Equilibrium pressures and concentrations

We can use the expressions for the Gibbs energy (in conjunction with the requirement that reaction free energies are zero at equilibrium) to determine the equilibrium pressures and concentrations for given reactions. For a reaction A B, the change in free energy is thus given by... 

The value of the law of mass action is that it gives us a tool for determining equilibrium pressures and concentrations for a reaction for which we can calculate the standard free energy of reaction. Since the activities of the solids and liquids do not appear in the expression, one always has to check if so much of any of these has reacted that it is not present as a liquid or a solid state any longer. If this is the case, then the reaction described by AG° has run to completion, and the equilibrium has not been established. The dimensionless quantity,, is a constant that the right-hand-... 

Previous Considerations have been confined to the effect of pressure and concentration upon coverage, but in an electrochemical equilibrium the activity and chemical potentials of the species adsorbing at the interface will also be a function of the potential difference A4>. For a solution containing unit activity of the species the effective pressure of the species at the interface is given by... 

Two situations are found in leaching. In the first, the solvent available is more than sufficient to solubilize all the solute, and, at equilibrium, all the solute is in solution. There are, then, two phases, the solid and the solution. The number of components is 3, and F = 3. The variables are temperature, pressure, and concentration of the solution. All are independently variable. In the second case, the solvent available is insufficient to solubilize all the solute, and the excess solute remains as a solid phase at equilibrium. Then the number of phases is 3, and F = 2. The variables are pressure, temperature and concentration of the saturated solution. If the pressure is fixed, the concentration depends on the temperature. This relationship is the ordinary solubility curve. 

The equilibrium conversion can be calculated from knowledge of the free energy, together with physical properties to account for vapor and liquid-phase nonidealities. The equilibrium conversion can be changed by appropriate changes to the reactor temperature, pressure and concentration. The general trends for reaction equilibrium are summarized in Figure 6.8. 

In Figure 10.10a, it can be seen that for porous membranes, the partial pressure and concentration profiles vary continuously from the bulk feed to the bulk permeate. This is not the case with nonporous dense membranes, as illustrated in Figure 10.10b. Partial pressure or concentration of the feed liquid just adjacent to the upstream membrane interface is higher than the partial pressure or concentration at the upstream interface. Also, the partial pressure or concentration is higher just downstream of the membrane interface than in the permeate at the interface. The concentrations at the membrane interface and just adjacent to the membrane interface can be related according to an equilibrium partition coefficient KM i. This can be defined as (see Figure 10.10b) ... 

Determination of the extent of reaction or position of equilibrium under various conditions of temperature, pressure and concentrations. 

On a nucleation rate versus pressure diagram (Figure 4-2c), melt nucleation rate below the crystal-melt equilibrium pressure and crystal nucleation above the pressure are roughly S3mimetric. In Equation 4-9, only AG would vary with pressure or concentration. Hence, both melt nucleation rate and crystal nucleation rate increase monotonically with departure from equilibrium. There is no peak nucleation rate. 

In its strictest sense the phase rule assumes that the equilibrium between phases is not influenced by gravity, electrical or magnetic forces, or by surface action. Thus, the only variables are temperature, pressure, and concentration if two are fixed, then the third is easily determined (another reason for the constant 2 in Equation 2.3). 

By a degree of freedom we mean the number of variable factors (e.g., temperature, pressure, and concentration) which must be fixed to completely define a system at equilibrium. 

CHEMICAL EQUILIBRIUM. The fundamental law of chemical equilibrium was enunciated by Le Chalclier (I884i. and may be stated as follows If any stress or force is brought to bear upon a system in equilibrium, the equilibrium is displaced in a direction which lends to diminish the intensity ol the stress or force. This is equivalent to the principle of least aclion. Its great value to the chemist is that it enahles him to predict the effect upon systems in equilibrium ol changes in temperature, pressure, and concentration. 

To discuss equilibrium in a chemical reaction system, it is convenient to introduce the activity at of a species to replace the chemical potential of a species because a is more closely related to partial pressures and concentrations of species. The activity of a species is defined by... 

There are three variable factors, viz., temperature, pressure and concentration, on which the equilibrium of a system depends. In some cases, we have to mention only one factor to define the system completely, sometimes two or three. So, the degree of freedom (or variance) of a system is defined as, the least number of variable factors such as temperature, pressure or concentration which must be specified so that the remaining variables are fixed automatically and the system is completely defined. 

Flow imparts both extension and rotation to fluid elements. Thus, polymer molecules will be oriented and stretched under these circumstances and this may result in flow-induced phenomena observed in polymer systems which include phase-changes, crystallization, gelation or fiber formation. More generally, the Gibbs free energy of polymer blends or solutions depends under non-equilibrium conditions not only on temperature, pressure and concentration but also on the conformation of the macromolecules (as an internal variable) and hence, it is sensitive to external forces. 

Standard (electrode) potential — (E ) represents the equilibrium potential of an electrode under standard-state conditions, i.e., in solutions with the relative activities of all components being unity and a pressure being 1 atm (ignoring the deviations of fugacity and activity from pressure and concentration, respectively) at temperature T. A pressure of 1 bar = 105 Pa was recommended as the standard value to be used in place of 1 atm = 101,325 Pa (the difference corresponds to 0.34 mV shift of potential). If a component of the gas phase participates in the equilibrium, its partial pressure is taken as... 

PROBLEM Given the following reaction 3H2(g) + N2(g) <—> 2NH3(g) + 22 kcal heat energy. What is the heat of reaction for the reverse reaction What would you do to the temperature, pressure, and concentrations of the reactants and products to shift the equilibrium so that more ammonia is made ... 

The terms adsorption and desorption are often used to indicate the direction from which the equilibrium states have been approached. Adsorption hysteresis arises when the amount adsorbed is not brought to the same level by the adsorption and desorption approach to a given equilibrium pressure or bulk concentration. The relation, at constant temperature, between the amount adsorbed and the equilibrium pressure, or concentration, is known as the adsorption isotherm. 

We shall assume that there is no penetration of gas into the solid (i.e. no absorption) so that zone I is occupied solely by the adsorbent and therefore c = 0. In zone ID, the adsorbable gas is at sufficient distance from the solid surface to have a uniform concentration, c8, and here z > t. In this legion the concentration is dependent only on the equilibrium pressure and temperature. In Figure 2.1a, zone II is the adsorbed layer , which is an intermediate region confined within the limits z = 0 and z = f. Here, the local concentration, c, is higher than the concentration of the gas in zone HI and is dependent on z. 

Equation (2.34) is often referred to as the Gibbs adsorption equation where the interdependence of r and p is given by the adsorption isotherm. TTie Gibbs adsorption equation is a surface equation of state which indicates that, for any equilibrium pressure and temperature, the spreading pressure II is dependent on the surface excess concentration r. The value of spreading pressure, for any surface excess concentration, may be calculated from the adsorption isotherm drawn with the coordinates n/p and p, by integration between the initial state (n = 0, p = 0) and an equilibrium state represented by one point on the isotherm. 

To avoid some possible difficulties in determining chemical potentials, Lewis proposed a new property called the fugacity /. At low pressure and concentration, the fugacity is a well-behaved function. The fugacity function can define phase equilibrium and chemical equilibrium. For an ideal gas, the fugacity of a species in an ideal gas mixture is equal to its partial pressure. As the pressure decreases to zero, pure substances or mixtures of species approach an ideal state, and we have... 

Equations (6.299) and (6.300) show that Onsager s reciprocal rules hold. The Js eq and Jweq have a microscopic definition represented by perturbation matrix elements and a macroscopic definition represented by the equilibrium exchange rate. As long as the criteria of linearization are satisfied, the statistical rate theory may be used to describe systems with temperature differences at an interface besides the driving forces of pressure and concentration differences. 

The number of degrees of freedom (sometimes also referred to as the variance) is the number of variable factors, such as temperature, pressure, and concentration that must be fixed in order to define the condition of a system at equilibrium. Thus, a one-component system in one phase, say a gas, would have two degrees of freedom a one component system in two phases (liquid and gas) would have one degree of freedom. A system of one component and three phases would have no degrees of... 

As described earlier, the relation between the amount of substance adsorbed by an adsorbent and the equilibrium pressure or concentration at constant temperature is called the adsorption isotherm. The adsorption isotherm is the most important and by far the most often used of the various equilibria data that can be measured. To represent the variation of the amount of adsorption per unit area or unit mass with pressure, Freundlich proposed the equation... 

According to the phase rule, a three-component, two-phase system has three degrees of freedom. Thus, by specifying the temperature, pressure, and concentration of one component in one phase, the state of the system is defined. The component concentration in one phase defines one point on the equilibrium curve, and this point marks one end of a tie line. The other end is determined thermodynamically either from experimental data or on the basis of liquid activity coefficient predictions methods. 

The aim of the present paper is to present the adsorption equilibrium of binary Oj/l systems, as well as of pure sorbates on natural clinoptilolite and to try to predict the behaviour of each sorbate in mixtures under arbitrary pressures and concentration. 

The output data from reformer II for the process gas and the calculated results of the dusty gas model and simplified models I and II are presented in Table 6.16. The measured and calculated temperatures, pressures and concentrations of the process gas at the exit of reformer II are in good agreement (Table 6.16). AH models give almost the same exit conversion and yield for methane and carbon dioxide. This unit is operating relatively close to thermodynamic equilibrium, though it is slightly shifted away from equilibrium compared with unit I. 

Adsorption isotherm The relation at constant temperature between the amount adsorbed and equilibrium pressure or concentration... 

Skill 2.2a-Predict the effect of temperature, pressure, and concentration on chemical equilibrium (LeChatelier s principle) and the reaction rate Introduction to dynamic equilibrium... 

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