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Henry's law constant for hydrogen in high temperature water with dissolved lithium and boron.

INTRODUCTION

n dual-cycle nuclear reactors such as pressurized pres·sur·ize  
tr.v. pres·sur·ized, pres·sur·iz·ing, pres·sur·iz·es
1. To maintain normal air pressure in (an enclosure, as an aircraft or submarine).

2.
 water reactors (PWRs) and CANDUs, the water of the primary coolant coolant (kōō´lnt),
n
 is kept alkaline to minimize corrosion product transport and contains dissolved molecular hydrogen to maintain reducing conditions. The concentration of dissolved hydrogen in PWRs is generally controlled within the range 25-50 [cm.sup.3] (STP STP or standard temperature and pressure, standard conditions for measurement of the properties of matter. The standard temperature is the freezing point of pure water, 0°C; or 273.15°K;. )/kg, the value depending on the reactor. The rationale stems from early radiolysis ra·di·ol·y·sis
n. pl ra·di·ol·y·ses
Molecular decomposition of a substance as a result of radiation.



ra
 studies that determined the mechanisms by which excess hydrogen promotes back-reactions with radical species formed by the reaction of radiation with water in the core, so that potentially damaging products such as oxygen or hydrogen peroxide hydrogen peroxide, chemical compound, H2O2, a colorless, syrupy liquid that is a strong oxidizing agent and, in water solution, a weak acid. It is miscible with cold water and is soluble in alcohol and ether.  are avoided. The minimum levels to prevent oxidizing conditions had been determined (Solomon, 1978) to be within the range 10-15 [cm.sup.3] (STP)/kg.

Those early radiolysis studies were generally carried out at room temperature. Later information from modelling and experiments indicates that at operating temperatures (>300[degrees]C), where radiolysis yields are high but reaction rates are rapid, the minimum concentration of hydrogen to suppress oxidizing conditions is much les---within the range <1-5 [cm.sup.3] (STP)/kg (Frattini, 1999). CANDU CANDU CANada Deuterium Uranium (Atomic Energy of Canada Limited)  reactors, in fact, have traditionally operated with lower dissolved hydrogen levels than PWRs. Their heavy-water-moderated and -cooled design employs pressure tubes of the alloy Zr-21/2 Nb, rather than the stainless-steel-clad pressure vessel Pressure vessel

A cylindrical or spherical metal container capable of withstanding pressures exerted by the material enclosed. Pressure vessels are important because many liquids and gases must be stored under high pressure.
 of the PWRs. Since zirconium zirconium (zərkō`nēəm), metallic chemical element; symbol Zr; at. no. 40; at. wt. 91.22; m.p. about 1,852°C;; b.p. 4,377°C;; sp. gr. 6.5 at 20°C;; valence +2, +3, or +4.  alloys are susceptible to hydriding, a coolant concentration of dissolved hydrogen of 3-10 [cm.sup.3] (STP)/kg is specified to minimize the possibility of uptake by the metal (note, although the CANDU coolant is heavy water, [D.sub.2]O, protium protium /pro·ti·um/ (pro´te-um) see hydrogen.

pro·ti·um
n.
See hydrogen-1.



protium

the mass 1 isotope of hydrogen, symbol 1
 or light hydrogen, [H.sub.2] is added; in the core, this equilibrates rapidly with the deuterium deuterium (dtēr`ēəm), isotope of hydrogen with mass no. 2. The deuterium nucleus, called a deuteron, contains one proton and one neutron.  atoms in the [D.sub.2]O and at the levels added causes negligible isotopic downgrading).

Another difference between the coolant chemistry of PWRs and that of CANDUs is that the former employs dissolved boron boron (bōr`ŏn) [New Gr. from borax], chemical element; symbol B; at. no. 5; at. wt. 10.81; m.p. about 2,300°C;; sublimation point about 2,550°C;; sp. gr. 2.3 at 25°C;; valence +3.  oxide as a 'burnable' neutron poison or absorber. At the start of a reactor cycle, when the core contains fresh fuel enriched in the fissile fis·sile  
adj.
1. Possible to split.

2. Physics Fissionable, especially by neutrons of all energies.

3. Geology Easily split along close parallel planes.
 isotope [sup.235]U, boron concentrations up to 2000 mg/kg (as B) may be added to temper the neutron flux Noun 1. neutron flux - the rate of flow of neutrons; the number of neutrons passing through a unit area in unit time
flux - the rate of flow of energy or particles across a given surface
. This concentration diminishes steadily to zero during the cycle. The boron affects the radiolysis in that the [sup.10]B (n, [alpha])[sup.7] Li reaction deposits energy in the coolant and leads to somewhat higher steady-state concentrations of species such as hydrogen peroxide and oxygen at the start of cycle than at the end. Interestingly, recent modelling indicates that the threshold levels of hydrogen for suppressing radiolysis are little different at the start of cycle from at the end (Frattini, 1999).

The later PWRs with fuel that is rather more enriched than conventional units, along with CANDU reactors, have in-core boiling--the latter actually reaching net steam quality (<4%) at the core outlet while the former are generally restricted to sub-cooled boiling. The distribution of hydrogen between the vapour and liquid phases and the influence on the distribution of chemistry control agents such as boron and lithium (the latter for pH control) are of interest, since the radiolysis may be significantly affected.

The results of experiments from which the Henry's law constants were determined for hydrogen in natural water and for deuterium in heavy water, at high temperature (187 <t/[degrees]C < 306) were presented in previous papers (Yang et al., 1998; Morris et al., 2001x). The experimental technique utilized the H or D concentration dependency of the electrical resistance of palladium equilibrated with hydrogen (or deuterium) gas mixtures and aqueous solutions.

Experiments were also made involving solutions of hydrogen ([H.sub.2]) in water ([H.sub.2]O) with dissolved lithium hydroxide Lithium hydroxide (LiOH) is a corrosive alkali hydroxide. It is a white hygroscopic crystalline material. It is soluble in water, and slightly soluble in ethanol. It is available commercially in anhydrous form, or as the monohydrate.  and boron oxide. Interpretation of these data was deferred pending measurement of the solubility solubility

Degree to which a substance dissolves in a solvent to make a solution (usually expressed as grams of solute per litre of solvent). Solubility of one fluid (liquid or gas) in another may be complete (totally miscible; e.g.
 of hydrogen in water solutions with boron oxide, since no data were available in the literature. The results of these latter measurements have recently been published (Setthanan et al., 2006), and hence the Henry's law constants for hydrogen in water solutions with dissolved lithium and boron have been calculated, and are presented in this paper.

THEORY

Solution Equilibria

The equilibria involving hydrogen ([H.sub.2]), water ([H.sub.2]O) and palladium may be represented as:

[H.sub.2(g)] [equivalent to] 2[H.sub.(Pd)] (1)

[H.sub.2(aq)] [equivalent to] 2[H.sub.(Pd)] (2)

The equilibrium constant Noun 1. equilibrium constant - (chemistry) the ratio of concentrations when equilibrium is reached in a reversible reaction (when the rate of the forward reaction equals the rate of the reverse reaction)  [K.sub.1] ([P.sub.g], T) for Equation (1) at total pressure [P.sub.g, temperature T may be written:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII ASCII or American Standard Code for Information Interchange, a set of codes used to represent letters, numbers, a few symbols, and control characters. Originally designed for teletype operations, it has found wide application in computers. ] (3)

where [a.sub.H] is the activity at the atom ratio [x.sub.H] in the single-phase Pd-H solid solution and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are the fugacity fugacity /fu·gac·i·ty/ (fu-gas´it-e) a measure of the escaping tendency of a substance from one phase to another phase, or from one part of a phase to another part of the same phase.

fu·gac·i·ty
n.
 and pressure of hydrogen in the equilibrium gas; [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the fugacity coefficient.

The equilibrium 1 has been extensively studied. Recent measurements were made in the temperature range 300 < T/K < 1300 (Lasser and Powell, 1986). For the conditions of these experiments with pure [H.sub.2] gas at low pressure, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and for dilute solutions of H in Pd,

In [a.sub.H](T) = -[[alpha].sub.H](T)[x.sub.H] + In [x.sub.H] (4)

where [[alpha].sub.H] is the deviation from ideality i·de·al·i·ty  
n. pl. i·de·al·i·ties
1. The state or quality of being ideal.

2. Existence in idea only.

Noun 1.
 of the Pd-H solution. From Equation (4), as [x.sub.H] [right arrow] 0, In [a.sub.H] [right arrow] In [x.sub.H] (Henry's law) and the Equation (1) is ideal in terms of Sievert's law.

For the [H.sub.2]-Pd system, the results are as follows: From Equation (3) with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

and,

ln [[K.sub.1](T)/G[Pa.sub.-1]] = 2ln [1 + 1.981 exp(-768.0/T)/[[1 -exp(-800.0/T)].sup.3] + 1.8951 x [10.sup.3]/T - [4.293 x [10.sup.-4][T.sup.7/2]/[1-exp(-5986/T)] + 9.197 (6)

and

[[alpha].sub.H](T) = 2265/T [1 + 445/T] - 1 (7)

The equilibrium constant [K.sub.2] (P, T) for Equation (2) may be written as,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the mol fraction of [H.sub.2] in [H.sub.2]O and is assumed to be sufficiently low that the aqueous solution is ideal in terms of Henry's law.

It is to be noted that some experiments involving the gas phase (Equation 1) were conducted with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] with the addition of an inert gas inert gas or noble gas, any of the elements in Group 18 of the periodic table. In order of increasing atomic number they are: helium, neon, argon, krypton, xenon, and radon. . Also, experiments with the [H.sub.2]/[H.sub.2]O system (Equation 2) were conducted at P > [P.sup.0], where P.sup.0] is the vapour pressure of water Vapour pressure of water can be used in many experiments, particularly experiments relating to gases. A common classroom experiment in which the vapour pressure at various temperatures table is used is when trying to find the molar mass of butane.  at the temperature T, in order to suppress boiling. The reference pressure adopted for the reporting of data is [P.sup.0] and it may be shown (Denbigh, 1968) that the equilibrium constants K1 ([P.sup.0], T) and [K.sub.2] ([P.sup.0], T) are given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

where [V.sub.H] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are the partial molar molar /mo·lar/ (mo´lar)
1. pertaining to a mole of a substance.

2. a measure of the concentration of a solute, expressed as the number of moles of solute per liter of solution. Symbol M, , or mol/L.
 volumes of H in Pd and of [H.sub.2] in [H.sub.2]O, respectively, and R is the gas constant.

The Henry's law constant for the equilibrium

[H.sub.2(g)] [equivalent to] [H.sub.2(aq)] (11)

is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

The Henry's law constant at infinite dilution [K.sup.[infinity].sub.H]([P.sub.0], T), with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], is given by (Denbigh, 1968),

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)

Experiments with aqueous solutions were made at temperature T, pressure P (>[P.sub.0]) and from Equation (5) as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], [x.sub.H] [right arrow] 0,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)

From Equation (4) as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] with Equations (10) and (8),

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)

Monitoring of H in Pd

The concentration [x.sub.H] (P, T) was monitored in the experimental study of Equation (2) by measuring the electrical resistance of a palladium wire immersed in the aqueous [H.sub.2]/[H.sub.2]O solution. Previous studies (Morris et al., 2001b) involving Equation (1) in the temperature range 60 < t/[degrees]C < 330 gave the calibration equation for the Pd/H wire sensor as:

[LAMBDA The Greek letter "L," which is used as a symbol for "wavelength." A lambda is a particular frequency of light, and the term is widely used in optical networking. Sending "multiple lambdas" down a fiber is the same as sending "multiple frequencies" or "multiple colors. ] = 1.0 + (925.0[T.sup.-1] + 1.09)[x.sub.H] (16)

with correlation coefficient Correlation Coefficient

A measure that determines the degree to which two variable's movements are associated.

The correlation coefficient is calculated as:
 r = 0.95, where A [equivalent to] [lambda](T, [x.sub.H])/[lambda](T, [x.sub.H] = 0) and [lambda] is the electrical resistance. As [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], [x.sub.H] - 0, Sievert's law applies to the Equation (2) experiments and,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)

where m is a constant.

From Equations (16) and (17):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)

Equation (13), with Equations (14), (15), and (18) becomes:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

Measurements in Equation (2) system were made at pressures [P.sub.0] < P [less than or equal to] 15.5 MPa and the exponential term of Equation (9) is significant. Determination of A (T, [x.sub.H]) gives [x.sub.H] (P, T) from Equation (16). From Equations (10), (8), and (4),

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)

Hence [x.sub.H] ([P.sub.0], T) may be calculated and the equivalent pressure [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] ([P.sub.0], T) is determined by Equations (5), (6), and (7).

In the experimental work, the Pd sensor was placed in an autoclave autoclave

Vessel, usually of steel, able to withstand high temperatures and pressures. The chemical industry uses various types of autoclaves in manufacturing dyes and in other chemical reactions requiring high pressures.
 with continuous recirculation Noun 1. recirculation - circulation again
circulation - the spread or transmission of something (as news or money) to a wider group or area
 of the aqueous solution. The aqueous solution was re-equilibrated with hydrogen at ambient temperature Outside temperature at any given altitude, preferably expressed in degrees centigrade. . Hence [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the concentration of hydrogen in pure water, was calculated:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (e.g.) is the partial pressure of [H.sub.2] in the equilibrating gas and [K.sub.H] ([T.sub.ft]) is the Henry's law constant for hydrogen in water at the temperature of the feed tank (Yang et al., 1998, Figure 2). In the presence of dissolved solutes, the concentration [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], was calculated (Schumpe, 1993)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (22)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (23)

where [h.sub.i] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are the solute solute /so·lute/ (sol´ut) the substance dissolved in solvent to form a solution.

sol·ute
n.
 or ion specific parameter and the hydrogen gas specific parameter and [c.sub.i] is the concentration of the solute or ion. The concentrations of [H.sup.+] and O[H.sup.-] were determined by measurement of the pH of the solutions. [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the gas specific parameter at 298.15 K and [h.sub.T] is the gas specific temperature parameter. Values for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and [h.sub.T] have been published (Schumpe, 1993; Weisenberger and Schumpe, 1996). The solute specific parameter for dissolved B(OH)3 is [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]=0.07 [m.sup.3] [kmol.sup.-1] (Setthanan et al., 2006).

Hence [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is known and the ratio [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] may be calculated. This ratio will in general deviate from the Henry's law constant [K.sub.H] ([P.sup.0], 11 from Equation (12), since [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN in the [H.sub.2]-[H.sub.2]O gas mixture

From Equation (12),

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (24)

Hence,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (25)

EXPERIMENTAL

The sensor comprised a palladium wire of 0.25 mm diameter welded to a silver wire and connected to a Keithley multimeter model DMM See multimeter.

DMM - Digital Multimeter
2000 in a four-wire configuration. The details and schematic diagram of the sensor have been described elsewhere (Yang et al., 1998; Morris et al., 2001x). The resistance of the silver wire was calibrated over the experimental temperature range and then eliminated from the measured total resistance since the measured resistance comprised the resistance of the palladium and silver wires. Temperature was measured using platinum resistance temperature detectors (RTD RTD returned to duty (US DoD)
RTD Rated
RTD Ready to Drink
RTD Richmond Times-Dispatch
RTD Regional Transportation District
RTD Research, Technological Development
RTD Research and Technology Development
RTD Real-Time Data
).

The sensor was located in an autoclave where the temperature can be controlled to [+ or -]0.5[degrees]C precision. The pressure was maintained at 10.8 MPa for aqueous hydrogen experiments. The gas concentration in the solution was controlled at the feed tank where gas mixtures (0-100% hydrogen, balanced with argon argon (är`gŏn) [Gr.,=inert], gaseous chemical element; symbol Ar; at. no. 18; at. wt. 39.948; m.p. −189.2°C;; b.p. −185.7°C;; density 1.784 grams per liter at STP; valence 0. ) were bubbled continuously to maintain a gas/aqueous hydrogen equilibrium at temperature 30 [+ or -] 0.1[degrees]C. The concentration of dissolved hydrogen was calculated using Henry's law with [K.sub.H] (30[degrees]C) = 7.348 GPa/mol (Wilhelm et al., 1977). The partial pressure of hydrogen gas in the gas bubbles was deduced from the concentration of hydrogen in the gas cylinder gas cylinder nbombona de gas

gas cylinder gas nbouteille f de gaz

gas cylinder gas n
 assuming saturation with water at 30[degrees]C. The salting-out effect of the dissolved hydrogen concentrations in LiOH and/or [H.sub.3]B[O.sub.3] solutions was corrected (Setthanan et al., 2006).

[FIGURE 1 OMITTED]

The solution from the feed tank was fed into the autoclave using a pump through a heat exchanger heat exchanger

Any of several devices that transfer heat from a hot to a cold fluid. In many engineering applications, one fluid needs to be heated and another cooled, a requirement economically accomplished by a heat exchanger.
 and pre-heater prior to the autoclave. The outlet solution from the autoclave was then fed back to the feed tank via a heat exchanger (to recover heat) and a cooler. The details of the experimental loop and experimental procedures have been described previously (Yang et al., 1998; Morris et al., 2001x). The hydrogen and oxygen concentrations were also measured using Orbisphere sensors. The hydrogen concentration measured from the Orbisphere sensor was within 4 % error from the expected concentration.

Three sets of experiments were conducted with aqueous solutions of Li and B:

1. [H.sub.2]/[H.sub.2]O solutions with [B] = 2000 ppm, [Li] = 4 ppm, 490 < T< 581 K, P= 13.8 MPa.

2. [H.sub.2]/[H.sub.2]O solutions with [B] = 3300 ppm, [Li] = 2.5 ppm, 559 < T< 581 K, P= 13.8 MPa.

3. [H.sub.2]/[H.sub.2]O solutions with [B] = 2450 [+ or-] 190 ppm, 278 < [Li] < 16 300 ppm, T= 569 K, P= 13.8 MPa.

RESULTS AND DISCUSSION

Calculations were made by the procedures described previously (Morris et al., 2001x). The measured data and calculated quantities are presented in Tables 1-3 for the three sets of experiments. Values of [K.sup.[infinity].sub.H] ([P.sup.0], T) are plotted versus [T.sup.-1] from Tables 1 and 2 and Figure 1. This figure includes the empirical equation presented by Fernandez-Prini and Crovetto (1989) to describe their experimental data for the [H.sub.2]/[H.sub.2]O system (Equation 25, Morris et al., 2001a). It is seen that the presence of boron in solution significantly lowers the value of [K.sup.[infinity].sub.H]. For example at T = 570 K, [K.sup.[infinity].sub.H] = 1.25 Gpa[(mol fraction [H.sub.2]).sup.-1] for the B-free system. With [B] = 2000 ppm and [Li] =4 ppm, [K.sup.[infinity].sub.H] = 1.21 Gpa[(mol fraction [H.sub.2]).sup.-1]; with [B] = 3300 ppm, and [Li] =2.5 ppm, [K.sup.[infinity].sub.H] = 0.96 Gpa[(mol fraction [H.sub.2]).sup.-1].

The experimental method assumes that the measured change of the electrical resistance of the Pd sensor is due solely to dissolved H, according to according to
prep.
1. As stated or indicated by; on the authority of: according to historians.

2. In keeping with: according to instructions.

3.
 Equation (16), which arises solely from the dissolved [H.sub.2] in the aqueous phase aqueous phase
n.
The water portion of a system consisting of two liquid phases, one that is primarily water and a second that is a liquid immiscible with water.
 according to Equation (2). The possibility that B and/or Li may enter the Pd lattice, to influence the electrical resistance of the Pd, or the possibility of hydrogen generation by a redox redox (rē`dŏks): see oxidation and reduction.  reaction, may be considered as follows:

B[(OH).sub.3(aq)] + 3[H.sup.+.sub.(aq) + [3e.sup.-] [equivalent to] [B.sub.(s)]+ 3[H.sub.2]0; [E.sup.0] = -0.89 V (26)

[Li.sup.+.sub.(aq)] + 1/2[H.sub.2(g)] [equivalent to] Li(s)+ [H.sup.+.sub.(aq)]; [E.sup.0] = -3.05 V (27)

[Pd.sup.2+.sub.(aq)] + [H.sub.2(g)] [equivalent to] [Pd.sub.(s)] + 2[H.sup.+.sub.(aq)]; [E.sup.0] = +0.915 V (28)

where [E.sup.0] is the standard electrode potential. Consideration of these equilibria indicate that uptake of B and/or Li into the Pd lattice is remote, and further, the generation of hydrogen gas by chemical reaction is remote. For example, for the possible reaction leading to B deposition, Equation (26):

[DELTA][G.sup.o] = -zF[E.sup.0 = 258 kJ - -RT In K (29)

with

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (30)

From Table 2:

1. At [B] = 3000 ppm [equivalent to] 0.28 mol B/L, pH 5.7, [[H.sup.+]] = [10.sup.-5.7], [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and from Equations (29) and (30) at T = 300 K, [a.sub.b] = [10.sup.-63].

2. At T = 600 K, neglecting changes of [DELTA][G.sup.o] and pH, [a.sub.b] = 8 x [10.sup.-41].

The activity of elemental boron in the solution is vanishingly small and would not be expected to result in any significant absorption of B in the Pd sensor.

Furthermore, the data listed in Tables 1-3 giving the resistance ratio A as a function of the concentration of dissolved hydrogen, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], agree closely with Equation (16). The correlation coefficient r for the regression equations for the various sets of data is generally r [greater than or equal to] 0.999. If there were any extraneous influence on the electrical resistance of the sensor, deviations from Equation (16) would be expected.

The data from Table 3 are plotted in Figure 2. The presence of lithium in solution also lowers the Henry's law constant but at the concentrations pertinent to reactor coolants (<4 ppm) the effect is small. It can be ignored in calculating effects of solubility on radiolysis in boiling CANDU cores, for example (the fact that CANDU coolant is [D.sub.2]O rather than [H.sub.2]O will not affect this conclusion; the isotope effect at such low concentrations of Li will be negligible).

[FIGURE 2 OMITTED]

In the low-temperature [D.sub.2]O moderator of a CANDU, soluble boron may be used for long-term neutronic control, but at concentrations below 10 ppm. Although the data do not extend to moderator temperatures, and although the D versus H isotope effects are not available, it is unlikely that deuterium out-gassing to the moderator cover-gas will be affected by such low concentrations of boron. In PWR PWR pressurized-water reactor

Noun 1. PWR - a nuclear reactor that uses water as a coolant and moderator; the steam produced can drive a steam turbine
pressurized water reactor
 coolants with high concentrations of boron, the effect may be significant enough to be included in modelling in-core chemistry, particularly if there is concentration of solutes in deposits by boiling, for example. In terms of practical application to chemistry control the effect should be inconsequential in·con·se·quen·tial  
adj.
1. Lacking importance.

2. Not following from premises or evidence; illogical.

n.
A triviality.
.

Values for the fugacity coefficient [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are similar to those previously observed (Morris et al., 2001a), with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

CONCLUSION

The presence of both B and Li in aqueous solution causes a lowering of the Henry's law coefficients for [H.sub.2] in [H.sub.2]O, relative to values for pure water. For the pressurized water reactor Noun 1. pressurized water reactor - a nuclear reactor that uses water as a coolant and moderator; the steam produced can drive a steam turbine
PWR

water-cooled reactor - nuclear reactor using water as a coolant
 (PWR), with [B] ~2000 ppm, [Li] ~4 ppm, Table 1, the value of [K.sup.[infinity].sub.H] is lowered approximately 3%. This indicates that in a boiling system, the hydrogen gas stripped to the vapour phase would be 3 % less than that in pure water; the minimum concentration (Frattini, 1999) in the liquid to ensure suppression of radiolysis in an advanced PWR core with sub-cooled boiling would still be exceeded, however.
NOMENCLATURE

a                           activity

[a.sub.H]                   activity of H in palladium

[c.sub.i]                   concentration of solute or ion (kmol/
                            [m.sup.3])

[E.sup.0]                   standard electrode potential (V)

F                           Faraday (9.65 x [10.sup.4] C/mol)

[MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE IN
ASCII]                      fugacity of [H.sub.2] gas

[DELTA][G.sup.o]            standard free energy change of reaction (J)

[h.sub.i]                   solute or ion specific parameter (Equation
                            22) ([m.sup.3]/kmol)

[MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE IN
ASCII]                      hydrogen gas specific parameter ([m.sup.3]/
                            kmol)

[MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE IN
ASCII]                      hydrogen gas specific parameter at 298 K
                            ([m.sup.3]/kmol)

K                           equilibrium constant

[K.sub.1]                   equilibrium constant for [H.sub.2(g)]-Pd,
                            Equation (1)

[K.sub.2]                   equilibrium constant for [H.sub.2(aq)-Pd,
                            Equation (2)

[K.sup.[infinity].sub.H]    Henry's law constant (GPa/mol fraction
                            [H.sub.2])

[K.sup.'.sub.H]             Ratio: [MATHEMATICAL EXPRESSION NOT
                            REPRODUCIBLE IN ASCII] (GPa/mol fraction
                            [H.sub.2])

m                           empirical constant

[MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE IN
ASCII]                      partial pressure of [H.sub.2] (Pa)

[P.sub.g]                   pressure of the gas phase (Pa)

[P.sup.0]                   vapour pressure of water (Pa)

P                           total pressure (Pa)

R                           gas constant (8.31 J/mol K)

t                           temperature ([degrees]C)

T                       temperature (K)

[v.sub.H]                   partial molar volume of H in Pd ([cm3]/
                            mol H)

[MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE IN
ASCII]                      partial molar volume of [H.sub.2] in
                            [H.sub.2]O ([cm.sup.3]/mol [H.sub.2])

[x.sub.H]                   atom ratio of H to Pd

[MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE IN
ASCII]                      mol fraction of [H.sub.2] in water solution

[MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE IN
ASCII]                      mol fraction of [H.sub.2] in pure water

z                           number of moles of electrons

[[alpha].sub.H]             empirical value for the deviation of the
                            Pd-H solution from ideality

[lambda]                    electrical resistance of Pd wire ([OMEGA])

[LAMBDA]                    electrical resistance ratio

[MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE IN
ASCII]                      fugacity coefficient of [H.sub.2] gas.


Manuscript received 25 June 2007; revised manuscript received 20 August 2008; accepted for publication 14 July 2008.

REFERENCES

Denbigh, K. G., "The Principles of Chemical Equilibrium chemical equilibrium, state of balance in which two opposing reversible chemical reactions proceed at constant equal rates with no net change in the system. For example, when hydrogen gas, H2, and iodine gas, I2 ," 2nd ed., Cambridge University Press Cambridge University Press (known colloquially as CUP) is a publisher given a Royal Charter by Henry VIII in 1534, and one of the two privileged presses (the other being Oxford University Press). , Cambridge, UK (1968).

Fernandez-Prini, R. and R. J. Crovetto, "Evaluation of Data on Solubility of Simple Apolar apolar /apo·lar/ (a-po´ler) having neither poles nor processes; without polarity.

apolar

having neither poles nor processes; without polarity.
 Gases in Light and Heavy Water at High Temperature," Phys. Chem. Ref. Data 18, 1231 (1989).

Frattini, P., "Oxygen & Hydrogen Behaviour in PWR Primary Circuits," EPRI EPRI Electric Power Research Institute
EPRI European Parliaments Research Initiatives
 TE-114133, Electric Power Research Institute, Palo Alto Palo Alto, city, California
Palo Alto (păl`ō ăl`tō), city (1990 pop. 55,900), Santa Clara co., W Calif.; inc. 1894. Although primarily residential, Palo Alto has aerospace, electronics, and advanced research industries.
, CA, USA (1999).

Lasser, R., and G. L. Powell, "Solubility of H, D and T in Pd at Low Concentrations," Phys. Rev. B 34, 578 (1986).

Morris, D. R., L. Yang, F. Giraudeau, X. Sun and F. R. Steward, "Henry's Law Constant for Hydrogen in Natural Water and Deuterium in Heavy Water," Phys. Chem. Chem. Phys. 3, 1043-1046 (2001a).

Morris, D. R., L. Yang, X. Sun and F. R. Steward, "The Electric Resistance of Dilute Solutions of Hydrogen or Deuterium in Palladium," Can. Met. Quart quart: see English units of measurement. . 40, 91-96 (2001b).

Schumpe, A., "The Estimation of Gas Solubilities in Salt Solutions," Chem. Eng. Sci. 48, 153 (1993).

Setthanan, U., D. R. Morris and D. H. Lister, "Solubilities of [H.sub.2] in [H.sub.2]O and [D.sub.2] in [D.sub.2]O with Dissolved Boric Acid boric acid, any one of the three chemical compounds, orthoboric (or boracic) acid, metaboric acid, and tetraboric (or pyroboric) acid; the term often refers simply to orthoboric acid. The acids may be thought of as hydrates of boric oxide, B2O3.  and Lithium Hydroxide," Can. J. Chem. 84, 65-668 (2006).

Solomon, Y., "An Overview of Water Chemistry for PWRs," Proc. Int. Conf. on Water Chem. of Nuclear; Reactor Systems, Bournemouth UK (1977) BNES BNES British Nuclear Energy Society , London, UK (1978).

Weisenberger, S. and A. Schumpe, "Estimation of Gas Solubilities in Salt Solutions at Temperatures from 273 K to 363 K," AIChE J. 42, 298 (1996).

Wilhelm, E., R. Battino and R. W Wilcock, "Low-Pressure Solubility of Gases in Liquid Water," Chem. Rev. 77, 219 (1977).

Yang, L., X. Sun, F. R. Steward and D. R. Morris Ber. Bunsen-Ges, "Measurements of Henry's Law Constant for Hydrogen in Water Utilizing a Palladium Differential Resistance Sensor," Phys. Chem. 102, 780-785 (1998).

Franck Giraudeau, Derek H. Lister, David R. Morris, * Uncharat Setthanan, Frank R. Steward and Lei Tai The Lèi tái (Traditional: 擂臺 Simplified: 擂台 – “Beat (a drum) Platform”) is a raised fighting platform, without railings, where often fatal weapons and bare-knuckle martial arts tournaments were once held.  Yang Department of Chemical Engineering, University of New Brunswick The University of New Brunswick (UNB) is a Canadian university located in the province of New Brunswick. The university has two main campuses: the principal campus founded in 1785 in Fredericton and a smaller campus which was opened in Saint John in 1964. , Fredericton, NB, Canada E3B 5A3

* Author to whom correspondence may be addressed. E-mail address: dkmorris@arogers.com
Table 1. [H.sub.2]/[H.sub.2]0 solutions with [B]=2000 ppm, [Li]=4 ppm,
490 < T< 581 K, P=13.8 MPa, pH 5.80 at 30[degrees]C

T (K)    [MATHEMA-    [LAMBDA]   [K.sup.         [K.sub.H]    [phi]
         TICAL                   [infinity]                   [H.sub.2]
         EXPRESSION              .sub.H]
         NOT                     ([P.sup.O],
         REPRO-                  T) (Gpa[(mol
         DUCIBLE                 fraction
         IN ASCII]               [H.sub.2])
                                 .sup.-1])

491.5         0.66      1.008    3.06               3.23        0.95
              3.23      1.017                       2.65        1.15
              7.21      1.025                       2.63        1.16
             12.95      1.035                       2.60        1.18

493.2         0.66      1.008    2.93               2.84        1.03
              3.23      1.017                       2.70        1.09
              7.21      1.025                       2.53        1.16
             12.95      1.033                       2.48        1.18

500.8         0.66      1.007    2.81               2.77        1.01
              3.23      1.015                       2.55        1.10
              7.21      1.023                       2.51        1.12
             12.95      1.031                       2.40        1.17

510.5         0.66      1.007    2.52               2.55        0.99
              3.23      1.014                       2.28        1.11
              7.21      1.021                       2.26        1.11
             12.95      1.028                       2.20        1.15

510.6         0.66      1.006    2.27               2.15        1.05
              3.23      1.013                       2.15        1.05
              7.21      1.020                       2.05        1.11
             12.95      1.027                       1.98        1.15

520.4         0.66      1.006    2.21               2.26        0.98
              3.23      1.012                       2.04        1.09
              7.21      1.019                       2.03        1.09
             12.95      1.025                       1.95        1.13

529.6         0.66      1.005    1.88               1.86        1.01
              3.23      1.011                       1.77        1.06
              7.21      1.017                       1.76        1.07
             12.95      1.022                       1.68        1.12

539.5         0.66      1.005    1.79               1.87        0.96
              3.23      1.010                       1.66        1.08
              7.21      1.016                       1.66        1.08
             12.95      1.021                       1.63        1.10

549.4         0.66      1.004    1.55               1.62        0.95
              3.23      1.009                       1.49        1.04
              7.21      1.014                       1.38        1.12
             12.95      1.019                       1.45        1.07

559.3         0.66      1.004    1.39               1.40        0.99
              3.23      1.008                       1.33        1.04
              7.21      1.013                       1.32        1.05
             12.95      1.017                       1.28        1.08

569.3         0.66      1.004    1.21               1.25        0.97
              3.23      1.007                       1.14        1.06
              7.21      1.011                       1.16        1.04
             12.95      1.015                       1.13        1.07

576.3         0.66      1.003    1.17               1.20        0.97
              3.23      1.007                       1.12        1.04
              7.21      1.011                       1.11        1.05
             12.95      1.014                       1.10        1.06

581.6         0.66      1.003    1.00               1.05        0.96
              3.23      1.006                       0.96        1.05
              7.21      1.010                       0.95        1.05
             12.95      1.013                       0.95        1.05

Table 2. [H.sub.2]/[H.sub.2]0 solutions with [B] = 3000 ppm,
[Li]=2.5 ppm, 559 < T< 581 K, P=13.8 MPa, pH 5.71 at 30[degrees]C
each data set represents theaverage from (usually) three Pd/H sensors

T (K)    [MATHEMATICAL    [LAMBA]                 [K.sup.[infinity].
         EXPRESSION NOT                           sub.H] ([P.sup.O],
         REPRODUCIBLE                             T) (Gpa[(mol
         IN ASCII]                                fraction
                                                  [H.sub.2]).sup.-1])

559.4         0.64     1.003 [+ or -] 0.004%      1.16 [+ or -] 0.03
              3.11     1.008 [+ or -] 0.011%
              6.95     1.011 [+ or -] 0.015%
             12.48     1.015 [+ or -] 0.017%

576.6         0.64     1.003 [+ or -] 0.004%      0.96 [+ or -] 0.01
              3.11     1.007 [+ or -] 0.005%
              6.95     1.009 [+ or -] 0.007%
             12.48     1.013 [+ or -] 0.009%

581.2         0.64     1.003                      0.92
              3.11     1.006
             12.48     1.012

Table 3. [H.sub.2]/[H.sub.2]0 solutions with [B]=2450 [+ or -] 190 ppm,
278 < [Li] < 16 300 ppm, T=569 K, P=13.8 MPa each data set represents
the average from (two or) three Pd/H sensors

Li (ppm)   pH at           [MATHEMATICAL     [LAMBDA]
           30[degrees]C    EXPRESSION NOT
                           REPRODUCIBLE
                           IN ASCII]

278         8.14            0.65             1.004 [+ or -] 0.012%
                            3.14             1.008 [+ or -] 0.010%
                            7.02             1.011 [+ or -] 0.029%
                           12.60             1.015 [+ or -] 0.036%

812         8.99            0.64             1.004 [+ or -] 0.016%
                            3.12             1.008 [+ or -] 0.018%
                            6.98             1.011 [+ or -] 0.035%
                           12.52             1.015 [+ or -] 0.056%

1710       10.69            0.64             1.003 [+ or -] 0.004%
                            3.10             1.008 [+ or -] 0.006%
                            6.93             1.011 [+ or -] 0.007%
                           12.44             1.015 [+ or -] 0.006%

4050       11.44            0.62             1.003 [+ or -] 0.006%
                            3.02             1.007 [+ or -] 0.018%
                            6.76             1.010 [+ or -] 0.017%
                           12.13             1.015 [+ or -] 0.050%

6900       11.45            0.60             1.003 [+ or -] 0.000%
                            2.94             1.007 [+ or -] 0.027%
                            6.57             1.010 [+ or -] 0.025%
                           11.79             1.013 [+ or -] 0.027%

8890       11.62            0.59             1.003 [+ or -] 0.004%
                            2.88             1.007 [+ or -] 0.033%
                            6.44             1.009 [+ or -] 0.037%
                           11.56             1.012 [+ or -] 0.037%

13600      11.72            0.57             1.003 [+ or -] 0.008%
                            2.75             1.006 [+ or -] 0.035%
                            6.14             1.009 [+ or -] 0.055%
                           11.03             1.013 [+ or -] 0.054%

16300      11.85            0.55             1.003 [+ or -] 0.005%
                            2.69             1.006 [+ or -] 0.018%
                            6.02             1.009 [+ or -] 0.019%
                           10.80             1.012 [+ or -] 0.029%

                           [K.sup.[infinity].
[MATHEMATICAL              sub.H] ([P.sup.O],
EXPRESSION NOT             T) (Gpa[(mol
REPRODUCIBLE               fraction
IN ASCII]                  [H.sub.2]).sup.-1])

 0.65                       1.23 [+ or -] 0.06
 3.14
 7.02
12.60

 0.64                       1.30 [+ or -] 0.09
 3.12
 6.98
12.52

 0.64                       1.23 [+ or -] 0.01
 3.10
 6.93
12.44

 0.62                       1.18 [+ or -] 0.04
 3.02
 6.76
12.13

 0.60                       1.02 [+ or -] 0.05
 2.94
 6.57
11.79

 0.59                       0.94 [+ or -] 0.07
 2.88
 6.44
11.56

 0.57                       1.00 [+ or -] 0.10
 2.75
 6.14
11.03

 0.55
 2.69
 6.02
10.80                      0.85 [+ or -] 0.04
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Author:Giraudeau, Franck; Lister, Derek H.; Morris, David R.; Setthanan, Uncharat; Steward, Frank R.; Yang,
Publication:Canadian Journal of Chemical Engineering
Date:Dec 1, 2008
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