING, CAF COMPRESSIBILITY EFFECTS COMPRESSIBILITY FACTOR Compressible Flow COMPRESSION PLASMA FLOWS COMPRESSION POINT COMPRESSION ZONE COMPRESSION-IGNITION ENGINES COMPRESSORS COMPTON SCATTERING COMPUTATIONAL FLUID DYNAMIC MODELS Computational fluid dynamics Computational methods Computational methods for radiative transfer in disperse systems COMPUTER AIDED DESIGN, CAD COMPUTER PROGRAMMES COMPUTERS CONCAVE SURFACE, FLOW OVER CONCENTRATING COLLECTOR CONCENTRATION-DEPENDENT CHLORIDE DIFFUSIVITY Concept of regularization CONCRETE CONCURRENT MULTISCALE PROBLEMS CONDENSATE INUNDATION CONDENSATION COEFFICIENT CONDENSATION CURVE CONDENSATION IN ENCLOSURES CONDENSATION IN TUBE BANKS CONDENSATION IN TUBES CONDENSATION OF A PURE VAPOR CONDENSATION OF MOVING VAPOR INSIDE VERTICAL TUBES CONDENSATION OF MULTICOMPONENT VAPORS CONDENSATION ON OUTSIDE OF TUBES IN CROSSFLOW CONDENSATION RELAXATION OF SUPERSATURATED VAPOR CONDENSATION SHOCKS CONDENSATION, OF DROPS CONDENSATION, OVERVIEW CONDENSERS CONDUCTANCE PROBES, FOR LOCAL VOID FRACTION CONDUCTANCE, ELECTRICAL CONDUCTION CONDUCTION AND CONVECTION COMBINED CONDUCTION COMBINED WITH RADIATION CONDUCTION DRYING CONDUCTION EQUATION CONDUCTION IN HEAT EXCHANGER WALLS CONDUCTIVE HEAT FLUX CONDUCTIVITY CONDUCTIVITY RATIO CONDUCTIVITY, ELECTRICAL CONDUCTIVITY, OF PLASMA CONE CLASSIFIER Configuration factors for radiation transfer between diffuse surfaces CONFINED SPRAY FLAME CONFORMAL MAPPING CONFORMAL POTENTIALS CONICAL SHOCK WAVE CONJUGATE HEAT TRANSFER CONSERVATION EQUATIONS CONSERVATION EQUATIONS, SINGLE-PHASE Conservation equations, Two-phase Conservation Laws CONSERVATIVE SYSTEMS CONSTANT RATE PERIOD, DRYING CURVE CONSTITUTIVE EQUATIONS CONSTITUTIVE RELATION, THERMODYNAMICS Contact angle CONTACT CONDUCTANCE CONTACT DISCONTINUITIES CONTACT RESISTANCE CONTAINMENT CONTINUITY EQUATION CONTINUITY SHOCKS CONTINUITY WAVES CONTINUOUS CASTING CONTINUOUS CRYSTALLIZERS CONTINUOUS FILTERS CONTINUOUS WAVE LASERS Continuum Continuum Hypothesis CONTINUUM MECHANICS CONTINUUM MODELS Contraction, Flow and Pressure Loss in CONTRACTORS CONTROL THEORY CONVECTION CONDENSATION CONVECTION DRYING CONVECTION RADIATION CONVECTIVE BOILING CONVECTIVE HEAT FLUX CONVECTIVE HEAT TRANSFER CONVECTIVE HEAT TRANSFER ENHANCEMENT CONVECTIVE MASS TRANSFER CONVERGENCE FACTORS CONVERGENCE OF SERIES CONVERGING BOUNDARIES CONVERSION FACTORS COOL FLAME EVAPORATION COOLANTS, REACTOR COOPER CORRELATION, FOR NUCLEATE BOILING COORDINATE SYSTEM COPPER CORE, NUCLEAR REACTOR CORED BRICK HEAT EXCHANGERS CORIOLIS EFFECT CORIOLIS EFFECT, IN ATMOSPHERIC CIRCULATION CORIOLIS MASS FLOWMETER CORLISS VALVE CORONA DISCHARGE, ELECTROSTATIC PRECIPITATION CORONARY ARTERIES Correlated k-models CORRELATION CORRELATION ANALYSIS CORRELATION COEFFICIENT CORRELATION, FOR CONVECTIVE HEAT TRANSFER CORRELATIONS FOR NOx EMISSIONS FROM A SWIRL BURNER CONCEPT CORRESPONDING STATES, PRINCIPLE OF CORROSION FOULING CORROSION, PREDICTION METHODS FOR CORRUGATED CONDENSED TUBES CORRUGATIONS, PLAIN, PERFORATED, AND SERATED COUETTE VISCOMETER COULTER COUNTER COUNTER CURRENT FLOW LIMITATION, CCFL COUNTER CURRENT TWO-PHASE FLOW COUNTERIONIC ATTRACTION Coupled (combined) radiation and conduction COUPLED AUTOREGULATED OSCILLATING CELLS COUPLED CONDUCTION AND CONVECTION COUPLED HEAT AND MASS FLUXES Coupled radiation and convection Coupled radiation, convection and conduction COVALENT BONDING COWPER STOVES CRACKING CRAMER'S RULE CRE CREAGER-OFITSEROV PROFILE CREEPING FLOW CRITICAL CHOKING CRITICAL CONCENTRATION CRITICAL DEPOSITION VELOCITY Critical Flow CRITICAL FLOW RATE, IN ORIFICES CRITICAL HEAT FLUX IN BOILING LIQUID METALS CRITICAL HEAT FLUX IN COILS CRITICAL HEAT FLUX, CHF CRITICAL POINT, DRYING CURVE CRITICAL POINT, THERMODYNAMICS CRITICAL PRESSURE CRITICAL PRESSURE RATIO Critical Reynolds number CRITICAL SEDIMENTATION POINT CRITICAL STATE CRITICAL SURFACE TENSION CRITICAL TEMPERATURE CRITICAL TEMPERATURE, FOR SUPERCONDUCTIVITY CRITICAL TRANSITION VELOCITY CRITICAL ZONE CRITICALITY CROCCO TRANSFORMATION CROCCO'S THEOREM CROSS CORRELATION CROSS FLOW HEAT TRANSFER CROSS FLUXES CROSS SECTIONS CROSS SPECTRUM Crossflow CRUDE OIL CRYOGENIC FLUIDS CRYOGENIC PLANT CRYOGENIC PUMP CRYOGENIC USE OF STEEL CRYOSCOPIC CONSTANT CRYOSTATS CRYSTAL GROWTH CRYSTAL STRUCTURE ASYMMETRY CRYSTAL SUBLIMATION AND GROWTH CRYSTALLIZATION CRYSTALLIZATION FOULING CRYSTALLIZERS CRYSTALS CSIRO CUBIC LATTICES CUNNINGHAM COEFFICIENT CURRENT VOLTAGE CHARACTERISTICS CURRENTS, NEARSHORE CURVED FLOW CURVILINEAR CHANNELS CYANOGEN COMBUSTION CYCLIC HYDROCARBONS CYCLOHEXANOL CYCLONE FURNACES CYCLONE REYNOLDS NUMBER CYCLONE SEPARATOR CYCLONE STOKES NUMBER CYCLONES CYLINDER, INVISCID FLOW AROUND CYLINDERS, FLOW OVER CYLINDRICAL COORDINATES CYLINDRICAL FINS CYLINDRICAL POLAR COORDINATES
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CHEMICAL EQUILIBRIUM

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Chemical equilibrium is the thermodynamic equilibrium in a system where direct and reverse chemical reactions are possible. If chemical equilibrium takes place in the system, the rates of all reactions proceeding in two opposite directions are equal. Therefore, the macroscopic parameters of the system do not change and the relationship between concentrations of reacting substances remains constant at a given temperature. Equilibrium for any chemical reaction is expressed by an equality ∑νiμi = 0, where μi is the chemical potential of each reagent (i = 1,2, . . .) and νi is the stoichiometric coefficient of each substance in an equation of chemical reaction (it is positive for initial substances and negative for products of a reaction).

The dependence of chemical equilibrium on external conditions is expressed by the Le Chatelier-Braun principle (1885-1886). It consists of the following correlation: Let equilibrium take place and then influence the system, changing some external conditions (temperature, pressure, concentrations of reacting substances). The equilibrium of a reaction tends to follow such direction that allows the reduction of an external influence. A temperature increase will cause a displacement of the equilibrium to the direction of such reaction that proceeds with heat absorption. A pressure increase will cause equilibrium displacement to follow the direction of such reaction that leads to a volume decrease. The introduction of any additional reagent in the system will propel equilibrium displacement to a direction where this reagent is consumed.

The total Gibbs energy change of a chemical reaction aA + bB = cC + dD (when temperature and pressure are constant) is expressed by the equation

where R is the gas constant, p is the pressure, T is the absolute temperature, αi refers to the activities of the reacting substances and is the standard Gibbs energy's change of that reaction (αi = 1). The value of can be calculated on the basis of standard values of the Gibbs energies of formation (ΔfG0) of the reagents at 298.15 K and of known thermodynamic relationships that determine the temperature and pressure dependencies of Gibbs energy change.

If equilibrium is attained, then

Here, αequil are the activities corresponding to the equilibrium state and Ka is the equilibrium constant expressed in terms of activities. Hence, it follows that . The last relationship is the van't Hoff isotherm equation (or van't Hoff equation). It permits the determination of a probable direction of the reaction under given conditions. The process will take place when ΔrGP,T < 0, i.e., when . Analogous relationships can be obtained when the equilibrium constant (Kp) is expressed in terms of partial pressures (Pi) of the reagents:

The "equilibrium constant of reaction" is the result of the mass action law, which determines a correlation between the masses of reacting substances under equilibrium. According to this law, the reaction's rate depends on the concentrations of reacting substances. The rate constant of a given reaction at fixed temperature is a constant value; therefore, the relationship of the rate constants of direct and reverse reactions is a constant value too. This relationship is a function of temperature only.

The equations that express a relationship between the -value and equilibrium constant of reaction allow the calculation of the equilibrium of chemical reactions, avoiding expensive and prolonged experiments. For such calculations, it is necessary to have reliable values of thermodynamic functions for all reacting substances.

Various experimental methods are used to determine equilibrium constants of chemical reactions. There are static and dynamic methods as well as the circulation method. The last is a specific combination of the static and dynamic methods. When static methods are used, the reaction mixture stays at a given temperature until an adjustment of the equilibrium takes place. Then "tempering" and chemical analysis of the reaction mixture are carried out. "Equilibrium tempering" is the fast-cooling of the reaction mixture to a low temperature where the rate of reaction is very small.

The more common dynamic method of defining equilibrium constants has often been called the transportation method. A steady stream of inert gas is passed over the mixture of substances that is maintained at a constant temperature. This "carrier" gas removes the volatile components of the reaction at a rate that depends on the rate of gas flow. The vapors of the reagents are condensed or collected by absorption or chemical combination at the colder portion of the apparatus. The experiments are carried out at different rates of gas flow. The equilibrium pressures of volatile reagents are determined by extrapolation of the results up to zero rate of the carrier gas.

A modification of the dynamic method used for investigating heterogeneous equilibria is the circulation method. The gas mixture is circulated in a closed space; circulation is carried out by means of electromagnetic pump. Equilibrium is attained when passing this mixture many times over the solid phase into the furnace. Tempering of the gas mixture is done when it is taken out from the hot zone and passed through a capillary. In view of the large linear rate of gas flow, this mixture becomes cold rapidly and its composition is not changed.

The most direct way of measuring equilibrium constants of chemical reactions is through the measurement of electromotive forces (the e.m.f. method). For example, the reaction

is a process of potential generation for the Daniel galvanic element:Zn0/Zn2+//Cu0/Cu2+ A zinc plate (one electrode) is immersed into a solution of zinc sulfate and a copper plate (the other electrode) is immersed into a solution of copper sulfate. A galvanic element (source of electromotive force) can be created if both electrodes are connected by a tube that contains a solution-conductor. The dissolution of zinc (process: Zn0 = Zn2+ + 2e) takes place at one electrode; the precipitation of copper (process: Cu2+ + 2e = Cu0) takes place at the second electrode. Therefore, the common potential forming reaction is: Zn0 + Cu2+ = Zn2+ + Cu0 The Gibbs energy change for such reaction is given by the formula , where n is the number of gramme-equivalents of reagent; F is Faraday's constant (nF is the number of coulombs of electricity passed); and ET is the electromotive force of the galvanic element at a given temperature. The value of the Gibbs energy of reaction can be used for calculating its equilibrium constant (K): .

The equilibrium state is a thermodynamic state of a system that is permanent in time. This invariability is not connected with some external process taking place. There are different kinds of equilibria. If the equilibrium is "steady," then any adjacent states of the system are less steady. It would be necessary to spend external work for transition from the equilibrium state to these adjacent states. It is also typical that steady equilibrium can be approached from two opposite directions. However, this discussion is concerned with steady equilibria only or "chemical equilibria." From the physicist's point of view, steady equilibrium is dynamic. It is attained when the rates of direct and reverse reactions are equal, but not under conditions when the process is stopped in general. The equality dG = 0 is a general condition for "steady" and "unsteady" equilibria, but the value of the second differential of Gibbs energy is positive under steady equilibrium (d2G > 0) and negative under unsteady equilibrium (d2G < 0). The conditions of stability of the equilibrium can be deduced using the second law of thermodynamics. These are: 1) the pressure increases at a constant temperature if volume decreases [(dP/dV)T < 0]; and 2) the value of heat capacity is positive (Cp > 0).

The degree of stability of the different states of chemical systems can vary. States which possess some relative stability are called "metastable" states. Such states have often arisen due to kinetic factors, which create difficulties for the transition of a system from the metastable (unsteady) state to a steady equilibrium state.

The development of thermodynamic theory of equilibria—in particular, equilibria of chemical reactions—owed much to J. W. Gibbs (1873-1878) and Le Chatelier (1885), who discovered the principle of displacement of equilibria under conditions of external change. The theory of chemical equilibria was developed further by F. H. van't Hoff (1884-1886).

REFERENCES

Gibbs, J. W. (1950) Thermodynamic Works. Translation from English, Gostekhteorizdat, M.-L.

Munster, A. (1971) Chemical Thermodynamics. Translation from German.

Kubaschewski, O. and Alcock, C. B. (1979) Metallurgical Thermochemistry, Pergamon Press Ltd., Oxford. New York. Toronto. Sydney. Paris. Frankfurt.

Karapetyans, M. Kh. (1981) Introduction to Theory of Chemical Processes, Vysshaya Shkola, M. (in Russian).

Vasiliev, V. P. (1982) Thermodynamic Properties of Solutions of Electrolytes, Vysshaya Shkola, M. (in Russian).

References

  1. Gibbs, J. W. (1950) Thermodynamic Works. Translation from English, Gostekhteorizdat, M.-L.
  2. Munster, A. (1971) Chemical Thermodynamics. Translation from German.
  3. Kubaschewski, O. and Alcock, C. B. (1979) Metallurgical Thermochemistry, Pergamon Press Ltd., Oxford. New York. Toronto. Sydney. Paris. Frankfurt.
  4. Karapetyans, M. Kh. (1981) Introduction to Theory of Chemical Processes, Vysshaya Shkola, M. (in Russian).
  5. Vasiliev, V. P. (1982) Thermodynamic Properties of Solutions of Electrolytes, Vysshaya Shkola, M. (in Russian).

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