Synthesis of Submicron Silver Powder by the Hydrometallurgical Reduction of Silver Nitrate with Hydrazine Hydrate and a Thermodynamic Analysis of the System
DINABANDHU GHOSH and SAMUDRA DASGUPTA
A silver powder of submicron size was produced from the aqueous solutions of its compounds. The silver compounds tried out were silver nitrate and silver oxide, and the reducing agents employed were dimethyl formamide (DMF), hydrazine hydrate, and sodium azide. The solvent mediums were distilled water for the reductions with DMF and sodium azide, and a 2:1 (by volume) mixture of distilled water and ethanol for the reductions with hydrazine hydrate. Of the three reductants, hydrazine hydrate (N2H4ÆH2O) alone was successful in reducing both the silver compounds to a submicron (<500 nm) metallic silver powder, as revealed by X-ray diffraction (XRD) studies and scanning electron microscopy (SEM) analyses. Additionally, the thermo- dynamic equilibrium of the system AgNO3-N2H4ÆH2O in the water–ethanol mixture (2:1) was studied at 298 K; the equilibrium constant data so generated was found to compare very well with those derived from the established data of enthalpies and free energies of formation, and half-cell potentials. The following activity coefficient (Raoultian)–composition relationship for hydrazine hydrate in its dilute solution in water (plus ethanol) at 298 K is proposed:
2 lnðcN2H4:H2OÞ¼1862ð 371Þ 2055ð 424Þð1 XN2H4 H2OÞ
DOI: 10.1007/s11663-007-9123-5 The Minerals, Metals & Materials Society and ASM International 2008
I. INTRODUCTION used are: sodium borohydride in the presence of dodecanethiol (for synthesizing gold particles 1 to POWDERS of noble metals such as gold, silver, and 3 nm in size with a surface coating of thiol),[2] tetrakis palladium have of late gained tremendous industrial (hydroxymethyl) phosphonium chloride (for preparing acceptance, owing to some exciting and pathbreaking a hydrosol of gold clusters),[3] and hydrazine dissolved applications. Silver powders of submicron scale find in the mixture of di(2-ethyl-hexyl) sulfosuccinate, extensive use as catalysts and in conductive adhesives, isooctane, and water (for synthesizing silver nanod- display devices, and the fabrication of thick film isks).[4] A number of more recent studies[5–16] exclu- materials. To meet the requirements of these applica- sively on silver synthesis have been concerned with a tions, it is necessary to suitably change the chemical nanosized silver powder,[5,9,10–12,16] nanostructures,[6] and physical properties of the products during their [8,13,15] [1] and composites. Many of these works followed preparation. One such special requirement may be to the liquid-phase reduction route,[6,7,11–14] using reduc- have monosized submicron or nanoparticles of the ing agents like polyglycol[6] and ethylenediamine tetra- final product. This type of ultrafine metal powder can acetic acid.[7] In the present work, to produce submi- be prepared by a variety of means, such as sol-gel cron silver powder from silver compounds such as synthesis, spray pyrolysis, plasma synthesis, inert gas silver nitrate and silver oxide, the different reducing condensation, electrodeposition, etc., in addition to the agents tried out are: sodium azide (NaN3) in aqueous wet chemical synthesis route, which is followed in the medium, dimethyl formamide (DMF) in aqueous present work with aqueous (with or without ethanol) medium, and hydrazine hydrate (N2H4ÆH2O) in a solvents. The presence of ethanol in the medium is water–ethanol mixture (2:1, by volume). Sodium azide expected to prevent the formation of bigger particles in is supposed to be a powerful reducing agent with the the final product in a low-temperature recovery pro- low oxidation number (-1/3) for nitrogen (N) in it. (It cess. Some of the important reducing agents previously may help to recall that N can possess up to a +5 oxidation number.) The possible mechanism of the DINABANDHU GHOSH, Professor, SAMUDRA DASGUPTA, reduction by DMF is that DMF breaks the water formerly Undergraduate Student, are with the Department of Metal- molecule into oxygen and hydrogen; the latter, in turn, lurgical Engineering, Jadavpur University, Kolkata 700032, India. reduces the metallic salt. The third reducing agent, Contact e-mail: [email protected] SAMUDRA DASGUPTA, Scientist, is with the Aeronautical Development Establishment, Defence hydrazine hydrate (N2H4ÆH2O), is also expected to be a Research and Development Organisation, Bangalore 560075, India. good reducing agent, with the low oxidation number Manuscript submitted November 13, 2006. (-2) of N. Article published online February 5, 2008.
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 39B, FEBRUARY 2008—35 In addition to the synthesis of submicron silver 3000P and PHILIPS* PW 1710/1840) and scanning powder, the thermodynamic equilibrium of the system AgNO3-N2H4 Æ H2O in the water-ethanol mixture (2:1) is studied in the present work and the resulting *PHILIPS is a trademark of Philips Electronic Instruments Corp., thermodynamic data (the standard free energy change Mahwah, NJ. of the reduction reaction) is compared with the estab- lished data.[17,18] This allows the proposal for the electron microscopy (SEM) (JEOL** JSM 5200) activity coefficient–composition relationship for hydra- zine hydrate in its dilute solution in water (plus ethanol) at 298 K. **JEOL is a trademark of Japan Electron Optics Ltd., Tokyo.
II. EXPERIMENTAL PROCEDURE analyses for phase identification and particle size deter- mination. A. Ordinary Runs with DMF, NaN3, and N2H4ÆH2O for the Synthesis of Ag B. Special Runs with N2H4ÆH2O for Thermodynamic The steps involved in the ordinary runs were as Analysis follows. (1) Preparation of solvent: 30 mL of distilled water Of the three reducing agents, hydrazine hydrate alone (for the reducing agents DMF and NaN3), or a mixture was found to successfully precipitate metallic silver and, of 20 mL of distilled water and 10 mL of ethanol (for hence, was chosen for subsequent thermodynamic anal- the reducing agent N2H4ÆH2O) was transferred to a ysis. These special experimental runs were conducted, to 100 mL beaker, with the help of 10-, 20-, or 30-mL study the thermodynamic equilibrium of the system pipettes; both beakers and pipettes were made of Pyrex AgNO3-N2H4ÆH2O in a 2:1 (volumetric ratio) water- glass (supplied by Science India, Kolkata, India). A very ethanol mixture and to determine the activity coefficient– small quantity of gelatin powder, a hydrophilic colloid, composition relationship for hydrazine hydrate in its was added to prevent the possible coagulation of the dilute solution in water (plus ethanol) at 298 K. For this precipitated particles during the subsequent reduction purpose, to a fixed quantity of silver nitrate solution stage. Now, the solvent was constantly subjected to (1.000 g, i.e., 5.88 millimol, of silver nitrate dissolved in a stirring by an electromagnetic stirrer-cum-heater (Remi solvent of 20 mL of distilled water and 10 mL of Equipments, Mumbai, India, model 2MLH) at 298 K. ethanol), taken in a 100 mL beaker, drops of hydrazine (2) Preparation of solution: Typically, 1 g of the hydrate were added from the burette, beginning with one chosen silver compound (silver nitrate or silver oxide), drop (1 drop ” 0.05 mL ” 1.03 millimol of hydrazine [19] 99.8 pct pure (Nice/Loba Chemie, Mumbai, India), was hydrate with a density of 1.03 g/mL; the clarification added to the solvent. The mass measurements were about the measurement and reproducibility of the drop made in a single-pan balance (Dhona Instruments Pvt. volume is given subsequently) and progressively increas- Ltd., Kolkata, India, model: 160 D) with the precision ing up to 10 drops, in a series of ten experiments, of 0.1 mg. The magnetic stirring was continued, to ensuring equilibrium in each case. The attainment of ensure the homogenization of the solution. equilibrium was instantaneous, since the kinetics of silver (3) Reduction: Drops of the chosen reducing agent precipitation was exceedingly fast. The wet precipitate of (DMF, sodium azide, or hydrazine hydrate), 99 pct pure silver was then, as in the ordinary runs, heated on the (S.D. Fine–Chem Ltd., Mumbai, India), were added from hotplate at a low temperature (about 323 K), to slowly a graduated Pyrex glass burette, with the smallest division drive away the liquid phase out of the beaker. The mass of 0.1 mL on it, to the homogenous solution at 298 K of the resulting dry, freeflowing silver powder was then (controlled within ±2 K by the temperature controller of measured by the balance, from which the percent the stirrer-cum-heater mentioned previously) and 1-atm reduction for each run was obtained. Considering the pressure, to examine whether any precipitates (of silver) importance of these special runs, the reproducibility of would form. If a precipitate started forming, steps (4) and the results (percent reduction) was verified with another (5) were taken on completion of the precipitation. ten-experiment set of repeat runs and found to be (4) Recovery: The resulting mixture (the remaining excellent; the deviation in each run was within ±1 pct. solution and the precipitate) was heated on a hotplate (Science India, Kolkata, India), equipped with a tem- 1. Measurement and reproducibility of the drop volume perature controller that controlled within ±2 K, at 323 Since the reducing agent hydrazine hydrate was added to 333 K, to evaporate away the aqueous phase (with or in drops into the reaction mixture, it was necessary to without ethanol), leaving behind dry, freeflowing (silver) establish the accuracy and reproducibility of the drop powder in the beaker. The conventional method of volume. This was done as follows. filtration for separating the precipitate from the solution First, the density of hydrazine hydrate was ascer- would not work here, owing to the ultrafineness of the tained by transferring a pipetted quantity (20 mL) of the precipitated particles as well as the possible loss of liquid to a clean, preweighed (1) beaker or (2) measuring material adhering to the filter paper. cylinder. From the increase in mass of the container, the (5) Analysis: The powder produced was next sub- density of hydrazine hydrate was obtained, which was jected to X-ray diffraction (XRD) (SEIFERT XRD 1.03 g/mL in either case and exactly the same as that
36—VOLUME 39B, FEBRUARY 2008 METALLURGICAL AND MATERIALS TRANSACTIONS B reported in the standard handbook.[19] This small by the reaction of sodium azide with the two silver experiment also provided the calibration of the glass- compounds (AgNO3 and Ag2O, respectively) revealed ware used in the reduction runs. that they were merely the insoluble silver azide salts and Next, the measuring unit of the reducing agent was not metallic silver. Thus, sodium azide was also with- chosen to be the drop of hydrazine hydrate that would drawn from further consideration. In contrast, both the be released from the burette though close, manual compounds (dissolved in a 2:1 volumetric mixture of control of the stopcock, aided by the restraining action water and ethanol) responded to the third reducing of a rubberband put around the stopcock that would agent (hydrazine hydrate), as revealed by the XRD allow only discrete drop formation rather than a steady analyses (Figures 3 and 4) of the resulting precipitates, flow of the liquid. Now, to determine the mass of each which confirmed the formation of metallic silver (runs drop of hydrazine hydrate, the liquid was transferred S3 and S6). The SEM images (Figures 5 and 6) of these from the burette, in three separate batches composed of metallic precipitates (runs S3 and S6) further established 10, 50, and 100 drops, to a preweighed, small beaker. that the highly soluble silver nitrate produced finer Dividing the increase in the mass of the beaker by the (<500 nm) silver powders than the sparingly soluble number of drops involved, the (average) mass of each silver oxide, which produced approximately 800-nm drop of hydrazine hydrate was obtained for each of the silver powders. three batches, and these three values were found to be exactly equal, up to the third decimal place. Now, from B. Thermodynamic Analysis of Reduction of AgNO by the known density, the (average) volume of each drop of 3 N H ÆH O in Water–Ethanol Mixture (2:1) in Special hydrazine hydrate was calculated as 0.05 mL. Another 2 4 2 Runs crosscheck on this value was that the volume difference recorded on the burette corresponded very closely with The results obtained from the special runs for the mass of hydrazine hydrate transferred (the density of thermodynamic analysis of the reduction of silver nitrate the liquid being known) during each set of runs. (Strictly by hydrazine hydrate in a 2:1 (volumetric ratio) aqueous speaking, the measurements of masses were found to be more accurate than those of volumes, because of the high precision of the balance.) Considering the repro- ducibility of the average drop volume thus achieved in the three trial sets, each of which employed a large number of samples, the standard deviation of individual drop volumes from the average value was expected to be close to zero and, hence, the volume of each individual drop was, with almost no error, taken as 0.05 mL.
III. RESULTS AND DISCUSSION A. Synthesis of Submicron Ag Powder in Ordinary Runs The two selected compounds of silver were subjected to reactions with the selected reductants, to assess the reduction feasibility of the individual silver compound– reductant combinations. The silver compounds tried out were silver nitrate and silver oxide, while the reducing agents employed were DMF, sodium azide, and hydra- zine hydrate, as mentioned previously. The experimental conditions and the results obtained for each run are shown in Table I. Table I reveals that DMF had no reducing effect on either of the silver compounds and, hence, was not considered for further analysis. Likewise, the XRD Fig. 1—XRD pattern of the precipitate obtained from the reduction analyses (Figures 1 and 2) of the precipitates obtained of silver nitrate solution with sodium azide at 298 K.
Table I. Observations Recorded with Different Silver Compound–Reductant Combinations at 298 K
Run Silver Compound Reductant Reduction Medium Precipitate Description
S1 AgNO3 DMF water no precipitate S2 AgNO3 NaN3 water white, silver azide S3 AgNO3 N2H4ÆH2O water + ethanol gray, silver, <500 nm S4 Ag2O DMF water no precipitate S5 Ag2O NaN3 water gray, silver azide S6 Ag2ON2H4ÆH2O water + ethanol gray, silver, 800 nm
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 39B, FEBRUARY 2008—37 Fig. 2—XRD pattern of the precipitate obtained from the reduction of silver oxide solution with sodium azide at 298 K. Fig. 4—XRD pattern of the precipitate obtained from the reduction of silver oxide solution with hydrazine hydrate at 298 K.
Fig. 5—SEM image of silver powder produced by the reduction of silver nitrate solution with hydrazine hydrate at 298 K.
Both Figure 7 and Table II clearly indicate that Fig. 3—XRD pattern of the precipitate obtained from the reduction 8.24 millimol (412 mg) of hydrazine hydrate is required of silver nitrate solution with hydrazine hydrate at 298 K. under the given set of conditions (298 K and 1 atm pressure) for an almost complete (99 pct) reduction of 1 g of silver nitrate into metallic silver in the given mixture of water and ethanol are shown in Table II as solution. Now, based on the results of Table II,a well as in Figure 7, the reaction being represented as thermodynamic analysis will be made of the system, primarily to determine the equilibrium constant of 4AgNO3ðÞþaq N2H4 H2OaqðÞ Reaction [1] as well as to examine the (dilute) solution ¼ 4AgðsolidÞþN2ðgasÞþ4HNO3ðaqÞþH2O ðaqÞ behavior of hydrazine hydrate in water (plus ethanol). Rewriting Reaction [1] in the ionic form, with the ½1 standard states specified, gives Eq. [2]:
38—VOLUME 39B, FEBRUARY 2008 METALLURGICAL AND MATERIALS TRANSACTIONS B Fig. 6—SEM image of silver powder produced by the reduction of silver oxide solution with hydrazine hydrate at 298 K.
þ 4Ag ð1 molal hypotheticalÞþN2H4 H2O ðlÞ Fig. 7—Progress of reduction of 1 g (5.88 millimol) of silver nitrate þ by hydrazine hydrate in a 2:1 (by volume) mixture of water and eth- ¼ 4Ag ðsÞþN2ðgÞþ4H ð1 molal hypotheticalÞ anol. þ H2O ðlÞ½2 the solution unchanged, and that the water (solvent) was Let us consider that y drops (each drop carrying in excess (20 mL, i.e., 1111 millimol) compared to the 1.03 millimol) of hydrazine hydrate is added to 1 g solutes:
þ þ 4Ag þ N2H4 H2O ¼ 4Ag þ N2 þ 4H þ H2O Initially (millimol); 5:88 1:03y 00:8 atm 0 excess ½3 Equilibrium (millimol); 5:88 4x 1:03y x 4x 0:8 atm 4x excess
(5.88 millimol) of silver nitrate in the solvent mixture of The equilibrium constant of Reaction [2] at 298 K, 20 mL water and 10 mL ethanol at the start of the K[2], 298, in terms of Raoultian activities (ai) and Henrian reaction and that x millimol of hydrazine hydrate has activities (hi), is reacted out at equilibrium. The initial and final/equilib- 4 4 a aN h rium millimol can be species-wise shown as follows, with Ag 2 Hþ K½2 ; 298 ¼ 4 ½4 the simplified version of Eq. [2], noting that the system hAgþ aN2H4 H2O was open to atmosphere (80 pct N ) and the nitrogen 2 where a = 1 (pure); a = p = 0.8 atm; h =h ÀÁAg ÀÁN2 N2 Hþ Agþ ¼ generated through reaction fumed off, keeping the 2 solubility of nitrogen (corresponding to 0.8 atm N2)in CHþ=CAgþ f HNO3 =f AgNO3 (the development of this
Table II. Progress of Reduction of 1-g (5.88 millimol) of Silver Nitrate Solution by the Addition of Each Drop (0.05 mL) of Reducing Agent (Hydrazine Hydrate) at 298 K
Drops of Reductant Millimol of Reductant Mass of Ag Precipitate (g) Millimol of Ag Precipitate Percent Reduction 1 1.03 0.1673 1.55 26.36 2 2.06 0.3187 2.95 50.17 3 3.09 0.4138 3.83 65.14 4 4.12 0.5039 4.67 79.42 5 5.15 0.5506 5.10 86.73 6 6.18 0.5910 5.47 93.03 7 7.21 0.6240 5.78 98.30 8 8.24 0.6289 5.82 98.98 9 9.27 0.6300 5.83 99.15 10 10.30 0.6300 5.83 99.15
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 39B, FEBRUARY 2008—39 relationship as well as the thermodynamic validity of the hypothetical). This means that the (Henrian) activity of single-ion activity ratio hH+/hAg+ are provided subse- the solute is defined as the product of the (Henrian) quently), where f HNO3 =f AgNO3 is the ratio of the mean activities of its ions at equilibrium. Considering HNO3 Henrian activity coefficients of HNO3 and AgNO3 in the as the single solute in the (aqueous) solution, the mixed electrolyte system HNO3-AgNO3 in water, and the following two defining relationships, in terms of Hen- molar concentrations CH+ and CAg+ are equal to 4x/20 rian standard states (using the symbol h), are thus and (5.88–4x)/20, respectively, where the factor 20 rep- obtained: + resents the volume (mL) of water, the ionic species H + G ¼ G þ G ½6 and Ag being expected to dissolve only in the water, a HNO3ðhÞ HþðhÞ NO3 ðhÞ polar solvent, and not in the ethanol, a nonpolar solvent; and aN2H4 H2O ¼ c XN2H4 H2O ¼ c N2H4 H2O N2H4 hHNO3 ¼ hHþ hNO3 ½7 H2O (1.03y – x)/1283, ci and Xi representing the Raoul- tian activity coefficient and mole fraction of species i, respectively, the factor 1283, obtained from the expres- (It may be noted in passing that Eq. [7] is easily sion 1000[(20 · 1)/18 + (10 · 0.789)/46], representing deduced from Eq. [6], by considering the equilibrium relation G G G for the dissociation of the total millimol present in 20 mL of water (density HNO3 ¼ Hþ þ NO3 and molecular weight are 1 g/mL and 18) and 10 mL of HNO3 into its ions and the general free energy–activity ethanol (density and molecular weight are 0.789 g/mL[19] relation Gi Gi ðhÞ ¼ RT ln hi for the species i at tem- and 46) together, hydrazine hydrate (present in a small perature T.) Similarly, considering AgNO3 as the single amount of 0.64 to 5.76 millimol) being soluble in both the solute, the preceding two relationships take the follow- solvents[19] and millimol of the other species such as ing forms: + + Ag ,H , and N2 (having a solubility of 1.55 mL in G G G 8 [19] AgNO3ðhÞ ¼ AgþðhÞ þ NO3 ðhÞ ½ 100 mL water at 293 K and 1 atm N2, which means 1.01 · 10-2 millimol nitrogen in 20 mL water at 298 K and 0.8 atm N2) present in water being negligible, also. hAgNO3 ¼ hAgþ hNO3 ½9 Equation [4] can now be written as
4 8 pN C f Since the standard state free energy G NO3 ðhÞ is a K c 2 Hþ HNO3 5 ½2 ; 298 N2H4 H2O ¼ 4 8 ½ constant term (at the given temperature), manipulation C f XN H H O Agþ AgNO3 2 4 2 of the standard free energy change for Reaction [1] with the help of Eqs. [6] and [8] will end up in the same Regarding the thermodynamic validity of the single- standard free energy change for Reaction [2], given that the standard states of both AgNO and HNO in ion activities hH+ and hAg+ (in Eq. [4]), it may be 3 3 recalled that thermodynamics, in principle, does not aqueous phase refer to that of 1 molal hypothetical in permit the evaluation of the free energies, activities, Reaction [1]. This shows that Reactions [1] and [2] are activity coefficients, etc., of the individual ionic species, thermodynamically equivalent. Considering the fact that owing to the fact that in an electrolytic solution, the same standard free energy change gives rise to the same equilibrium constant for Reactions [1] and [2] at a electroneutrality imposes the condition that the number of moles of the individual ionic species (the cation and given temperature (following DG = -RT ln K), the the anion) cannot be varied independently and, hence, following equality is established: they cannot simultaneously act as independent variables h /h h /h 10 in the expression for the total free energy of the solution. Hþ Agþ ¼ HNO3 AgNO3 ½ Thus, the individual (ionic) partial molar free energy, activity, or activity coefficient may not have any Next, considering the question of the thermodynamic operational significance. However, in spite of this validity of the single-ion activity ratio hH+/hAg+,itis limitation, it is advantageous to express a number of seen that the validity is already established through the thermodynamic developments in terms of hypothetical result of Eq. [10], both hHNO3 and hAgNO3 being ionic activities, as long as they are applied as products or experimentally measurable. This, thus, gives a physical [20,21] ratios, which are operationally significant. In the quality to the activity ratio. Now, the activity ratio hH+/ present case (Eq. [4]), the ratio of the ionic activities hAg+ (or hHNO3 =hAgNO3 ) will further be expressed in hH+/hAg+ can be expressed in terms of measurable terms of concentrations (noting that the molality and quantities, as shown subsequently. But prior to that, it molar concentration are almost interchangeable for will be established that Eqs. [1] and [2] are thermody- dilute species) and activity coefficients, and this should namically equivalent and that both of them lead to the be done with caution, because the present system is a same expression for the equilibrium constant, as given ternary, mixed electrolyte type, comprised of water by Eq. [4]. (solvent), HNO3, and AgNO3, the two solutes having - The Henrian (one molal hypothetical) standard state the common ion NO3. Let us first find out the activity of an electrolyte (solute), irrespective of whether it is relations that would strictly apply for HNO3 and completely dissociated in the solvent or not, is advan- AgNO3, respectively, if each were present as a single tageously defined such that its chemical potential (i.e., electrolyte undergoing complete dissociation in the the partial molar free energy) equals the sum of the binary solution comprised of water and the electrolyte values for the ions in their standard states (one molal (HNO3 or AgNO3). With CHþ ¼ CNO3 ¼ CHNO3 and
40—VOLUME 39B, FEBRUARY 2008 METALLURGICAL AND MATERIALS TRANSACTIONS B CAgþ ¼ CNO3 ¼ CAgNO3 ; these activity relations would to measurable quantities through the following rela- be tionships:
hHNO3 ¼ hHþ hNO3 ¼ðCHþ fHþÞðCNO3 fNO3 Þ hHþ/hAgþ ¼ hHNO3 /hAgNO3 2 2 2 ¼ðCHNO3 Þ ðf HNO3 Þ ½11 ¼ðCHþ/CAgþÞðf HNO3 /f AgNO3 Þ 2 ¼ðCHNO3 /CAgNO3 Þðf HNO3 /f AgNO3 Þ ½16 hAgNO ¼ hAgþ hNO3 ¼ðCAgþ fAgþÞðCNO3 fNO3 Þ 3 These results of Eq. [16] have been used in Eq. [4]to C 2 f 2 12 ¼ð AgNO3 Þ ð AgNO3 Þ ½ arrive at Eq. [5], as mentioned previously. The evaluation of the mean ionic activity coefficients where f and f are the Henrian ionic activity coefficient ± f and f in the mixed electrolyte system and mean ionic activity coefficient of the species HNO3 AgNO3 HNO -AgNO in water is now taken up. For the ternary indicated by the subscript and f 2 f f : Thus, from 3 3 ¼ þ solution of water-HNO -AgNO (designated as 1–2–3) the single electrolyte consideration (which is wrong in 3 3 with constant total molality m (which equals m + m ), the present case of a mixed electrolyte system), the 2 3 Harned’s rule gives the following two relationships[22] activity ratio hHNO3 =hAgNO would be obtained as 3 for the mean activity coefficient f±, for the solutes 2 and 2 2 3 in the mixed electrolyte solution, written in terms of hHNO3 /hAgNO3 ¼ðCHNO3 /CAgNO3 Þ ðf HNO3 /f AgNO3 Þ the present system, replacing molalities mi by concen- 13 ½ trations Ci:
log f HNO ¼ logf ða ÞCAgNO ½17 Now, considering the system as a mixed electrolyte 3 HNO3ð0Þ HNO3=AgNO3 3 one, which it really is, with the common ion CNO3 ,itis found that, unlike previously, C is a single-valued NO3 log f AgNO3 ¼ logfAgNO3ð0Þ ðaAgNO3=HNO3 ÞCHNO3 ½18 variable and equal to (CH+ + CAg+), appearing as a where f is the (Henrian) activity coefficient of a common term in the expressions for hHNO3 and hAgNO3 ; HNO3ð0Þ as shown here: pure HNO3 solution of (total) concentration C (which, in the present case, is CH+ + CAg+ =(4x/ hHNO3 ¼ hHþ hNO3 ¼ðCHþ fHþÞðCNO3 fNO3 Þ 20) + ((5.88 - 4x)/20) = 5.88/20 = 0.294 mol/L, as ¼ðC ÞðC Þðf Þ2 ½14 mentioned previously, as well as found from Table III, Hþ NO3 HNO3 constructed later), which is found to be 0.735,[23]
andfAgNO3ð0Þ; which is correspondingly defined, is found to be 0.603[23]; a is an empirical coefficient, hAgNO3 ¼ hAgþ hNO3 ¼ðCAgþ fHþÞðCNO3 fNO3 Þ HNO3=AgNO3 which is a small function of total concentration C ¼ðC ÞðC Þðf Þ2 ½15 Agþ NO3 AgNO3 (which is constant at 0.294 mol/L, for all the runs in Table II and hence, subsequently, in Table III) and is where f HNO3 and f AgNO3 are mean ionic activity independent of the fraction of each electrolyte (HNO3 coefficients in the mixed electrolyte system HNO3- AgNO in water. Notably, the ionic activity h ; and AgNO3) present, thus being perfectly satisfied to 3 NO3 remain constant by the experimental conditions given following the ionic concentration CNO3 ; is also a single- valued variable in the system and, hence, has the same in Table II and, subsequently, in Table III;and a ¼ a (since the two electrolytes value in Eqs. [14] and [15]. (In contrast, in the single HNO3=AgNO3 AgNO3=HNO3 have the common ion NO-), based on the Bronsted– electrolyte case, the activity hNO would have different 3 3 Guggenheim equations.[22] Now, a can be values in Eqs. [11] and [12].) Using Eqs. [14] and [15], HNO3=AgNO3 expressed in terms of the specific ion interaction and noting that CHNO3 ¼ CHþð6¼ CNO3 Þ and constants B ; B ; and B (KCl being the CAgNO ¼ CAgþð6¼ CNO Þ; the ratio of the ionic activ- HNO3 AgNO3 KCl 3 3 [22] ities hH+/hAg+ in the present system is variously related reference electrolyte), as follows:
Table III. Values of Different Terms in Equation [5] Calculated from the Results of Table II and Using Equations [20] and [21];
pN2 = 0:8 atm; KÆc Abbreviated for K[2], 298ÆcN2H4 H2O; 1 Drop Reductant (Hydrazine Hydrate) ” 1.03 millimol Hydrazine Hydrate
4 Drops of Ag Precipitate, CH+, mol/L CAg+, mol/L XN2H4 H2O 10
Reductant (y) millimol (4x) (4x/20) f HNO3 ((5.88 – 4x)/20) f AgNO3 ðð1:03y xÞ=0:1283Þ ln (K Æ c) 1 1.55 0.0775 0.682 0.2165 0.619 5.01 4.04 2 2.95 0.1475 0.699 0.1465 0.634 10.31 7.46 3 3.83 0.1915 0.709 0.1025 0.644 16.62 9.45 4 4.67 0.2335 0.720 0.0605 0.654 23.01 12.02 5 5.10 0.2550 0.725 0.0390 0.658 30.20 13.87 6 5.47 0.2735 0.730 0.0205 0.663 37.51 16.50 7 5.78 0.2890 0.734 0.0050 0.666 44.93 22.19
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 39B, FEBRUARY 2008—41 1 aHNO3=AgNO3 ¼ =2ðBHNO3 BAgNO3 Þ 1 ¼ =2ððBHNO3 BKClÞ ðBAgNO3 BKClÞÞ 1 ¼ =2ðDBHNO3 DBAgNO3 Þ½19
The values for DBHNO3 and DBAgNO3 for C = 0.294 mol/L are found to be 0.11 and -0.19, respectively, by interpolation of the data given for C = 0.1 and 0.5 mol/ [24] L, which yields a value of 0.15 for aHNO3=AgNO3 from Eq. [19]. So, Eqs. [17] and [18] can now be rewritten as
log f HNO3 ¼ log (0.735) 0.15CAgNO3 ½20
log f AgNO3 ¼ log (0.603) þ 0.15CHNO3 ½21 2 Fig. 8—Plot of lnðK cÞ vs ð1 XN2H4 H2OÞ using results of Table III.
KÆc represents ðK½2 ; 298 cN2H4 H2OÞ. Table III presents the values of different terms in Eq.
[5], except for pN2 ; which is fixed at 0.8 atm, using the results of Table II as well as Eqs. [20] and [21], for the results of Table III, and the following equation for the first seven runs. regression curve emerges: In order to establish the activity coefficient–composi- tion relationship for hydrazine hydrate in its dilute 2 lnðK cN2H4 H2OÞ¼3:31ðln XN2H4 H2OÞ solution in water (plus ethanol) at 298 K, Darken’s[25] þ 50:2ð 1:7Þ ln X quadratic formalism for the binary system in the terminal N2H4 H2O (dilute) regions is pursued, which is a modification of the þ 195ð 11Þ½26 regular solution behavior and takes the following form after adding ln K on either side of the formalism: It is important to note that, while Eq. [26] is meant for almost the entire composition range ð5:01 10 4 lnðK cN2H4 H2OÞ¼½lnðK c N2H4 H2OÞ a 2 XN2H4 H2O 1:0Þ; Eq. [23] is limited to the dilute þ að1 XN2H4 H2OÞ ½22 4 concentration regime ð0 XN2H4 H2O 44:93 10 Þ where K is the equilibrium constant of Reaction [2] at only of the system water (plus ethanol)–hydrazine hydrate. Now, because when X equals 1, 298 K, i.e., K , c is the Raoultian activ- N2H4 H2O [2], 298 N2H4 H2O c equals 1, also, Eq. [26] gives ity coefficient of hydrazine hydrate at its zero concen- N2H4 H2O tration (infinite dilution) in water (plus ethanol), and a is ln K ¼ 195ðÞ 11 ½27 the temperature-dependent solution parameter. Strictly speaking, the present system is not a binary one of water (solvent) and hydrazine hydrate (dilute solute) only, but contains ethanol, in addition; water (87 mol pct) and ethanol (13 mol pct) have been grouped together into a single solvent, without much loss of accuracy, to simulate the binary characteristics of Darken’s formal- 2 ism. Now, a plot of lnðK cN2H4 H2OÞ vs ð1 XN2H4 H2OÞ using the results of Table III, shown in Figure 8, generates the following equation for the regression line, with the 0.95 confidence intervals shown in parenthesis:
lnðK cN2H4 H2OÞ¼2057ð 360Þ 2 2055ð 424Þð1 XN2H4 H2OÞ ½23 which yields a ¼ 2055 ½24 and lnðK c N2H4 H2OÞ¼2 ½25
To evaluate ln K, another plot, lnðK cN H H OÞ vs 2 4 2 Fig. 9—Plot of lnðK cÞ vs lnðXN2H4 H2OÞ; using results of Table III. lnðXN H H OÞ; is made in Figure 9, again using the 2 4 2 KÆc represents ðK½2 ; 298 cN2H4 H2OÞ.
42—VOLUME 39B, FEBRUARY 2008 METALLURGICAL AND MATERIALS TRANSACTIONS B Putting back the value of ln K into Eq. [23] gives the DH HNO 400H O DH HNO desired activity coefficient–composition relationship of 3 2 3 ¼ðH H Þþ400ðH H Þ½32 hydrazine hydrate in water (plus ethanol), which is HNO3 HNO3 H2O H2O where H i is the molar enthalpy of the species i in its lnðcN2H4 H2OÞ¼1862ð 371Þ 2055ð 424Þ standard state (pure liquid) and H i is the molar enthalpy 2 ð1 XN2H4 H2OÞ ½28 of the species i in the aqueous phase (HNO3 :H2O=1: 400). Now, substituting the values given in Table IV for the two left-hand-side terms, and considering the dilute- Next, the value of ln K, which is given by Eq. [27]and ness of the solution (mole fraction of water being 400/ leads to Eq. [28], may be compared with that computed 401, i.e., 0.9975), for which H ! H ; Eq. [32] from the already published thermodynamic data. It may H2O H2O yields be recalled that K is the equilibrium constant of Reaction [2] at 298 K, i.e., K[2], 298, and hence, the H HNO H HNO ¼ 205:9 þ 173:0 ¼ 32:9 kJ/mol standard free energy change of Reaction [2] is evaluated, 3 3 using Eq. [27], as ½33 G T K D ½2 ; 298 ¼ R ln ¼ 483( 27) kJ ½29 Considering the fact that the entropy contributions of condensed (liquid) phases are not significant, particu- The value of DG [2], 298 is now independently com- larly when the difference in their entropies is involved, it puted by the following two methods and compared with is justified that that given by Eq. [29]. SHNO3 S HNO3 0 ½34 1. Method 1 (using standard free energies of formation data) Combining Eqs. [33] and [34], and using the relation- Reaction [2] is rewritten in the molecular form, to ship G = H–TS, the corresponding free energy differ- facilitate the use of standard free energies of formation ence (at 298 K) is of compounds, as follows: GHNO3 G HNO3 32:9 kJ/mol ½35 4AgNO3 (1 molal hypothetical) þ N2H4 H2O (l) ¼ 4Ag (s) þ N2 (g) þ 4HNO3 (1 molal hypothetical) Now the difference between the partial molar free þ H O (l)r ½30 energy of HNO3 in HNO3-400H2O aqueous phase, 2 GHNO3 ; and the partial molar free energy of HNO3 in 1 molal hypothetical (Henrian) standard state (in water), Now, G HNO3ðÞ1molal ; can be given by, for 298 K DG ½2 ;298 ¼DG ½30 ;298 ¼ DG H2O;298 þ 4DG HNO3 ð1molalÞ;298 GHNO3 G HNO3ð1molalÞ RT ln h RT ln X 14:8 kJ/mol 36 4DG AgNO3 ð1molalÞ;298 DG N2H4 H2O;298 ½31 ¼ HNO3 ¼ HNO3 ¼ ½
considering the mole fraction of HNO3ðXHNO3 Þ of 1/ The four standard free energies of formation on the 401, i.e., 0.0025, small enough to fall on the Henry’s law right-hand side of Eq. [31] have either been directly line (h = X ). Subtracting Eq. [36] from Eq. [35] gives [17] i i obtained from the standard data book or derived, as the difference between the molar free energies of HNO3 shown in Table IV and explained subsequently. in the two standard states, Henrian (1 molal hypothet- The difference in (standard) enthalpy of formations of ical) and Raoultian (pure liquid): HNO (pure liquid) and HNO (in 400 moles of water) can 3 3 be expressed in terms of integral total enthalpy of mixing as G HNO3ð1molalÞ G HNO3 ¼ 18:1 kJ/mol ½37
[17] [17] Table IV. Standard Enthalpies of Formation at 298 K (DH298), Standard Free Energies of Formation at 298 K (DG298), and [18] Standard Entropies of Formation at 298 K (DS298) of the Relevant Compounds in Their Pure States and in Aqueous Phases
Species DH 298; kJ/mol DS 298; J/deg mol DG 298; kJ/mol
HNO3 (liquid) -173.0 — -79.7 HNO3 (aq)400 -205.9 — -97.8 N2H4 (liquid) 50.5 -452.7 185.4 N2H4ÆH2O (liquid) -242.5 -685.8 -38.1 H2O (liquid) -285.8 — -237.2 AgNO3 (aq)400 -100.5 — -32.7
Note: The number following the symbol aq applies only to DH 298; not to DG 298; and indicates the number of moles of water per mole of solute; for the standard free energy of formation in aqueous solution, the concentration is always that of the hypothetical solution of unit molality.[17] The terms in italics are derived ones and are explained in the text.
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 39B, FEBRUARY 2008—43 Now, Eq. [37] also represents the difference between DG ½2 ; 298 can be obtained by adding the DG values of the standard free energy of formation of HNO3 in the 1- Eqs. [42] through [45], which is -507.5 kJ, again in good molal hypothetical (Henrian) state and in the pure liquid agreement with the -483(±27) kJ of Eq. [29] and lending (Raoultian) state, both at 298 K, and hence further support to the activity coefficient–composition relationship of hydrazine hydrate, given by Eq. [28]. DG DG ¼ 18:1 kJ/mol ½38 HNO3ð1molalÞ HNO3 Thus, the two important results obtained from the thermodynamic analysis of the reduction of silver nitrate (AgNO ) by hydrazine hydrate (N H ÆH O) in a 2:1 Substituting the value (-79.7 kJ/mol) of DG HNO3;298 3 2 4 2 from Table IV into Eq. [38] gives (volumetric ratio) water–ethanol mixture can be sum- marized as follows. DG ¼ 97:8 kJ/mol ½39 HNO3ð1molalÞ; 298 (1) The standard free energy change of Reaction [2] at which is shown in italics in Table IV. 298 K is given by The standard entropies of formation at 298 K, DS 298, DG ½2 ; 298 ¼ RT ln K½2 ; 298 ¼ 483ð 27ÞkJ ½29 of N2H4 (liquid) and N2H4ÆH2O (liquid), as shown in Table IV, are obtained by using the standard entropies of N2,H2, and O2, which are 191.5, 130.6, and 205.1 J/ (2) The activity coefficient–composition relationship deg mol,[18] respectively, and considering the entropies for hydrazine hydrate in its dilute solution in water of the liquid species to be negligible compared with the (plus ethanol) at 298 K is given by gaseous species, in the following two formation reac- ln c 1862 371 tions: ð N2H4 H2OÞ¼ ð Þ 2 2055ð 424Þð1 XN H H OÞ ½28 N2ðgÞþ2H2ðgÞ¼N2H4ðlÞ½40 2 4 2
N2ðgÞþ3H2ðgÞþ1=2O2ðgÞ¼N2H4 H2O ðlÞ½41 IV. CONCLUSIONS The corresponding DG 298 values (in italics) are now Synthesis of submicron silver powder was taken up obtained by computing DH 298 298ðÞDS 298 : along a hydrometallurgical route. The silver com- Now that all four standard free energies of formation pounds considered were silver nitrate and silver oxide, are available, DG ½2 ;298 can be found out from Eq. [31], while the reducing agents employed were sodium azide which is -459.5 kJ and in good agreement with the - (NaN ), dimethyl formamide (DMF), and hydrazine 483(±27) kJ of Eq. [29]. This, thus, lends additional 3 hydrate (N2H4ÆH2O). The solvent medium was distilled support to the activity coefficient–composition relation- water for reductions with sodium azide and DMF, ship of hydrazine hydrate, given by Eq. [28]. and was a 2:1 (by volume) mixture of distilled water and ethanol for reductions with hydrazine hydrate. 2. Method 2 (using standard half-cell potential data) Additionally, the thermodynamic equilibrium of the The following set of reactions, some of which are system AgNO3-N2H4ÆH2O in the water–ethanol mix- molecular and some ionic, result in Eq. [2] on addition: ture (2:1) was studied at 298 K. The salient points are as follows. N2H4 H2O ðlÞ¼N2H4ðlÞþH2O ðlÞ; DG ¼ 13:7kJ 1. Of the three reducing agents, hydrazine hydrate alone ½42 was successful in reducing both the silver compounds to a submicron (<500 nm, in the case of silver ni- trate) metallic silver powder. The DMF reduced nei- N2H4ðlÞ¼N2ðgÞþ2H2ðgÞ; DG ¼ 185:4kJ ½43 ther of them and the sodium azide produced solid silver azide rather than metallic silver in each case. 2. The standard free energy change of the reduction þ 2H2ðgÞ¼4H (1 molal hypothetical) þ 4e; DG ¼ 0kJ reaction
½44 þ 4Ag ð1 molal hypotheticalÞþN2H4 H2OðlÞ þ ¼ 4Ag ðsÞþN2ðgÞþ4H ð1 molal hypotheticalÞ 4Agþ (1 molal hypothetical) þ 4e ¼ 4Ag (s); þ H2O ðlÞ DG ¼ 308.4 kJ ½45 was determined from the equilibrium study and was The DG values in Eqs. [42] and [43] are obtained from found to be -483(±27) kJ at 298 K. This agrees very Table IV, and those in Eqs. [44] and [45] are obtained by well (deviation ±5 pct) with the values of -459.5 and using the relationship DG = -nFE0, where n is the -507.5 kJ independently obtained from established number of gram equivalents (i.e., number of electrons), F data of standard free energies of formation and is Faraday’s constant (96,487 J/V g eqv), and E0 is the standard half-cell potentials at the same temperature. standard half-cell reduction potential (which is 0 V for 3. The following activity coefficient–composition + + H /1/2 H2 and 0.799 V for Ag /Ag). The value of relationship for hydrazine hydrate in its dilute
44—VOLUME 39B, FEBRUARY 2008 METALLURGICAL AND MATERIALS TRANSACTIONS B solution in water (plus ethanol) at 298 K was 11. L. Liao, J. Xiong, and K. Xie: Rare Met. Mater. Eng., 2004, obtained: vol. 33 (5), pp. 558–60. 12. H.H. Nersisyan, J.H. Lee, H.T. Son, C.W. Won, and D.Y. Maeng: lnðc Þ¼1862ð 371Þ Mater. Res. Bull., 2003, vol. 38 (6), pp. 949–56. N2H4 H2O 13. Y. Jin, K. Tang, C. An, and L. Huang: J. Cryst. Growth, 2003, 2055ð 424Þð1 X Þ2 vol. 253 (1–4), pp. 429–34. N2H4 H2O 14. Y. Jiang, B. Xie, J. Wu, S. Yuan, Y. Wu, H. Huang, and Y. Qian: J. Solid State Chem., 2002, vol. 167 (1), pp. 28–33. 15. Z. Jian, J. Lijuan, and L. Xiaohong: Rare Met. Mater. Eng, 1998, vol. 27 (6), p. 369. 16. Z. Zhang, B. Zhao, and L. Hu: J. Solid State Chem., 1996, vol. 121 (1), pp. 105–10. 17. R.H. Perry and D.W. Green: Perry’s Chemical Engineers’ Hand- REFERENCES book, 7th ed., McGraw-Hill, New York, NY, 1997, pp. 2.186–2.195. 18. O. Kubaschewski, C.B. Alcock, and P.J. Spencer: Materials 1. A. Rousset: Solid State Ionics, 1996, vol. 84, p. 293. Thermochemistry, 6th ed., Pergamon Press, Tarrytown, NY, 2. M. Brust, M. Walker, D. Bethell, D.J. Schiffrin, and R. Whyman: 1993, pp. 258–323. J. Chem. Soc., Chem. Commun., 1994, pp. 801–02. 19. R.H. Perry and D.W. Green: Perry’s Chemical Engineers’ Hand- 3. D.G. Duff, A. Baiker, and P.P. Edwards: J. Chem. Soc., Chem. book, 7th ed., McGraw-Hill, New York, NY, 1997, pp. 2.07–2.47. Commun., 1993, pp. 96–98. 20. H.S. Harned and B.B. Owen: The Physical Chemistry of Electrolytic 4. M. Maillard, S. Giorgio, and M.P. Pileni: J. Phys. Chem., 2003, Solutions 3rd ed., American Chemical Society Monograph Series, vol. B107, p. 2466. Reinhold Publishing Corporation, New York, NY, 1958, p. 7. 5. Y. Song, G. Liang, Q. Zhang, X. Lu, and C. Wei: Rare Met. 21. G.N. Lewis and M. Randall (revised by K.S. Pitzer and L. Mater. Eng., 2007, vol. 36 (4), pp. 709–12. Brewer): Thermodynamics, 2nd ed., McGraw-Hill, New York, NY, 6. J. Zhang, K. Liu, Z. Dai, Y. Feng, J. Bao, and X. Mo: Mater. 1961, p. 311. Chem. Phys., 2006, vol. 100 (2–3), pp. 313–18. 22. G.N. Lewis and M. Randall (revised by K.S. Pitzer and L. 7. E.V. Ortega and D. Berk: Ind. Eng. Chem. Res., 2006, vol. 45 (6), Brewer): Thermodynamics, 2nd ed., McGraw-Hill, New York, NY, pp. 1863–68. 1961, pp. 567–70. 8. L. Haurie, C.C. Ferna, A.I. Andez, J.M. Chimenos, C.C. Ferna, 23. H.S. Harned and B.B. Owen: The Physical Chemistry of Electro- M.A. Andez, D. Gonzalo, and F. Espiell: J. Mater. Sci., 2005, lytic Solutions, 3rd ed., American Chemical Society Monograph vol. 40 (9–10), pp. 2713–15. Series, Reinhold Publishing Corporation, New York, NY, 1958, 9. Y.H. Song, X.Z. Lan, Q.L. Zhang, and S.P. Yang: J. Xi’an Univ. pp. 731–33. Architect. Technol., 2005, vol. 37 (2), pp. 285–87. 24. G.N. Lewis and M. Randall (revised by K.S. Pitzer and L. 10. S.B. Rane, V. Deshapande, T. Seth, G.J. Phatak, D.P. Amalnerkar, Brewer): Thermodynamics, 2nd ed., McGraw-Hill, New York, NY, and B.K. Das: Powder Metall. Met. Ceram., 2004, vol. 43 (9–10), 1961, pp. 645–47. pp. 437–42. 25. L.S. Darken: Trans. Metall. Soc. AIME, 1967, vol. 239, p. 80.
METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 39B, FEBRUARY 2008—45