Hydrate formation, constants

In general, complexation of an aquometal ion occurs when the ligand is a stronger base than H20, and analogously may be considered an acid-base reaction. The stability (or formation) constant, KMl, is used to describe the interaction of the metal ion (Mz+, shown here with the hydration sheath surrounding the metal ion omitted for reasons of clarity) with a complexant (L" ) ... 

The hydrated metal ion M(HzO), reacts with the reagent anion R to form the neutral chelate MR, (formation constant K ), i.e. 

Fig. 4.15 The system La(III) acetylacetone (HA) - IM NaC104/benzene at 25°C as a function of lanthanide atomic number Z. (a) The distribution ratio Hl (stars, right axis) at [A ] = 10 and [HA] rg = 0.1 M, and extraction constants (crosses, left axis) for the reaction Ln + 4HA(org) LnA3HA(org) + 3FE. (b) The formation constants, K , for formation of LnA " lanthanide acetylacetonate complexes (a break at 64Gd is indicated) circles n = 1 crosses n = 2 triangles w = 3 squares w = 4. (c) The self-adduct formation constants, for the reaction of LnA3(org) + HA(org) LnA3HA(org) for org = benzene. (A second adduct, LnA3(HA)2, also seems to form for the lightest Ln ions.) (d) The distribution constant Ajc for hydrated lanthanum triacetylacetonates, LnAs (H20)2 3, between benzene and IM NaC104. (From Ref. 28.)...

A point that seems to have been coming out of all of our work is that in interactions, especially oxidation-reduction reactions involving oxygenated species, we have to consider such condensations as this. I shouldn t be surprised if they were involved in a lot of the reactions involving simple metal ions which are hydrated. A recent article (2) states that bichromate also condenses with an aquo complex of cobalt with a much higher formation constant than that for CrSCV2 and with... 

The hydration rate constant of C02, the dehydration rate constant of carbonic acid (H2C03), and p pK2 values (pTf, =6.03, pTf2 = 9.8 at 25 °C, 7=0.5 M) (63) are such that nearly 99% of dissolved carbon dioxide in water at pH < 4 exists as C02. However, these four different species may be considered as the reactive species under different pH conditions which can react with aqua metal ions or their hydroxide analogues to generate the metal carbonato complexes. The metal bound aqua ligand is a substantially stronger acid than bulk H20 ( )K= 15.7). Typical value of the p of H20 bound to a metal ion may be taken to be 7. Hence the substantial fraction of such an aqua metal ion will exist as M-OH(aq)(ra 1) + species at nearly neutral pH in aqueous medium. A major reaction for the formation of carbonato complex, therefore, will involve pH controlled C02 uptake by the M-OH(" 1)+ as given in Eq. (17). 

Preformed ligand + Ni(C104)2 hydrate in Formation constants NiL2+ (log K). 2663... 

Pope et al. (123) measured the formation constant of the 1 1 complex of 1,1-dihydroxyl-2,2,2-trichloroethane (chloral hydrate) and polyanions in nitrobenzene by using NMR spectrometry [Eq. (8)] ... 

The stability of a complex ion is measured by its formation constant Kf (or stability constant), the equilibrium constant for formation of the complex ion from the hydrated metal cation. The large value of Kf for Ag(NH3)2+ means that this complex ion is quite stable, and nearly all the Ag+ ion in an aqueous ammonia solution is therefore present in the form of Ag(NH3)2+ (see Worked Example 16.12). 

Pyrolysis of the ethylene acetal of bicyclo[4.2.0]octa-4,7-diene-2,3-dione yields a-(2-hydroxyphenyl)-y-butyrolactonc 11 a mechanism involving a phenyl ketene acetal is proposed. Tartrate reacts with methanediol (formaldehyde hydrate) in alkaline solution to give an acetal-type species (9) 12 the formation constant was measured as ca 0.15 by H-NMR. Hydroxyacetal (10a) exists mainly in a boat-chair conformation (boat cycloheptanol ling), whereas the methyl derivative (10b) is chair-boat,13 as shown by 1 H-NMR, supported by molecular mechanics calculations. 

As an example of hydrate nucleation and growth, consider the gas consumption versus time trace in Figure 3. la for an agitated system operated at constant pressure and temperature. An autoclave cell (e.g., 300 cm3) containing water (e.g., 150 cm3) is pressurized with gas and brought to hydrate formation (P, T) conditions. The gas is added from a reservoir to maintain constant pressure as hydrates form with time. The rate of consumption of gas is the hydrate formation rate that can be controlled by kinetics, or heat or mass transfer. 

An alternative hydrate formation and dissociation experiment is shown in the temperature and pressure trace of Figure 3.1b. In this case, the volume is constant and the temperature is changed during the experiment. In the experimental apparatus an agitated autoclave cell (e.g., 300 cm3) housing a sight glass window contains water (e.g., 150 cm3) that is pressurized with methane gas to the upper... 

At high driving forces and with constant cooling hydrate formation is less stochastic than that at a low driving force or at constant temperature. 

K = hydrate formation growth rate constant, representing a combined rate constant for diffusion (mass transfer) and adsorption (reaction) processes... 

As a special case of this example, one might specify that a natural gas mixture is in very large excess relative to the water phase (as in a gas-dominated pipeline), so that the gas composition does not change upon hydrate formation. Effectively, C = 1 for the gas components, with an additional component for the water (total C = 2). With three phases (Lw-H-V), there must be one intensive variable (F = 2 - 3 + 2) for a constant gas mixture composition (in large excess) relative to the water phase, specifying that the highest pipeline pressure is sufficient to determine the temperature (and the other intensive variables) at which hydrates form with a gas of fixed composition. 

Since the value of AHu remains constant over a large range of pressures, the maximum in T is determined by the point at which the molar volume change is zero. The volume comparison must be made between the pure liquid hydrocarbon, liquid water, and hydrate, since the hydrocarbon must exist as liquid at pressures between the vapor pressure and the critical pressure. Maxima in hydrate formation temperatures above Q2 have been calculated, but they have yet to be measured. 

Semilogarithmic plots of formation pressure versus reciprocal absolute temperature yield straight lines, over limited temperature ranges, for hydrate formation from either liquid water, or ice. From Equation 4.13 such linear plots either indicate (1) relatively constant values of the three factors (a) heat of formation, AH, (b) compressibility factor, z, (c) stoichiometry ratios of water to guest or (2) cancellation of curvilinear behavior in these three factors. 

The value of fitting the Langmuir constants to simple hydrate formation data is in the prediction of mixture hydrate formation. When the formation data for the simple hydrates are adequately fitted, then mixtures of those guest components can be predicted with no adjustable parameters. Since there are only eight simple hydrate formers of natural gas which form si and sll, but an infinite variety of mixtures, such an advantage represents a substantial savings of time and effort. 

Figure 5.17 illustrates the effect on hydrate formation when ethane and propane are combined at constant temperature. Ethane acts as an inhibitor to sll formation due to competition of ethane with propane to occupy the large cages of sll. Propane also acts as an inhibitor to si formation when added to ethane+water. In this case, however, since propane cannot enter the si cavities, the fugacity of ethane is lowered as propane is added, destabilizing the si hydrate. Holder (1976) refers to this inhibiting capacity as the antifreeze effect. 

Encapsulation of the gas decreases the pressure to the three-phase (Lw-H-V) condition. The system pressure may be controlled by an external reservoir for addition or withdrawal of gas, aqueous liquid, or some other fluid such as mercury. After hydrate formation, the pressure is reduced gradually, the equilibrium pressure is observed by the visual observation of hydrate crystal disappearance. Upon isothermal dissociation, the pressure will remain constant for a simple hydrate former until the hydrate phase is depleted. 

In isobaric operation the system pressure is maintained constant, by the exchange of gas or liquid with an external reservoir. The temperature is decreased until the formation of hydrate is indicated by significant addition of gas (or liquid) from a reservoir. After hydrate formation the temperature is slowly increased (maintaining constant pressure by fluid withdrawal) until the last crystal of hydrate disappears. This point, taken as the equilibrium temperature of hydrate formation at constant pressure, may be determined by visual observation of hydrate dissociation or at a constant temperature as simple hydrates dissociate with heat input. 

The Center for Hydrate Research has been conducting hydrate experiments for over 30 years in efforts to improve flow assurance strategies. The first statistical thermodynamic model for hydrates was developed in 1959 and involved many assumptions, including the assumption that volume is constant. This model predicted hydrate formation temperatures and pressures reasonably well at temperatures near the ice point and at low pressures. However, as industry moves to deeper waters, there is a need for a hydrate model that can predict hydrate formation at higher temperatures and pressures. 

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