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Application of the Akinfiev-Diamond equation of state to neutral hydroxides of metalloids

Application of the Akin?ev–Diamond equation of state

to neutral hydroxides of metalloids (B(OH)3,Si(OH)4,As(OH)3)

at in?nite dilution in water over a wide range of the state parameters,including steam conditions

Nikolay N.Akin?ev a ,?,Andrey V.Plyasunov b

Institute of Geology of Ore Deposits,Petrology,Mineralogy and Geochemistry (IGEM),Russian Academy of Sciences,Staromonetnyi per.,

35,109017Moscow,Russia

Institute of Experimental Mineralogy (IEM),Russian Academy of Sciences,Chernogolovka,Moscow Region 142432,Russia

Received 5July 2013;accepted in revised form 12November 2013;available online 23November 2013

Abstract

The Akin?ev and Diamond (2003)equation of state (EoS)for aqueous nonelectrolytes was employed to describe hydrox-ides of metalloids (B(OH)3,Si(OH)4,As(OH)3)over a wide temperature and pressure ranges,including steam conditions.The EoS is based on the accurate knowledge of solvent (H 2O)properties and requires only three empirical parameters to be ?tted to experimental data,and these are independent of temperature and pressure.For nonvolatile components thermodynamic properties of species in the ideal gas state were evaluated using quantum chemical computations.The proposed approach has been tested to predict the whole set of thermodynamic properties of solutes (the chemical potential,entropy,molar vol-ume,and molar heat capacity)over a wide range of temperatures (273–1200K)and pressures (0.1–1000MPa),including the near-critical region and both low and high density regions of the solvent.Thus it can be used for modeling various geochem-ical processes over a whole range of solvent densities,including processes in boiling ?uids and a vapor phase as well.ó2013Elsevier Ltd.All rights reserved.

1.INTRODUCTION

An accurate description of the thermodynamic proper-ties of neutral (uncharged)aqueous species over a wide pressure –temperature range is an important task with many practical applications in geochemistry and technol-ogy.Nevertheless,presently available thermodynamic descriptions of non-electrolytes are far less accurate than those of ionic species.For instance,the well known Helgeson–Kirkham–Flowers (HKF)equation of state (EoS)(Tanger and Helgeson,1988)provides excellent pre-dictions of thermodynamic properties of aqueous ions over a wide range of conditions (273–873K,0.1–500MPa).

However,when extended to neutral aqueous species (Shock et al.,1989;Schulte et al.,2001),the HKF model does not predict correctly the behavior of non-electrolyte solutes in the near-critical and supercritical regions of water (Plyasu-nov,1991;O’Connell et al.,1996;Lin and Wood,1996),and in the low density region of the solvent

(q ?1<0:35g cm à3

)as well (Plyasunov and Shock,2001;Akin?ev and Diamond,2003).This general de?ciency is one of the reasons for the recent work to develop alterna-tive EoS for aqueous non-electrolytes (Harvey,1996;O’Connell et al.,1996;Plyasunov et al.,2000a,b;Sedlbauer et al.,2000).Recently a simple semiemprical virial-like EoS (Akin?ev and Diamond,2003)was proposed for describing the thermodynamic properties of aqueous volatile nonelec-trolytes at in?nite dilution.It is based on the accurate EoS for a solvent (H 2O)and requires only three empirical parameters to be ?tted to experimental data,and these

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1587.

E-mail address:akin?ev@igem.ru (N.N.Akin?ev).

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Geochimica et Cosmochimica Acta 126(2014)

338–351

parameters are independent of temperature and pressure. Knowledge of the thermodynamic properties of a solute in the ideal gas state,together with these three parameters, enables the prediction of the whole set thermodynamic properties of the solute at in?nite dilution(the partial molar chemical potential,entropy,volume,and heat capacity) over a wide range of temperatures(273–773K)and pres-sures(0.1–200MPa),including the near-critical and low density region of the solvent.Here we extend this approach for description of low and non-volatile hydroxides of met-alloids B(OH)3,Si(OH)4,and As(OH)3.These species occur ubiquitously in natural hydrothermal?uids and show a marked partition into the vapor phase upon boiling (Styrikovich et al.,1960;Kukuljan et al.,1999;Pokrovski et al.,2002).Their presence in high-temperature steam may create considerable corrosion problems in water–steam cycles in power plants’installations(Bellows and Harvey, 1999).Thus the thermodynamic description of these species in a wide range of state parameters is relevant in geochemical and technological applications.

2.METHODS

The standard state convention adopted in this work is the one de?ned by IUPAC(Mills et al.,1993):for a gaseous sub-stance it is the hypothetical state of the pure substance in the gaseous state at the standard pressure P?P and exhibiting ideal gas behavior(P ?0:1MPa).The standard state for solid phases is the state of the pure substance in the solid state at the standard pressure,the standard state of solutes in the liquid phase of water is the state at the standard molality m=1,at a given pressure P,exhibiting in?nitely di-luted solution behavior.Following the recommendations of IUPAC,the superscripts*and1are used to designate the properties of a pure substance and of a solute at in?nite dilu-tion,respectively.The subscripts1and2designate water and a solute.

The detailed derivation of the proposed EoS is given in the previous paper(Akin?ev and Diamond,2003).Ulti-mately,the chemical potential of an aqueous nonelectrolyte species at in?nite dilution at a given temperature T(in K) and pressure P(in MPa)is expressed as

g1 2;aq eP;TT?g o

2;g

eTTàRT ln N wte1ànTRT ln

tRT n ln

P M w

tRT q?

atb

103

0:5

:e1T

Here the pure water density q?

1is expressed in g cmà3,the

pure water fugacity f?

1–in MPa,R=8.31446J molà1Kà1,

the molar weight of water M w=18.0152g molà1,and the number of moles of water in1kg of water N w=1000/ M w%55.508,P =0.1MPa is the standard pressure.

Symbols g1

2;aq eT;PTand g o

2;g

eTTstand for the chemical

potential of a solute in the state of a standard aqueous solution and in the ideal gas state,respectively.The n,a, and b are the empirical parameters of the EoS that are independent of pressure and temperature:n is a“scaling”factor proposed by Plyasunov et al.(2000a)that re?ects a relative dimension of the solute in comparison to solvent molecule,and two others(a and b)account for the tempera-ture e?ects of hydration of the solute.Eq.(1)expresses the Gibbs energy of hydration,i.e.a transfer of the solute molecule from the ideal gas state at temperature T to the water environment at the same T and a pressure P,so it can be easily modi?ed to express the Henry constant of the solute,k H(T,P),

lnek HT?e1ànTln

tn ln

P M w

tq?

atb

103

0:5

;e2T

and its distribution coe?cient,K D(T,P sat.),between coex-isting solvent’s vapor and liquid phases

ln K D?àn ln

1;vap

1;liq

àatb

103

0:5

1;vap

àq?

1;liq

:e3T

Derivation of the expressions for k H,K D and derivatives of Eq.(1)corresponding to the partial molar volume and heat capacity of the solute are given in the Appendix.There are also expressions for the fugacity coe?cient of a solute at

in?nite dilution in water,u1

,and for the second cross virial coe?cient water-solute,B12,an important property,re?ect-ing deviations from ideality of water-solute mixtures at low water densities(Prausnitz et al.,1999).At near-critical con-ditions the partial molar properties of a solute at in?nite dilution in water are governed by the Krichevskii parame-ter,A Kr(see Levelt Sengers,1991),and the corresponding analytical expression for A Kr is also given in the Appendix.

To compute g1

2;aq

eP;TT,additionally to n,a,and b,one needs to know thermodynamic properties of the molecule

in the ideal gas state,g o

2;g

eTT,and to use the solvent’s EoS

to predict f?

and q?

at the speci?ed P,T point.As it was applied in the original Akin?ev and Diamond(2003)paper we have employed the multiparameter Hill’s EoS for H2O (Hill,1990)that is valid from triple point pressure and tem-perature to1000MPa(or the melting line)and1273K and provides an accurate representation of existing thermody-namic data of H2O in that range.Note that the di?erences between the Hill(1990)EoS for water and the overall pre-viously used Haar–Gallagher–Kell model(Kestin et al., 1984)or more recent EoS due to Wagner and Pru?(2002) in the T–P range used in this work are very small(see be-low).At higher state parameters,exceeding the range of applicability of the Hill(1990)equation of state,the Wag-ner and Pru?(2002)formulation has been used.

As it has been stated in Akin?ev and Diamond(2003), the use of Eq.(1)for volatile solutes,when properties of corresponding gaseous species are well known,brings to a fair description of their thermodynamic properties over a wide range of temperatures(273–773K)and pressures (0.1–200MPa),including the near-critical region of the sol-vent(see Fig.1EA of Electronic Annex).The EoS also yields the correct low pressure limit for all thermodynamic properties of the solute,thus it can also be employed in the low density region of the solvent.

N.N.Akin?ev,A.V.Plyasunov/Geochimica et Cosmochimica Acta126(2014)338–351339

For a nonvolatile species lacking the thermodynamic properties in the ideal gas state the quantum chemical com-putations were employed.Quantum chemical computations were performed using the Gaussian09W,Revision C.01 suite of programs(Frisch et al.,2009).For the molecules under consideration the6-311G+(d,p)basis set was used. Electron correlation e?ects were included by the use of den-sity functional theory(DFT)with the hybrid functional B3LYP.A structure optimization procedure preceded ther-mochemical calculations.All molecular structures were processed and analyzed for imaginary frequencies using the GaussView5program.The temperature dependence of thermochemical properties was computed using standard Gaussian procedure(the Readisotopes option).

If the temperature dependence of the heat capacity of a

gaseous molecule,C o

p2;g eTT,is determined,then the g o

2;g

eTT

can be expressed in a traditional way

g o 2;g eTT?g o

2;g

eT rTàS o

2;g

eT rTáeTàT rT

Z T

T r

C o

p2;g

eTTdTàT

Z T

T r

C o

p2;g

eTTdeln TT;e4T

where T r stands for standard temperature https://www.doczj.com/doc/2e16227885.html,-

bining(1)and(4)one can see that g1

2;aq eT;PTis linearly depen-

dent on g o

2;g eT rT;S o

2;g

eT rT,and the parameters of the EoS,n,a,

and b.Thus to determine any set of these values a linear regression of available experimental data(solubility data for solids with the known thermodynamic data that give

g1 2;aq eT;PT,and/or k H(T,P),K D(T,P sat)can be employed.

Details of any speci?c regression procedure are

3.RESULTS

3.1.B(OH)3

Raman spectroscopic studies of

tions(Schmidt et al.,2005)demonstrates three-coordinated B(OH)3species is the

B in hydrothermal?uids from acidic to conditions,over wide temperature and

least up to900K and2GPa).

The determination of the EoS parameters was done as follows.First,we note that

for K D and V1

2use only the empirical

EoS without the properties of the molecule gas state,so these experimental data are rectly estimate parameters n,a,and b for The densities of boric acid solutions up to peratures and pressures were measured in works(Alekhin et al.,1993;Hnedkovsky et al., polsky et al.,1996;Abdulagatov and Azizov, which the study of Hnedkovsky et al. vibrating-tube densimeter was employed,is by precise and accurate one and covers the largest range.Experimentally measured molar

boric acid at298K given(Hnedkovsky et

0.1MPa V1

2?39:6cm3molà1was used to

factor of B(OH)3,n.

The vapor–liquid distribution of boric high temperatures was measured in two studies et al.,1960;Kukuljan et al.,1999).determined K D at temperatures T=373.2–637.3K by the vaporization method with colorimetric analysis of the con-densate.The distribution constants were found to be inde-pendent of B(OH)3concentrations(3?10à3–0.35m).In a later work,Kukuljan et al.(1999)employed a method of static vapor–liquid equilibration of dilute(0.02–0.10m) solutions of boric acid with separate samplings of vapor and liquid coexisting phases and spectrophotometric analy-sis of concentrations.As seen in Fig.1,these two sets are in satisfactory(within30%)agreement at520–640K,but di-verge at lower temperatures.Thus the a and b values of the EoS were determined by the linear regression employing these data for temperatures T>520K only.Two older de-tailed studies(Jaulmes and Gontard,1937;Stackelberg et al.,1937)are devoted to the vapor–liquid distribution of boric acid in water at atmospheric pressure,and the resulting value of ln K D(373K)=à5.63±0.08is retrieved in(Plyasunov,2011a).This value is considered to be the most reliable at this temperature and it is also used to?t the EoS parameters.Additional values of K D are reported by Nikolaeva and Bychkov(2007),based on sampling of the coexisting vapor and liquid phases in the wells of the Mutnovskaya geothermal plant(Kamchatka,Russia)at very low concentrations of salts(less than0.005mol kgà1 of solution).As these data do not refer to a strictly de?ned, laboratory controlled,chemical system,they were not used in the data treatment.

Evaluated values of n,a,and b are given in Table1.The

1.Experimental(symbols)and the calculated with the

of the vapor–liquid distribution of boric acid.The

labeled(Plyasunov,2011a),is obtained by the treatment

of Jaulmes and Gontard(1937)and Stackelberg et al.

considered the most reliable value at temperatures

K,see text.

340N.N.Akin?ev,A.V.Plyasunov/Geochimica et Cosmochimica Acta126(2014)338–351

between coexisting vapor and liquid phases of water.At T>500K the model closely approximates the consistent data of Styrikovich et al.(1960)and Kukuljan et al. (1999).At lower temperatures the calculated curve passes through the black circle,representing K D at373.15(Plyasu-nov,2011a),evaluated from consistent data of Jaulmes and Gontard(1937)and Stackelberg et al.(1937)and consid-ered the most reliable value at temperatures below500K (Plyasunov,2011a).The value of the Krichevskii parameter for aqueous B(OH)3,calculated from parameters of the model,is equal toà79.1MPa,in an excellent agreement with the value ofà78±5MPa,recommended by Plyasu-nov(2012).

Fig.2shows experimental and calculated values of V1

2and

p2at various temperatures and at pressures of35and28MPa,

respectively.It can be seen that the Akin?ev–Diamond(2003) EoS provides an excellent description of the available experi-mental data in the near critical region of H2O.However the

p2predictions are somewhat overestimated,especially at low

temperatures.For instance,at T=303.5K and P=28MPa

the predicted C1

p2=191J molà1Kà1is higher than the experi-

mental(Hnedkovsky et al.,1995)at the same conditions (121J molà1Kà1).

The model predictions in combination with the ideal gas properties of B(OH)3from Table1result in the following values for boric acid in the standard aqueous solution (298.15K,0.1MPa):D f G1=à970.80kJ molà1,and

S1 2=135.27J molà1Kà1.The value of D f G1is close to

the CODATA(Cox et al.,1989)recommended result of D f G1=à969.27±0.82kJ molà1,while the value of S1

2deviates signi?cantly from the CODATA recommendation

=162.4±0.6J Kà1molà1.

To test the applicability of the model to dense aqueous ?uids,the set of values of the chemical potential of aqueous

boric acid,g1

(B(OH)3(aq)),was generated using available most reliable thermodynamic data of B(OH)3(aq)along the isobar of28MPa at298–648K(see Electronic Annex for details).The accuracy of these data is about0.8kJ molà1 at standard temperature and about1kJ molà1at the high-est temperature of648K.It was found that deviation of the current model does not exceed2.2kJ that corresponds to the deviation of the natural logarithm of a thermodynamic constant,ln K<0.4.However,the agreement may be con-siderably improved adopting corrected values for thermo-dynamic properties of gaseous species at standard state

conditions,D f G o

298

=à931.15kJ molà1,and

S o

=274.89J molà1Kà1.In this case deviations do not ex-ceed the estimated accuracy in the whole temperature range.In spite of a noticeable di?erence between

=135.27J molà1Kà1of the model for the aqueous spe-cies and the CODATA recommendation,

=162.4±0.6J Kà1molà1,a good agreement for the

temperature dependence of g1

takes place:presumably an

underestimated value of S1

298

(aq)is compensated by the

overestimated value of C1

3.2.Si(OH)4

The monomeric form Si(OH)4dominates the speciation of silica in water from steam densities(Hashimoto,1992;

Table1

Thermodynamic parameters of hydroxides adopted in this study.

Species Ideal gas properties EoS parameters

D f G o

298,

kJ molà1S o

298

J molà1Kà1

C p(T),J molà1Kà1n a,

cm3gà1

cm3K0.5gà1

B(OH)3à931.04278.61195.7à0.406á10à3áT+2.482á105áTà2à2.186á103áTà0.5à1.057à4.2561 4.0194 Si(OH)4à1239.66346.3796.1+0.1575Tà1.858106Tà2à1.162410à4

T2+3.31510à8T3a

à1.89330.92850à0.9409

As(OH)3à598.784307.9494.7à6.84610à2Tà1.557106Tà2à4.26510à5

T2+1.14710à8T3

à1.230à9.90307.6818 a Rutz and Bockhorn(2005).

Table2

Thermodynamic properties of solid phases adopted in the study.

Phase D f G°298,

kJ molà1S°298,

J molà1Kà1

V°298,

cm3/mol

C p(T)

J molà1Kà1

SiO2(quartz)aà856.23941.33822.68846.9445+3.4309á10à2áTà1.1297á106áTà2

(298–848K);D H848=1213J/mol;

60.2914+8.11696á10à3áT(848–2000K)

As2O3(claudetite)bà576.262113.34547.2699.830+4.49361á10à2áTà1.4393á106áTà2(298–588K) As2S3(orpiment)bà85981163.59470.5095.102+5.7823á10à2áT+2.5313á105áTà2(298–580K) FeAsS(arsenopyrite)à13660068.5c26.42c75.510+4.780á10à3áT+7.543á105áTà2(298–650K)c

a Johnson et al.,1992.

b Pokrovski et al.,1996.

c Pokrovski et al.,2002.

N.N.Akin?ev,A.V.Plyasunov/Geochimica et Cosmochimica Acta126(2014)338–351341

Opila et al.,1997,1999)to high water densities (Zotov and Keppler,2000,2002;Hunt et al.,2011)at moderate (approximately below 1mol (kg H 2O)à1)concentrations of silica,as shown by direct Raman spectroscopic and mass-spectroscopic studies and the analysis of the volatility of SiO 2(s)in steam as a function of water pressure.At high contents of silica its speciation in water is dominated by the mixture of the monomeric and a number of polymeric spe-cies (Zotov and Keppler,2000,2002;Newton and Manning,2002,2003;Tossell,2005;Newton and Manning,2008a,b;Hunt et al.,2011).

Thermodynamic properties of aqueous Si(OH)4can be determined from the numerous and generally highly consis-tent works on the solubility of solid phases of SiO 2,mostly of quartz,in water,covering very wide temperature (from 293to 1403K)and pressure (from 0.1to 2GPa)ranges.To evaluate parameters of the Akin?ev and Diamond (2003)EoS numerous experimental data on quartz solubility (see below)were employed.The whole set of experimental

data (Kennedy,1950;Morey and Hesselgesser,1951a,b;Wyart and Sabatier,1954,1955;Khitarov,1956;Fournier,1960;Kitahara,1960;Lier et al.,1960;Siever,1962;Morey et al.,1962;Wendlandt and Glemser,1963;Heitmann,1964;Weill and Fyfe,1964;Anderson and Burnham,1965,1967;Glemser et al.,1966;Crerar and Anderson,1971;Seward,1974;Novgorodov,1977;Hemley et al.,1980;Ragnarsdot-tir and Walther,1983;Walther and Orville,1983;Schwartz-entruber et al.,1987;Redkin and Chevychelova,1988,1991;Xie and Walther,1993;Yokoyama et al.,1993;Manning,1994;Lakshtanov et al.,1994;Tsukimura,1995;Rimstidt,1997;Newton and Manning,2000;Shmulovich et al.,2001;Zotov and Keppler,2002;Shmulovich et al.,2006;Konyshev and Aksyuk,2008;Newton and Manning,2008a;Davis et al.,2011)was divided in 3parts:

1.solubility data in a low density aqueous ?uid

(q ?1<0.2g cm à3

);

volumes,V 12,and heat capacities of dissolved B(OH)3,C 1

p 2,at subcritical (left)and supercritical experimental data from Hnedkovsky et al.(1995):empty circles correspond to the pressure of curves are the equation of state (EoS)predictions at in?nite dilution.

2.data with very high solubility values(m Si(OH)4>

1mol kgà1)where polymerization e?ects may take

place(Newton and Manning,2003);

3.the rest of data,containing the majority of quartz

solubility points at293–1273K,0.1–1000MPa.

Only the3rd part of experimental quartz solubility data has been used in the?tting procedure.Thermodynamic properties of Si(OH)4in the ideal gas state were recently determined by the analysis of the relevant experimental data in Plyasunov(2011b).The temperature dependence of heat capacity of the molecule was adopted from compre-hensive study of Rutz and Bockhorn(2005)where DFT cal-culations at di?erent levels of theory including CBS-QBS and G3MP2methods,as well as corrections for hindered rotations and scaling for vibration frequencies were em-

ployed.The adopted C o

p (T=300–1500K)values for gas-

eous Si(OH)4were approximated by a function and used in the treatment of data,see Table1.The?tting procedure to evaluate the parameters of the Akin?ev–Diamond model also included the values of D f G o and S°of Si(OH)4in ideal gas state at standard state conditions.

First,to?t the EoS parameters,the dataset for g1

2 (Si(OH)4(aq))has been generated using accepted experi-mental data on quartz solubility in water according to the reaction SiO2(quartz)+2H2O=Si(OH)4(aq),as

g1 2eSi OH

eaqTeT;PT?gequartzTeT;PTt2geH2OTeT;PT

àRT ln m Si;

(2012)recommended for Si(OH)4A Kr=à190±10MPa

evaluated from the available relevant data.We have used

this value as an anchor while?tting.So,the?tting proce-

dure was iterative.After any initial approximation for n,

values of the a,b parameters of the EoS together with

D f G o

298

egTand S o

298

egTof Si(OH)4were determined by a

linear regression of the available g1

(Si(OH)4(aq))experi-

mental data.Then the n parameter was modi?ed in compli-

ance with the adopted A Kr value(Eq.A7),and the?tting

cycle was repeated until n ceased changing.

The?nally retrieved values for gaseous Si(OH)4are

D f G o

298

=à1239.66±1.7kJ molà1,S o

298

=346.37±3.5J

molà1Kà1,and the EoS parameters are n=à1.8933;

a=0.9285±1.1cm3gà1;b=à0.9409±0.97cm3K0.5gà1

(2r con?dence)(Table1).Evaluated in this work values of

D f G o

298

and S o

298

for Si(OH)4in the ideal gas state are very

close to the data given in Plyasunov(2011b)on the basis of

the analysis of the solubility amorphous silica and quartz in

low-density steam:à1238.51±3.5kJ molà1,and S o

298

347.78±6.2J molà1Kà1,correspondingly.

A comparison of experimental data and the results of

the Akin?ev–Diamond EoS are shown in Fig.3,while the

detailed comparison is given in the Electronic Annex.As

seen in Fig.3,the whole set of experimental data included

into the regression procedure(293

P<1GPa,the water density q?

>0.2g cmà3)is fairly well

described by the model.

It is interesting to compare the Akin?ev–Diamond(2003)

model predictions with the Manning’s(1994)correlating

equation(see Electronic Annex).The average absolute di?er-calculated with the model values of quartz solubility in water at293

N.N.Akin?ev,A.V.Plyasunov/Geochimica et Cosmochimica Acta126(2014)338–351343

by the model very well(Fig.4).The Krichevskii parameter,?xed in the?tting procedure at the value,recommended in (Plyasunov,2012b),is equal to A Kr=à190MPa.

It is now possible to test model’s abilities to predict

quartz solubility in low density(q?

1<0.25g cmà3)aqueous

?uids.The comparison is made with the following data sets: Morey and Hesselgesser(1951a),excluding data at673K and P<30MPa,as it was previously(Plyasunov,2011b) concluded that they are likely to be unequilibrated; Heitmann(1964),excluding data at P<0.6MPa as recom-mended in Plyasunov(2011b);and Fournier and Thomp-son(1993).Numerous results at673and773K presented in(Wendlandt and Glemser,1963)were excluded from con-sideration,as it was shown(Plyasunov,2011b)that they strongly deviate from all other data on solubility of quartz in steam.The detailed comparison of the predicted and experimental values is given in the Electronic Annex.It should be noted that despite the fact,that steam solubilities data were not used in the regression procedure,they are reproduced by the Akin?ev–Diamond(2003)model fairly well,although there is a tendency to overestimate the solu-bilites.The average absolute di?erence in lg m Si between all 60accepted experimental and calculated solubilities is0.100 with a standard deviation of0.133.On the other hand the Manning(1994)equation in general strongly underesti-mates steam solubilities,with the average absolute di?er-ence in lg m Si equal to0.495and a standard deviation of 0.582.

At very high temperatures(>1273K)or pressures (>1GPa),where solubility of quartz in water exceed à1solution there are attractive interactions between silica

monomers,resulting in formation of a number of polymeric forms via bridging oxygens(Hunt et al.,2011).The forma-tion of new forms can be described either through activity coe?cients that are signi?cantly less than1,or through an explicit consideration of polymerization constant.How-ever this problem goes beyond the scope of the current study.

3.3.As(OH)3

Thermodynamic properties of aqueous As(OH)3have been experimentally investigated in numerous studies(Pok-rovski et al.,1996,2002and references therein)mostly in dense aqueous?uids in a temperature range of298–623K.Perfetti et al.(2008)also measured partial molar volumes and heat capacities of aqueous As(OH)3up to 623K and to30MPa.These authors used a total set of available experimental data to re?ne thermodynamic prop-erties of the As(OH)3,aq over a wide temperature–pressure range in a framework of the revised HKF EoS(Tanger and Helgeson,1988)valid for neutral aqueous species (Shock et al.,1989).In the present study we used smoothed values for g1

(As(OH)3,aq)generated by the HKF EoS with parameters from Perfetti et al.(2008)for temperatures273–873K and pressures P sat.–200MPa to regress empirical parameters of the EoS under consideration.So,the iterative regression procedure,similarly to the method chosen for

Si(OH)4,included the evaluation of D f G o

298

egTand

S o

298

egTof As(OH)3in the ideal gas state at standard state conditions together with the a,b EoS’parameters on the

base of HKF generated g1

(As(OH)3,aq)(T,P)values,while the n parameter was iteratively estimated using available experimental data on the As vapor–liquid distribution, K D(Pokrovski et al.,2002).The temperature dependence of the heat capacity of the gaseous molecule was computed using the DFT B3LYP/6-311+G(d,p)method by means of the Gaussian09W,Revision C.01(Frisch et al.,2009)suite of programs.The?nally estimated values are:

D f G o

298

egT=à598.784±1.8kJ molà1,S o

298

egT=307.94±3.5J molà1Kà1,n=à1.23,a=à9.9030±1.05;b= 7.6818±1.16(2r con?dence)(Table1).

The model predictions in combination with the ideal gas properties of As(OH)3from Table1result in the following values for aqueous arsenic acid at standard state conditions (298.15K,0.1MPa):D f G1=à639.80kJ molà1,and

=187.42J molà1Kà1.The value of D f G1is equal to the value adopted in Perfetti et al.(2008),and very close to the evaluation in the review of Nordstrom and Archer

(2003)D f G1=à640.03kJ molà1.The value of S1

is lower

than the one recommended by Perfetti et al.(2008)–S1

= 212.4±10.0J Kà1molà1,but is close to the recommenda-

tion of Nordstrom and Archer(2003)–S1

=195.83J Kà1

molà1.Values of g1

(As(OH)3(aq))generated using the cur-rent EoS with parameters from Table1are close to the HKF model predictions within experimental uncertainties re-ported by Perfetti et al.(2008):the mean deviation between these two sets of values in the whole range of temperatures (273–873K)and pressures(0.1–200MPa)averages0.2in the ln K units(see Electronic Annex for details).It appears,

4.Experimental(symbols)and calculated with the model

values of the distribution constant of silica between the vapor

liquid phases of water.(See above-mentioned references

further information.)

344N.N.Akin?ev,A.V.Plyasunov/Geochimica et Cosmochimica Acta126(2014)338–351

Fig.5.Partial molar volumes,V 12,(left)and heat capacities,C 1

p (right)of dissolved As(OH)3vs.temperature at given pressure.Symbols denote experimental data from Perfetti et al.(2008).Solid curves are the equation of state (EoS)predictions at in?nite dilution.

various As phases at P sat .(left)and at 50MPa (right).Symbols stand for experimental data,for As(OH)3(aq)from Table 1.Thermodynamic properties for As phases were adopted from arsenopyrite are corrected in comparison to Pokrovski et al.(2002)(Table 2).Underestimated to the presence of polynuclear As complexes in the solution (Pokrovski et al.,1996)that are not computation.(See above-mentioned references for further information .)

7.Natural logarithm of As(OH)3vapor–liquid distribution coe?cient,ln K D ,along the water saturation curve.Symbols experimental data of Pokrovski et al.(2002),while the corresponds to the model description.

N.N.Akin?ev,A.V.Plyasunov /Geochimica et Cosmochimica Acta 126(2014)338–351345

4.CONCLUSIONS

This work analyzes the application of the Akin?ev–Diamond(2003)EoS to hydroxides of metalloids (B(OH)3,Si(OH)4,As(OH)3)over a wide temperature and pressure ranges,including steam conditions.

First,we note that this application is successful.Indeed, accurate data on the solubility of quartz in water at 294–1173K and pressures up to1000MPa at concentra-

tions of quartz below1m,in total664points,are described with an accuracy comparable to that of the Manning(1994) equation,which is the current standard for correlating the solubility of quartz in water.In the high-temperature high-pressure region,where the concentration of dissolved silica exceed1m($0.02in mole fractions),the model underesti-mates solubilities,which evidently could be accounted for the formation of polymeric species of silica at these condi-tions.The description of the distribution of silica(as well as boric acid and As(OH)3)between the vapor and liquid phases of water is highly accurate.The model predicts steam solubilities of quartz in a very good agreement with avail-able experimental data,even when they were not included in the regression procedure,while the Manning(1994)equa-tion gives much lower solubilities at these conditions.

A good agreement between experimental and model solu-bilities is due to a fair prediction of the chemical potential of the dissolved species,g1

,in a wide range of state parameters including the low density(vapor)and high density(liquid)re-gions of the solvent(H2O).Temperature and pressure deriv-

atives of the master equation for g1

allow calculations of V1

2 and C1

of the solute.While the approach provides a good prediction for partial molar volumes and heat capacities near

the critical region of water,it overestimates C1

especially at low temperatures.Obviously,it is very di?cult to achieve a “perfect”description with an equation,containing only3 empirical parameters.The models of Sedlbauer et al.(2000) and Plyasunov et al.(2000a,b),recognizing this problem, use the auxiliary“additional”heat capacity function to bring the calculated and experimental heat capacities into a forced agreement.The cost of this decision is the signi?cant loss of the predictive capabilities of models.Therefore,we believe that there should be a formulation with a minimum number of parameters to correlate and predict data for poorly studied solutes,even if it is applicable mainly for chemical potentials (equilibrium constants).

For hydroxides of metalloids(and metals)an additional issue is the thermodynamic properties of species in the ideal gas state.The application of the quantum chemical calcula-tions(the“Gaussian”package in this work)signi?cantly facilitates the solution of this problem,providing reliable values of the heat capacity at various temperatures and rea-sonable values of the entropy of gaseous species.

The proposed EoS is based on the accurate knowledge

of the solvent’s properties,i.e.its fugacity,f?

,and density,

,at given state parameters.In this study we,as a rule, have used Hill’s(1990)EoS,while for the very high PT parameters(T>1000K,P>800MPa)the Wagner and Pru?(2002)(WP)formulation was employed.However, the worldwide geochemical packages,such as EQ3/6 (Wolery,1992),HCh(Shvarov and Bastrakov,1999; Shvarov,2008)employ the SUPCRT(Johnson et al., 1992)format for the thermodynamic database for aqueous species that is originally based on the Haar-Gallagher-Kell (Kestin et al.,1984)(HGK)model.If one incorporates the proposed EoS into these packages it is necessary to know possible errors that arise because of use of di?erent EoS for the solvent.Fig.8shows these deviations in reference to the most recent and accurate Wagner and Pru?(2002)

8.Deviations between Wagner and Pru?(2002)(WP) Haar–Gallagher–Kell(HGK)(Kestin et al.,1984),and WP (1990)EoS for water as a function of temperature at various pressures in MPa.Ordinate axes stand for ratios between the (continuous lines)or HGK(dashed lines)EoS property to corresponding one for the WP EoS.

9.Natural logarithm of fugacity coe?cients,ln u1

2,of various

solutes as a function of pressure at673K.All the curves

computed using the proposed EoS.Data for H2,CO2,and

adopted from Akin?ev and Diamond(2003),while

B(OH)3,As(OH)3,and Si(OH)4–from Table1.The dashed

?gure corresponds to the ideal behavior of a solute.

et Cosmochimica Acta126(2014)338–351

formulation.It can be seen that di?erences between WP and Hill EoS predictions do not exceed1%both for density and fugacity of H2O.As to the HGK model,deviations arise only at very high values of state parameters (T>1000K,P>800MPa),but also do not exceed2% for density and3%for the H2O fugacity.However,the HGK model should be used with care at these extra conditions.

The proposed EoS predicts e?ects of hydration of sol-utes in water environment.The impact of the e?ect can be measured by the fugacity coe?cient of a solute at in?nite

dilution,u1

2.The corresponding expression for this prop-

erty is given in the Appendix(Eq.A8),while its pressure (and H2O density)dependence at constant temperature of 673K is given in Fig.9.It is interesting to note that volatile components(H2,CO2,H2S)demonstrate positive ln u1

2 values that corresponds to a hydrophobic type of solute–solvent interaction,while for the hydroxides under consid-eration(B(OH)3,As(OH)3,Si(OH)4)the opposite–a hydrophilic interaction is typical.The strongest one is for silica,that is consistent with Si(OH)4being a least volatile component.

An advantage of the proposed EoS is that it works both in low and high density regions of the solvent.Thus it can be used for modeling various geochemical processes in a whole range of solvent densities,including processes in boil-ing?uids and vapor phase as well.An illustration of the EoS’capabilities for predicting minerals’solubilities with the formation of aqueous B(OH)3,Si(OH)4,and As(OH)3 in a wide range of solvent densities are presented in the Electronic Annex.

ACKNOWLEDGMENTS

We are grateful to the GCA Associate Editor J.-F.Boyly,Jean Dubessy and two anonymous reviewers for useful comments and suggestions that signi?cantly improved the manuscript.This re-search was funded by RFBR grants12-05-93107_a and11-05-00786_a.

APPENDIX A.

The de?nition of the Henry constant,used in this work, is as follows:

k HeT;PT?lim

x x!0f2eT;PT

;eA:1T

i.e.Henry’s constant may be de?ned at any T and P.In the equation above f2(T,P)is the fugacity of a solute.The ana-lytical expression for Henry’s constant(in MPa)in the framework of the Akin?ev and Diamond(2003)EoS is gi-ven below:

lnek HT g1

2;aq

eT;P;xTàg o

2;g

eTT

?e1ànTln f?

tn ln

P M w

tq?

atb

103

0:5

;eA:2T

where g1

2;aq

eT;P;xTstands for the chemical potential of a

solute in the state of a standard aqueous solution in the

mole fraction concentration scale,and the relation between

2;aq

eT;P;xTand g1

2;aq

eP;TTin Eq.(1)as follows:

2;aq

eT;P;xT?g1

2;aq

eT;PTtRT ln N w:eA:3T

The distribution of a species between the vapor and li-

quid coexisting phases of water is given by the distribution

constant,K D,and the following expression gives K D for the

Akin?ev and Diamond(2003)model:

ln K D lim

x liq!0

x vap

liq

?lim

m liq!0

m vap

liq

?àn ln

1;vap

1;liq

àatb

103

0:5

1;vap

àq?

1;liq

eA:4T

The Akin?ev and Diamond(2003)EoS results in the fol-

lowing equations for the partial molar volume and the heat

capacity of a species at in?nite dilution in water:

?V?

e1ànTtn RT

@q?

tRT

@q?

atb

103

0:5

eA:5T

and

?C o

p2;g

te1ànTeC?

àC o

p1;g

àR nt2n T

@q?o

àn

eT2

@q?

@2q?

@T2

àRT a2

@q?

@2q?

@T2

tbà0:25á101:5Tà1:5q?

t101:5áTà0:5

@q?o

t101:5T0:5

@2q?

eA:6T

An important quantity,which governs many properties

of an in?nitely diluted solute in the near-critical region of

a solvent is the Krichevskii parameter(Levelt Sengers,

1991),A Kr,de?ned as A Kr?e@P=@xTc

V;T;x?0

,where the

superscript c indicates evaluation at the solvent critical

point.The easiest way to calculate the value of the Kri-

chevskii parameter in the framework of the EoS for an

in?nitely diluted solute is through the relation between

A Kr and V1

at the critical point of a solvent(Levelt Sen-

gers,1991):

A Kr?

k T V?

n RT c

1;c

RT c q?

1;c

áatb

103

0:5

?96:393ent0:3228á?atbá1:2432 T;eA:7T

where k T?1?

@q?

is the isothermal compressibility coef-

?cient of pure water.The fugacity coe?cient of dissolved

species,u2,is de?ned as f2=Px2u2(Prausnitz et al.,

1999).The expression for the fugacity coe?cient of a

dissolved species at in?nite dilution in water,u1

,for the

Akin?ev and Diamond(2003)EoS is given below: N.N.Akin?ev,A.V.Plyasunov/Geochimica et Cosmochimica Acta126(2014)338–351347

ln u1

2?ln

k H

?e1ànTln

àln

tn ln

P M w

tq?

atb

103

0:5

eA:8T

An important measure of the deviation from the ideal behavior of a mixture’s component at low densities is the second cross virial coe?cient B12(Prausnitz et al.,1999). It can be shown that the expression for B12for the Akin-?ev–Diamond model is as follows:

B12?e1ànTB11t1

atb

103

0:5

M w:eA:9T

The numerical factor M w=18.0152g molà1(the molar weight of water)is necessary as B12and B11have dimen-sions cm3molà1and the dimension for the water density in the model is g cmà3.Note that the values of B11are known with high precision(Harvey and Lemmon,2004) over very large temperature ranges(300–2000K).

APPENDIX B.SUPPLEMENTARY DATA Supplementary data associated with this article can be found,in the online version,at https://www.doczj.com/doc/2e16227885.html,/10.1016/ j.gca.2013.11.013.

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Associate editor:Jean Francois Boily

N.N.Akin?ev,A.V.Plyasunov/Geochimica et Cosmochimica Acta126(2014)338–351351

The way常见用法

The way 的用法 Ⅰ常见用法： 1)the way+ that 2)the way + in which（最为正式的用法） 3)the way + 省略（最为自然的用法）举例：I like the way in which he talks. I like the way that he talks. I like the way he talks. Ⅱ习惯用法：在当代美国英语中，the way用作为副词的对格，“the way+ 从句”实际上相当于一个状语从句来修饰整个句子。 1)The way =as I am talking to you just the way I’d talk to my own child. He did not do it the way his friends did. Most fruits are naturally sweet and we can eat them just the way they are—all we have to do is to clean and peel them. 2）The way= according to the way/ judging from the way The way you answer the question, you are an excellent student. The way most people look at you, you’d think trash man is a monster. 3）The way =how/ how much No one can imagine the way he missed her. 4）The way =because

The way的用法及其含义(二)

The way的用法及其含义（二）二、the way在句中的语法作用 the way在句中可以作主语、宾语或表语： 1.作主语 The way you are doing it is completely crazy.你这个干法简直发疯。 The way she puts on that accent really irritates me. 她故意操那种口音的样子实在令我恼火。The way she behaved towards him was utterly ruthless. 她对待他真是无情至极。 Words are important, but the way a person stands, folds his or her arms or moves his or her hands can also give us information about his or her feelings. 言语固然重要,但人的站姿,抱臂的方式和手势也回告诉我们他(她)的情感。 2.作宾语 I hate the way she stared at me.我讨厌她盯我看的样子。 We like the way that her hair hangs down.我们喜欢她的头发笔直地垂下来。 You could tell she was foreign by the way she was dressed. 从她的穿著就可以看出她是外国人。 She could not hide her amusement at the way he was dancing. 她见他跳舞的姿势，忍俊不禁。 3.作表语 This is the way the accident happened.这就是事故如何发生的。 Believe it or not, that's the way it is. 信不信由你, 反正事情就是这样。 That's the way I look at it, too. 我也是这么想。 That was the way minority nationalities were treated in old China. 那就是少数民族在旧中

(完整版)the的用法

定冠词the的用法：定冠词the与指示代词this ,that同源,有“那(这)个”的意思,但较弱,可以和一个名词连用,来表示某个或某些特定的人或东西. (1)特指双方都明白的人或物 Take the medicine.把药吃了. (2)上文提到过的人或事 He bought a house.他买了幢房子. I've been to the house.我去过那幢房子. (3)指世界上独一无二的事物 the sun ,the sky ,the moon, the earth (4)单数名词连用表示一类事物 the dollar 美元 the fox 狐狸或与形容词或分词连用,表示一类人 the rich 富人 the living 生者 (5)用在序数词和形容词最高级,及形容词等前面 Where do you live?你住在哪? I live on the second floor.我住在二楼. That's the very thing I've been looking for.那正是我要找的东西. (6)与复数名词连用,指整个群体 They are the teachers of this school.(指全体教师) They are teachers of this school.(指部分教师) (7)表示所有,相当于物主代词,用在表示身体部位的名词前 She caught me by the arm.她抓住了我的手臂. (8)用在某些有普通名词构成的国家名称,机关团体,阶级等专有名词前 the People's Republic of China 中华人民共和国 the United States 美国 (9)用在表示乐器的名词前 She plays the piano.她会弹钢琴. (10)用在姓氏的复数名词之前,表示一家人 the Greens 格林一家人(或格林夫妇) (11)用在惯用语中 in the day, in the morning... the day before yesterday, the next morning... in the sky... in the dark... in the end... on the whole, by the way...

“the way+从句”结构的意义及用法

“tｈｅwａｙ+从句”结构的意义及用法首先让我们来看下面这个句子: Ｒead the foｌloｗｉnｇpassagｅａnd talkａbout ｉt wi ｔh your classmaｔes．Try tｏｔeｌl whaｔyｏu thiｎk ｏf Tom aｎd ｏｆｔhe ｗay the chiｌｄrenｔrｅated ｈim. 在这个句子中，ｔhe waｙ是先行词,后面是省略了关系副词that或in whｉch的定语从句。下面我们将叙述“the ｗaｙ+从句”结构的用法。 1.tｈe wａy之后，引导定语从句的关系词是tｈat而不是hoｗ,因此，<<现代英语惯用法词典＞＞中所给出的下面两个句子是错误的：Ｔhｉs is ｔｈeｗayｈowｉtｈａppened. This is the way how he ａlwａｙs treats me. 2．在正式语体中,thaｔ可被in which所代替;在非正式语体中，ｔhat则往往省略。由此我们得到theｗay后接定语从句时的三种模式：1) tｈe ｗaｙ＋ｔhａt-从句２）the way +ｉn whiｃh－从句3) the ｗay +从句例如：Ｔｈe way(in whiｃh ，thａt) ｔhｅｓｅｃomｒade ｓloｏｋａｔｐrobｌems is wrong．这些同志看问题的方法

不对。Ｔｈｅｗａy(that ,ｉn ｗhiｃh)yoｕ’ｒe doinｇit is comple ｔeｌy crａzy.你这么个干法,简直发疯。 Wｅａdmiｒｅd him for thｅｗay ｉｎｗhｉch he fａｃeｓdiｆficultieｓ． Waｌlａｃe ａｎd Ｄarwiｎｇreed ｏn the way ｉｎwhi ｃh ｄｉfｆｅrｅnt forms ｏf life had ｂegｕn.华莱士和达尔文对不同类型的生物是如何起源的持相同的观点。 Thｉs is ｔｈe ｗaｙ（tｈａｔ) hｅdｉd it. I lｉkeｄｔhe waｙ(ｔhat) ｓｈeｏｒganized ｔhe ｍeetｉng． 3.theｗay(tｈat)有时可以与hｏw(作“如何”解）通用。例如： That’s tｈe ｗaｙ(tｈaｔ) shｅspoke. = Tｈat’s how shｅspoke.

way 用法

表示“方式”、“方法”，注意以下用法： 1.表示用某种方法或按某种方式，通常用介词in(此介词有时可省略)。如： Do it (in) your own way. 按你自己的方法做吧。 Please do not talk (in) that way. 请不要那样说。 2.表示做某事的方式或方法，其后可接不定式或of doing sth。如： It’s the best way of studying [to study] English. 这是学习英语的最好方法。 There are different ways to do [of doing] it. 做这事有不同的办法。 3.其后通常可直接跟一个定语从句(不用任何引导词)，也可跟由that 或in which 引导的定语从句，但是其后的从句不能由how 来引导。如：我不喜欢他说话的态度。正：I don’t like the way he spoke. 正：I don’t like the way that he spoke. 正：I don’t like the way in which he spoke. 误：I don’t like the way how he spoke. 4.注意以下各句the way 的用法： That’s the way (=how) he spoke. 那就是他说话的方式。 Nobody else loves you the way(=as) I do. 没有人像我这样爱你。 The way (=According as) you are studying now, you won’tmake much progress. 根据你现在学习情况来看，你不会有多大的进步。 2007年陕西省高考英语中有这样一道单项填空题： ——I think he is taking an active part insocial work. ——I agree with you_____. A、in a way B、on the way C、by the way D、in the way 此题答案选A。要想弄清为什么选A，而不选其他几项，则要弄清选项中含way的四个短语的不同意义和用法，下面我们就对此作一归纳和小结。一、in a way的用法表示：在一定程度上，从某方面说。如： In a way he was right.在某种程度上他是对的。注：in a way也可说成in one way。二、on the way的用法 1、表示：即将来(去)，就要来(去)。如： Spring is on the way.春天快到了。 I'd better be on my way soon.我最好还是快点儿走。 Radio forecasts said a sixth-grade wind was on the way.无线电预报说将有六级大风。 2、表示：在路上，在行进中。如： He stopped for breakfast on the way.他中途停下吃早点。 We had some good laughs on the way.我们在路上好好笑了一阵子。 3、表示：(婴儿)尚未出生。如： She has two children with another one on the way.她有两个孩子，现在还怀着一个。 She's got five children，and another one is on the way.她已经有5个孩子了，另一个又快生了。三、by the way的用法

The way的用法及其含义(一)

The way的用法及其含义（一）有这样一个句子：In 1770 the room was completed the way she wanted. 1770年，这间琥珀屋按照她的要求完成了。 the way在句中的语法作用是什么？其意义如何？在阅读时，学生经常会碰到一些含有the way 的句子，如：No one knows the way he invented the machine. He did not do the experiment the way his teacher told him.等等。他们对the way 的用法和含义比较模糊。在这几个句子中，the way之后的部分都是定语从句。第一句的意思是，“没人知道他是怎样发明这台机器的。”the way的意思相当于how；第二句的意思是，“他没有按照老师说的那样做实验。”the way 的意思相当于as。在In 1770 the room was completed the way she wanted.这句话中，the way也是as的含义。随着现代英语的发展，the way的用法已越来越普遍了。下面，我们从the way的语法作用和意义等方面做一考查和分析：一、the way作先行词，后接定语从句以下3种表达都是正确的。例如：“我喜欢她笑的样子。” 1. the way+ in which +从句 I like the way in which she smiles. 2. the way+ that +从句 I like the way that she smiles. 3. the way + 从句(省略了in which或that) I like the way she smiles. 又如：“火灾如何发生的，有好几种说法。” 1. There were several theories about the way in which the fire started. 2. There were several theories about the way that the fire started.

way 的用法

way 的用法【语境展示】 1. Now I’ll show you how to do the experiment in a different way. 下面我来演示如何用一种不同的方法做这个实验。 2. The teacher had a strange way to make his classes lively and interesting. 这位老师有种奇怪的办法让他的课生动有趣。 3. Can you tell me the best way of working out this problem? 你能告诉我算出这道题的最好方法吗？ 4. I don’t know the way (that / in which) he helped her out. 我不知道他用什么方法帮助她摆脱困境的。 5. The way (that / which) he talked about to solve the problem was difficult to understand. 他所谈到的解决这个问题的方法难以理解。 6. I don’t like the way that / which is being widely used for saving water. 我不喜欢这种正在被广泛使用的节水方法。 7. They did not do it the way we do now. 他们以前的做法和我们现在不一样。【归纳总结】 ●way作“方法，方式”讲时，如表示“以……方式”，前面常加介词in。如例1； ●way作“方法，方式”讲时，其后可接不定式to do sth.，也可接of doing sth. 作定语，表示做某事的方法。如例2，例3；

the-way-的用法讲解学习

t h e-w a y-的用法

The way 的用法 "the way+从句"结构在英语教科书中出现的频率较高, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或 in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 一.在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮.

way的用法总结大全

way的用法总结大全 way的用法你知道多少，今天给大家带来way的用法，希望能够帮助到大家，下面就和大家分享，来欣赏一下吧。 way的用法总结大全 way的意思 n. 道路,方法,方向,某方面 adv. 远远地，大大地 way用法 way可以用作名词 way的基本意思是“路,道,街,径”,一般用来指具体的“路,道路”,也可指通向某地的“方向”“路线”或做某事所采用的手段,即“方式,方法”。way还可指“习俗,作风”“距离”“附近,周围”“某方面”等。 way作“方法,方式,手段”解时,前面常加介词in。如果way前有this, that等限定词,介词可省略,但如果放在句首,介词则不可省略。

way作“方式,方法”解时,其后可接of v -ing或to- v 作定语,也可接定语从句,引导从句的关系代词或关系副词常可省略。 way用作名词的用法例句 I am on my way to the grocery store.我正在去杂货店的路上。 We lost the way in the dark.我们在黑夜中迷路了。 He asked me the way to London.他问我去伦敦的路。 way可以用作副词 way用作副词时意思是“远远地,大大地”,通常指在程度或距离上有一定的差距。 way back表示“很久以前”。 way用作副词的用法例句 It seems like Im always way too busy with work.我工作总是太忙了。 His ideas were way ahead of his time.他的思想远远超越了他那个时代。 She finished the race way ahead of the other runners.她第一个跑到终点,远远领先于其他选手。 way用法例句

the_way的用法大全教案资料

t h e_w a y的用法大全

The way 在the way+从句中, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或 in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 如果怕弄混淆，下面的可以不看了另外，在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮. the way=according to the way/judging from the way 4)The way you answer the qquestions, you must be an excellent student. 从你回答就知道,你是一个优秀的学生. 5)The way most people look at you, you'd think a trashman was a monster. 从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物. the way=how/how much 6)I know where you are from by the way you pronounce my name. 从你叫我名字的音调中,我知道你哪里人. 7)No one can imaine the way he misses her. 人们很想想象他是多么想念她. the way=because 8) No wonder that girls looks down upon me, the way you encourage her. 难怪那姑娘看不起我, 原来是你怂恿的

the way 的用法

The way 的用法 "the way+从句"结构在英语教科书中出现的频率较高, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 一.在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮.

the way=according to the way/judging from the way 4)The way you answer the qquestions, you must be an excellent student. 从你回答就知道,你是一个优秀的学生. 5)The way most people look at you, you'd think a trashman was a monster. 从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物. the way=how/how much 6)I know where you are from by the way you pronounce my name. 从你叫我名字的音调中,我知道你哪里人. 7)No one can imaine the way he misses her. 人们很想想象他是多么想念她. the way=because 8) No wonder that girls looks down upon me, the way you encourage her. 难怪那姑娘看不起我, 原来是你怂恿的 the way =while/when(表示对比) 9)From that day on, they walked into the classroom carrying defeat on their shoulders the way other students carried textbooks under their arms. 从那天起,其他同学是夹着书本来上课,而他们却带着"失败"的思想负担来上课.

The way的用法及其含义(三)

The way的用法及其含义（三）三、the way的语义 1. the way=as（像） Please do it the way I’ve told you.请按照我告诉你的那样做。 I'm talking to you just the way I'd talk to a boy of my own.我和你说话就像和自己孩子说话一样。 Plant need water the way they need sun light. 植物需要水就像它们需要阳光一样。 2. the way=how（怎样，多么） No one can imagine the way he misses her.没人能够想象出他是多么想念她！ I want to find out the way a volcano has formed.我想弄清楚火山是怎样形成的。 He was filled with anger at the way he had been treated.他因遭受如此待遇而怒火满腔。That’s the way she speaks.她就是那样讲话的。 3. the way=according as （根据） The way you answer the questions, you must be an excellent student.从你回答问题来看，你一定是名优秀的学生。 The way most people look at you, you'd think a trash man was a monster.从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物。 The way I look at it, it’s not what you do that matters so much.依我看，重要的并不是你做什么。 I might have been his son the way he talked.根据他说话的样子，好像我是他的儿子一样。One would think these men owned the earth the way they behave.他们这样行动，人家竟会以为他们是地球的主人。

way的用法

一．Way：“方式”、“方法” 1.表示用某种方法或按某种方式 Do it (in) your own way. Please do not talk (in) that way. 2.表示做某事的方式或方法 It’s the best way of studying [to study] English.。 There are different ways to do [of doing] it. 3.其后通常可直接跟一个定语从句(不用任何引导词)，也可跟由that 或in which 引导的定语从句正：I don’t like the way he spoke. I don’t like the way that he spoke. I don’t like the way in which he spoke.误：I don’t like the way how he spoke. 4. the way 的从句 That’s the way (=how) he spoke. I know where you are from by the way you pronounce my name. That was the way minority nationalities were treated in old China. Nobody else loves you the way(=as) I do. He did not do it the way his friend did. 二．固定搭配 1. In a/one way：In a way he was right. 2. In the way /get in one’s way I'm afraid your car is in the way， If you are not going to help，at least don't get in the way. You'll have to move－you're in my way. 3. in no way Theory can in no way be separated from practice. 4. On the way (to……) Let’s wait a few moments. He is on the way Spring is on the way. Radio forecasts said a sixth-grade wind was on the way. She has two children with another one on the way. 5. By the way By the way，do you know where Mary lives? 6. By way of Learn English by way of watching US TV series. 8. under way 1. Elbow one’s way He elbowed his way to the front of the queue. 2. shoulder one’s way 3. feel one‘s way 摸索着向前走；We couldn’t see anything in the cave, so we had to feel our way out 4. fight/force one’s way 突破。。。而前进The surrounded soldiers fought their way out. 5.. push/thrust one‘s way（在人群中）挤出一条路He pushed his way through the crowd. 6. wind one’s way 蜿蜒前进 7. lead the way 带路，领路；示范 8. lose one‘s way 迷失方向 9. clear the way 排除障碍，开路迷路 10. make one’s way 前进，行进The team slowly made their way through the jungle.

the way的用法大全

在the way+从句中, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 如果怕弄混淆，下面的可以不看了另外，在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮. the way=according to the way/judging from the way 4)The way you answer the qquestions, you must be an excellent student. 从你回答就知道,你是一个优秀的学生. 5)The way most people look at you, you'd think a trashman was a monster. 从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物. the way=how/how much 6)I know where you are from by the way you pronounce my name. 从你叫我名字的音调中,我知道你哪里人. 7)No one can imaine the way he misses her. 人们很想想象他是多么想念她. the way=because 8) No wonder that girls looks down upon me, the way you encourage her. 难怪那姑娘看不起我, 原来是你怂恿的 the way =while/when(表示对比) 9)From that day on, they walked into the classroom carrying defeat on their shoulders the way other students carried textbooks under their arms.

“the-way+从句”结构的意义及用法知识讲解

“the way+从句”结构的意义及用法首先让我们来看下面这个句子： Read the following passage and talk about it with your classmates. Try to tell what you think of Tom and of the way the children treated him. 在这个句子中，the way是先行词，后面是省略了关系副词that 或in which的定语从句。下面我们将叙述“the way+从句”结构的用法。 1．the way之后，引导定语从句的关系词是that而不是how,因此，<<现代英语惯用法词典>>中所给出的下面两个句子是错误的：This is the way how it happened. This is the way how he always treats me. 2. 在正式语体中，that可被in which所代替；在非正式语体中，that则往往省略。由此我们得到the way后接定语从句时的三种模式：1) the way +that-从句2) the way +in which-从句3) the way +从句例如：The way(in which ,that) these comrades look at problems is wrong.这些同志看问题的方法不对。

The way(that ,in which)you’re doing it is completely crazy.你这么个干法，简直发疯。 We admired him for the way in which he faces difficulties. Wallace and Darwin greed on the way in which different forms of life had begun.华莱士和达尔文对不同类型的生物是如何起源的持相同的观点。 This is the way (that) he did it. I liked the way (that) she organized the meeting. 3.the way(that)有时可以与how(作“如何”解)通用。例如： That’s the way (that) she spoke. = That’s how she spoke. I should like to know the way/how you learned to master the fundamental technique within so short a time. 4．the way的其它用法：以上我们讲的都是用作先行词的the way，下面我们将叙述它的一些用法。

定冠词the的12种用法

定冠词the的12种用法定冠词the 的12 种用法，全知道?快来一起学习吧。下面就和大家分享，来欣赏一下吧。定冠词the 的12 种用法，全知道? 定冠词the用在各种名词前面，目的是对这个名词做个记号，表示它的特指属性。所以在词汇表中，定冠词the 的词义是“这个，那个，这些，那些”，可见，the 即可以放在可数名词前，也可以修饰不可数名词，the 后面的名词可以是单数，也可以是复数。定冠词的基本用法： (1) 表示对某人、某物进行特指，所谓的特指就是“不是别的，就是那个!”如： The girl with a red cap is Susan. 戴了个红帽子的女孩是苏珊。 (2) 一旦用到the，表示谈话的俩人都知道说的谁、说的啥。如：

The dog is sick. 狗狗病了。(双方都知道是哪一只狗) (3) 前面提到过的，后文又提到。如： There is a cat in the tree.Thecat is black. 树上有一只猫，猫是黑色的。 (4) 表示世界上唯一的事物。如： The Great Wall is a wonder.万里长城是个奇迹。(5) 方位名词前。如： thenorth of the Yangtze River 长江以北地区 (6) 在序数词和形容词最高级的前面。如： Who is the first?谁第一个? Sam is the tallest.山姆最高。但是不能认为，最高级前必须加the，如： My best friend. 我最好的朋友。 (7) 在乐器前。如： play the flute 吹笛子

Way的用法

Way用法 A:I think you should phone Jenny and say sorry to her. B:_______. It was her fault. A. No way B. Not possible C. No chance D. Not at all 说明：正确答案是A. No way，意思是“别想！没门！决不！” 我认为你应该打电话给珍妮并向她道歉。没门！这是她的错。再看两个关于no way的例句：（1）Give up our tea break? NO way! 让我们放弃喝茶的休息时间？没门儿！（2）No way will I go on working for that boss. 我决不再给那个老板干了。 way一词含义丰富，由它构成的短语用法也很灵活。为了便于同学们掌握和用好它，现结合实例将其用法归纳如下：一、way的含义 1. 路线

He asked me the way to London. 他问我去伦敦的路。 We had to pick our way along the muddy track. 我们不得不在泥泞的小道上择路而行。 2. （沿某）方向 Look this way, please. 请往这边看。 Kindly step this way, ladies and gentlemen. 女士们、先生们，请这边走。 Look both ways before crossing the road. 过马路前向两边看一看。 Make sure that the sign is right way up. 一定要把符号的上下弄对。 3. 道、路、街，常用以构成复合词 a highway（公路），a waterway（水路），a railway（铁路），wayside（路边）

way与time的特殊用法

way/time的特殊用法 1、当先行词是way意思为”方式.方法”的时候,引导定语从句的关系词有下列3种形式： Way在从句中做宾语 The way that / which he explained to us is quite simple. Way在从句中做状语 The way t hat /in which he explained the sentence to us is quite simple. 2、当先行词是time时,若time表示次数时,应用关系代词that引导定语从句,that可以省略; 若time表示”一段时间”讲时,应用关系副词when或介词at/during + which引导定语从句 1.Is this factory _______ we visited last year? 2.Is this the factory-------we visited last year? A. where B in which C the one D which 3. This is the last time _________ I shall give you a lesson. A. when B that C which D in which 4.I don’t like the way ________ you laugh at her. A . that B on which C which D as 5.He didn’t understand the wa y ________ I worked out the problem. A which B in which C where D what 6.I could hardly remember how many times----I’ve failed. A that B which C in which D when 7.This is the second time--------the president has visited the country. A which B where C that D in which 8.This was at a time------there were no televisions, no computers or radios. A what B when C which D that