Henry’s law dilute solutions

The standard state of an electrolyte is the hypothetical ideally dilute solution (Henry s law) at a molarity of 1 mol kg (Actually, as will be seen, electrolyte data are conventionally reported as for the fonnation of mdividual ions.) Standard states for non-electrolytes in dilute solution are rarely invoked. 

If followed in experimenrtally accessible dilute solutions, Henry s law would be manifested as a horizontal asymptote in a plot such as Figure 19.3 as the square of the molality ratio goes to zero. We do not observe such an asymptote. Thus, the modified form of Henry s law is not followed over the concentration range that has been examined. However, the ratio of activity to the square of the molality ratio does extrapolate to 1, so that the data does satisfy the definition of activity [Equations (16.1) and (16.2)]. Thus, the activity clearly becomes equal to the square of the molality ratio in the limit of infinite dilution. Henry s law is a limiting law, which is valid precisely at infinite dilution, as expressed in Equation (16.19). No reliable extrapolation of the curve in Figure 19.2 exists to a hypothetical unit molality ratio standard state, but as we have a finite limiting slope at = 0, we can use... 

For the concentration dependence of /jla, we can employ the dilute-solution Henry s law limit (fiA = /jla H rinxA) to obtain... 

Construct the equilibrium line. For dilute solutions, Henry s law will apply. In general, it will be applicable for pressures under 2 atm and liquid mole fractions less than 0.01. For this example, the liquid mole fraction x is (100 lb TCE/106 lb soln) (18/132) = 1.37 x 1CT5, where 18 and 132 are the molecular weights of water and trichloroethylene, respectively. Therefore, Henry s law will apply. 

For dilute solutions, Henry s law is usually a good choice for an equilibrium relationship. In this case, = mx, which is defined in relation to the overall mass transfer by Eq. (19). For a dilute solution... 

Also, for sufficiently dilute solutions, Henry s law always applies so that y = mx... 

The metallurgist is concerned with the formation of homogeneous solutions of small amounts of impurities in metals as well as with the formation of compounds. The limit of solubility of impurities is frequently very small, less than one atomic per cent in concentration, and in these dilute solutions Henry s law is applicable, i.e. the activity of a dilute solute is proportional to the concentration of solute in the solution. Consider a dilute solution of an element A which has a high vapour pressure in the pure state at the temperature T, the vapour being monatomic, in solution in element B which has an immeasurably low vapour pressure at the same temperature. Then if the pressure of A could be measured unambiguously for a range of dilute solutions it would be found that... 

For a dilute solution Henry s law can be expressed in terms of the molality ... 

Show that for a dilute solution, Henry s law becomes... 

In addition to the mole fraction, molality, and concentration, the composition of a solution can be represented by the mass percentage, by parts per million by mass, or by volume percentage. For dilute solutions, Henry s law can be expressed in terms of any of these composition measures, since all of them are proportional to the mole fraction in a dilute solution. 

The equihbrium partitioning of a chemical solute between a Hquid and vapor phase is governed by Henry s law when the Hquid mixture is very dilute in the solute. Henry s law generally is vaHd at concentrations below 0.01 mol/L of solution, although the upper limit can sometimes extend to 0.1 mol/L or higher (10). Over this concentration range, a direct proportionaHty, ie, Henry s constant, is observed between the partial pressure of the chemical in the gas phase and its mole fraction in the Hquid phase. Henry s constant, when expressed in this way, has units of pressure (3). 

Also, at infinite dilution, the Henry s law constant for solute i in solvent j is... 

Equation (15.13) can describe either an ideal solution [see Equation (14.7)] or a solution sufficiently dilute that Henry s law is followed [see Equation (15.5)]. In either case, it follows that... 

These equations are the same as Equation (14.6) and Equation (14.7), statements of Raoult s law thus, the solvent obeys Raoult s law when the solute obeys Henry s law. As Henry s law is a limiting law for the solute in dilute solution, Raoult s law... 

For dilute non-reacting solutions, Henry s Law is used to describe the linear equilibrium distribution of a compound between the bulk liquid and gas phases (Figure 3-3) ... 

The simplest possible case occurs when (1) both the operating and equilibrium lines are straight (i.e., the solutions are dilute) (2) Henry s law is valid (y"/x = yjx, = m) and (3) absorption heat effects are negligible. Under these conditions, the integral term in Eq. (14-21) may be computed by Colburn s equation [Tran.s. Am. Inst. Chem. Eng., 35,211(1939)] ... 

We have seen earlier (in Frames 32 and 33) that in order to be classified as an ideal solution then Raoult s Law (Frame 32, 33) must be obeyed over the entire concentration range. In the case of ideal dilute solutions Raoult s Law (Frame 32, equation (32.8) and Frame 33, equation (33.6)) must apply to the solvent and Henry s Law (Frame 33, equation (33.7)) must apply to the solute, albeit over a very small (dilute) and limited concentration range (see Figure 36.1). 

To use this result one must execute detailed measurements of the vapor pressures of the actual solutions at great dilution, where Henry s Law is obeyed. Extrapolation of the resulting straight line to the composition of pure solvent then establishes pf. Now the vectors and in Fig. 3.11.1 correspond to XiPf and P, respectively. A measurement of P, at the particular composition x, then yields the activity or activity coefficient in this regime. For more precise work Eq. (3.11.6) must be used, in the manner discussed earlier. 

If a gas phase is present, chemical species may volatilize from the liquid or solid phase, which is an important partitioning process in a variety of circumstances (e.g., transport in the unsaturated zone, or for treatment processes). The equilibrium vapor pressure can be used with the ideal gas law to estimate the mass in a given volume and temperature under equilibrium conditions. For solutions with more than one component, Raoult s law can be used to quantify the vapor pressure of each component. For dilute aqueous solutions, Henry s law describes the equilibrium relationship between dissolved chemicals and their vapor pressure ... 

The p -process. This is the process of transferring one s molecule from an ideal-gas phase into a dilute ideal solution (Henry s law) at fixed temperature... 

Therefore the effective enthalpy of solute transfer in SFC can be obtained experimentally for a set of solutes at different densities by determining solute retention as a function of temperature at constant density. The reference state in both the mobile and stationary phase is infinite dilution obeying Henry s Law therefore, solute-solute interactions do not influence the standard state. The standard state for AH-p is a hypothetical one in which the solute is at unit molar concentration having the same properties that it would have at infinite dilution (12. ... 

If the gas phase is ideal, the solution ideal and diluted, and Henry s law is valid for the mole fraction of the gas component i, then... 

In the unsymmetric standard state convention, where the solvent is referenced to its pure state (Raoult s law reference state) and the solutes to the infinite dilution state (Henry s law reference state), the standard partial molar volume is equal to the pressure derivative of the chemical potential at... 

Dilution of solution Henry s law Raoult s law Osmotic pressure Boiling point... 

For dilute solutions, solute-solute interactions are unimportant (i.e., Henry s law will hold), and the variation of surface tension with concentration will be linear (at least for nonelectrolytes). Thus... 

Substances at high dilution, e.g. a gas at low pressure or a solute in dilute solution, show simple behaviour. The ideal-gas law and Henry s law for dilute solutions antedate the development of the fonualism of classical themiodynamics. Earlier sections in this article have shown how these experimental laws lead to simple dieniiodynamic equations, but these results are added to therniodynaniics they are not part of the fonualism. Simple molecular theories, even if they are not always recognized as statistical mechanics, e.g. the kinetic theory of gases , make the experimental results seem trivially obvious. 

The vapor—hquid equiUbria of dilute solutions are frequentiy expressed in terms of Henry s law ... 

Henry s law is useful for handling equiUbria associated with gas absorption (qv) and stripping problems. Henry s law coefficients are useful for estimating terminal activity coefficients and have been tabulated for many compounds in dilute aqueous solutions (27). 

For dilute concentrations of manv gases and over a fairly wide range for some gases, the equihbrium relationship is given by Henry s law, which relates the partial pressure developed by a dissolved solute A in a liquid solvent B by one of the following equations ... 

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