A laser Raman spectroscopic study of aqueous orthophosphate salts

814

C. M. Preston and W . A. Adams

The Journal of Physical Chemistry, Vol. 83, No. 7, 1979

A Laser Raman Spectroscopic Study of Aqueous Orthophosphate Salts Carollne M. Preston' and W. A. Adams"' Glaciology Division, Inland Waters Directorate, Fisheries and Environment Canada, Ottawa, Ontario, Canada KIA OE7 (Received July 28, 1978;Revised Manuscript Received December 1. 1978) Publication costs assisted by Glaciology Division, Inland Wafers Directorate, Fisheries and Environment Canada

Raman spectroscopy has been used to study aqueous solutions of orthophosphate salts from 0.005 M to saturation levels. Both HzP04- and HP04'- salts show changes in band half-widths and frequencies with changing concentration and temperature. In particular, the growth of a low-frequency shoulder of the P-0 stretching bands of H2P04-(1074 cm-') and HP04'- (987 cm-') with increasing concentration appears to be characteristic of hydrogen-bonded phosphate dimers or higher polymers in solution. From resolution of the bands, the association constants for H2PO4- + H2P04- H4P208'-and HP0:- + HP042- HzPzOt-were estimated to be 0.6 f 0.3 and 0.3 f 0.1 L mol-', respectively. Na3P04and K3P04solutions undergo hydrolysis to form HP0,2-; it was possible to measure the solution concentration of HP0d2-and obtain a concentration quotient, Qh, for the hydrolysis. Q h was approximately 0.0084 at the lowest concentrations, and then decreased more rapidly with concentration for the sodium than for the potassium salt. AH for the third dissociation of phosphoric acid was estimated to be +5.8 kcal mol-' for K3P04and +4.8 kcal mol-' for Na3P04(measured from temperature dependence of the hydrolysis of 0.1 M solutions).

Introduction Although orthophosphates have been studied previously by infrared and Raman ~pectroscopy,~-~ there have been no Raman studies of orthophate equilibria at controlled temperatures, and over the wide concentration ranges which the laser has now made routinely accessible. As part of a laser Raman study of phosphoric acid,7we observed large changes in band shapes, half-widths, and frequencies with concentration for H,PO,- and HPO:-, and extensive hydrolysis in more dilute Po43-solutions; these concentration effects may account for some of the discrepancies in band frequencies and number of bands reported in earlier studies, which were carried out at fixed and relatively high concentrations. Raman spectroscopy has been extensively used to study ion pairing and hydration in aqueous nitrate solutions? and to a lesser extent for sulfate, b i ~ u l f a t eand , ~ perchlorate,1° but it has not been exploited in this way for phosphates. There are anomalies in the physical properties of phosphoric acid and orthophosphates in aqueous solution; for example, the minimum in the degree of dissociation of phosphoric acid around 1 M concentration,l1lz1and the low diffusion coefficientll and limiting equivalent conductance12J3of HzP04-. Extensive hydration of phosphate'l and, especially at higher concentrations, formation of hydrogen-bonded phosphate dimers have been postulated to account for vapor-pressure, transport-number, conductivity, and potentiometric titration data,14-21and some support for phosphate association has also come from ultrasonics,22NMR,23infrared spectroscopy of the OH stretching regions,24and isolation of salts with the formula MH5P2O8,where M = NH,, Na, K, Rb, and C S . ~At~ the same time, two other recent potentiometric studies of phosphoric acid have concluded that it is unnecessary to invoke the existence of complex specie^.^^,^^ The present work has been undertaken, first, to document changes in the Raman bands of orthophosphates over wide ranges of concentration and temperature which have not been studied previously and, second, to investigate the potential of Raman spectroscopy for understanding the physicochemical nature of phosphate solutions, in particular, questions of anion hydration, and the possibility of phosphate complex formation and anion-cation pairing. 0022-3654/79/2083-08 14$01.00/0

Experimental Section Salt solutions were prepared from commercial products (Fisher Certified) without further purification, except for KHzP04which was recrystallized from ethanol-water and dried to constant weight. The concentration of the stock solution made from the recrystallized salt was checked by titration against NaOH, and several stock solutions were analyzed for sodium, potassium, and orthophosphate. Concentrations ranged from 0.005 M to saturation levels. For the Raman spectra, samples were filtered through 0.45-pm Millipore filters (only some of the most concentrated solutions were not filtered) into 1 X 1 X 4 cm clear glass cuvets. The Raman spectra were recorded on a Jarrell-Ash-25-400 spectrometer equipped with a photon counting system and a Spectra-physics Model 165-03 argon-ion laser; laser power levels ranged between 400 and 1000 mW. Initially spectra were obtained using the 488.0-nm line, but later the 514.5-nm line was used to reduce background fluorescence. Spectra were recorded with an effective slit width of 8 cm-l at 514.5 nm, and with slit widths of 4-8 cm-' a t 488.0 nm. All spectra were obtained at a sample temperature of 25.0 f 0.2 "C unless otherwise indicated. For some experiments at 514.5 nm, a sample cell with a silvered back was used to collect light scattered directly away from the slits.28 This extra reflection at approximately normal incidence did not change the experimentally obtained depolarization ratios, and increased the signal-to-noise by approximately 50%. The optical arrangement incorporated a polarization rotator immediately before the sample cell. The light scattered at 90" was focused by a camera lens and passed through a polarization scrambler mounted in front of the entrance slit. To measure depolarization ratios, the polarization of the incident laser beam was rotated by 90" using the polarization rotator. This arrangement of rotator-single-pass sample cell-scrambler (no analyzer is used) gives a maximum depolarization ratio ( p ) of 6/7. Using CC14 as a standard for calibration and alignment, it was found that p was CO.01 for the highly polarized band at 458 cm-l, and approximately 0.82-0.88 for the depolarized bands a t 219 and 314 cm-l. CC14was also used as an external intensity standard, and polarized and depolarized spectra in the region of 150-550

Published 1979 by the American Chemical Society

Laser Raman Study of Orthophosphate Salts

The Journal of Physical Chemistry, Vol. 83, No. 7, 1979 815

TABLE I: Raman Bands of Aqueous H2PO; (Na, K, and NH,) at 25 "C for 0.01-6.0 M Solutionsa -depolrzn ratio this work

position of band max

-

ref 3

IR

assignment 3-5

vb,m

dp?

0,7

-514 874':

b ,m s,sh

dp? 0.015

0.9 0.1

940

b ,vw

0.48

d

P( OH), symm str v 9 (B2) P(OH), asym str

1074c3d

s,sh

0.057

d?

VI

1150

vb ,vw

0.58

0.2

' 6

380'

bending modes -520 b,m4 V,(Al) 877 w4,s5 946

s43'

(AI)

PO, symm str

1075

(Bl)

PO, asym str

s49j

1152 s4*'

Exciting lines 488.0 and 514.5 nm. b broad, sh sharp, s strong, m medium, w weak. May be split, but not possible t o resolve bands. Limiting frequencies of band maxima a t low concentrations, see Table 11. Broad and asymmetric on lowfrequency side at higher concentrations, see Table 11, Figure 1.

cm-l were recorded using the sample cell in the same orientation a t least once for each experiment or set of continuous experiments. It was found that the laser, operating in the "light control" mode, was very stable, and the intensity (i.e., integrated area) of the 458-cm-' band of CC14 generally varied by no more than 5%, and often by less than 1% during the course of a day. All peak areas have been reported relative to that of the CC14 458-cm-' band. Band areas were measured by drawing a smooth baseline, arid then photocopying the spectra and cutting out and weighing individual bands. Solution concentrations ranged from 0.005 M to saturation levels. At the very low concentrations the spectra were of rather poor quality, and in addition soine of the bands broadened considerably and this increased the difficulty of analysis. It seemed that more sophisticated methods of analysis would have been inappropriate. Positions of band maxima (urnax) are reported to f 2 cm-', and full-widths at half-height to *0.5 cm-'. For the variable-temperature studies, no external intensity standard was used, but the laser power was maintained at a constant level, so that relative integrated intensities of the same sample at different temperatures could be compared. For the temperature experiments on the 0.1 M Na3P04 and K3P04 solutions, the solution concentrations of HPOZ- and PO:- a t each temperature were obtained from the ratios of the areas of the 987-cm-l band of HPOZ- and the 934-cm-l band of PO?- as follows. If [Pot-] = c1 and [HPOZ-] = c2, c1 c2 = c, where c, is the stoichiometric concentration of M3P04(0.1 M). Then 1934 = J1c1, and IS,,= J2cz = J2(c,- cl), where Jl and J2 are the relative molar scattering factors (RMSF's) for the bands a t 934 and 987 cm-l. We can define R = I987/Ig34, and by substitution and rearrangement obtain c1 = Jzc,/(JlR + J2). 3 2 was available from the concentration studies of M2HP0,1,and J1from the plot Of IgS4 vs. solution concentration of Pot- (Figure 4). It is necessary to assume only that the RMSF's do not change with temperature. This seemed reasonable, as the studies of HzP04- and HP042-had shown that, as the temperature increased, there were only small decreases in band intensity that would be expected with decreasing solution density. Some density measurements (*l%) were made to determine the molar ratios of water and solute in the concentrated solutions of NaH2P04, K2HP04, and K3P04. These were made by weighing a fixed volume (5 or 10 mL) a t 25 "C. Band resolution was carried out using a Dupont 310 curve resolver with a fit based on the 1050-cm-' band of 10 M aqueous LiN03.

+

Aqueous NoH2P04

v

h

-

1

1400

I

I

1000

I200

,

48BOnm

25°C

l

l

l

600

800 cm-1

l

l

400

,

zoo

Figure 1. Raman spectra of 0.1, 1.0, and 6.0 M NaH,PO, in aqueous solution at 25 O C from 200 to 1400 cm-' (exciting line 488.0 nm).

TABLE 11: Concentration Dependence of the Position of Band Maximum ( u r n = ) and Full-Width a t Half-Height ( A T l , , ) for t h e 874- and 1074-cm-' Bands (P(OH), and PO, Symmetric Stretches) of Aqueous Na-, K-, and NH,H,PO, at 25 " C a

[IWF"I ,

874 cm-'

mol L-' urnax 0.010 0.10 0.20 0.50 1.0 1.5 2.0 2.5 3.0 4.0 6.0

874 874 876 875 876 879 879 881 884 883 892

1074 cm-'

width, slit

ATl/,

vmax

ATl/,

cm-'

25.1 23.6 23.6 24.7 27.0 29.0 30.5 31.8 33.0 35.4 38.4

1075 1074 1075 1074 1074 1074 1073 1071 1070 -1070 -1040

24.2 24.0 25.0 26.7 30.0 35.6 43.8 56.0 60.6 76.0 96.4

8 8 8 8 4,s 4,8 4,8 4 8 4 4

Exciting lines 488.0 and 514.5 nm.

Results MH2P04. Raman spectra of aqueous Na, K, and NH4H2P04show a t least six bands. There are two broad weak bands at approximately 380 and 515 cm-l, and four bands at 874,940,1074, and 1150 cm-l(874 and 1074 cm-l are limiting values at low concentrations; the frequencies of other bands do not appear to be significantly concentration dependent). These bands have been partially assigned in previous studies (Table 1),3-5 based on a model of approximately CZusymmetry for the HzPO4- anion, and our observations of number of bands, frequency, relative intensity, and depolarization ratios are in general agreement with earlier work.

816

C. M. Preston and W. A. Adams

The Journal of Physical Chemistry, Vo/. 83, No. 7, 1979

TABLE 111: Temperature Dependence of vmax and A T l l 2for t h e 874- and 1074-cm-' Bands of 0.1 M MH,PO, (M = Na, K ) and 1.0 M NaH,PO, in Aqueous Solution" 0.1 M (Na, K ) 874 cm-' temp,"C

4 10 15 18 '2 5 31 37 43 50 60 a

1 . 0 M (Na)

1074 cm-'

874 cm-'

urnax

Air, 1 2

877 877 876 877 874

22.7 22.2 22.4 23.6 23.6

1075 1075 1074 1076 1074

22.9 23.0 23.4 23.8 24.0

874

23.1

1077

24.0

872 871

23.2 23.6

1077 1077

24.8 25.8

A T /z

1074 cm-'

AT' 1 2

urnax

AVliZ

879 879

26.4 26.6

1072 1075

29.2 29.0

877 876 876 87 6 875 875

27.0 27 .O 27.6 28.2 28.0 28.8

1074 1074 1075 1075 1074 1076

30.2 30.0 30.4 30.6 31.6 31.4

Exciting line 514.5 nm, slit width 8 cm-'.

TABLE IV: Raman Bands of Aqueous HP0,'- (Na,HPO, and K,HPO,) a t 25 "C for 0.01-6.0 M Solutions" depolrzn ratio position of band max

this work

- 390

ref 3

assignment 3 - 5

b,m

-0.95

0.89

-530

b,m

-0.78

0.8

v,(E) O,P(OH) bend vz(A, 1, V,(El 1 PO, def V,(Al) POH str v,(A,) PO , symm str V'i(E) PO ,asym str

850

b,m

0.091

0.2

987b

s,sh

0.038

0.15

vb ,w

0.63

d

1080

" Exciting lines 488.0 and 514.5 nm. centration.

IR

539 m4

~ 860 w , m4 989 m 4 , j 1078 s49'

Broadens and becomes asymmetric o n the low-frequency side with increasing con-

Both the 874- and 1074-cm-l bands show significant changes with concentration (Table 11). Figure 1 shows spectra of 0.1,1.0, and 6.0 M aqueous NaH2P04at 25 "C. At very low concentrations, only the two strong bands at 874 and 1074 cm-' can be observed, and the 874-cm-l band (P(OH), symmetric stretch) is broadened (see Figure 6, ref 7 for the spectrum of 0.01 M KH,P04). As the concentration is increased, the frequency of the 874-cm-l band increases, while its half-width at first decreases (to about 0.2 M) and then increases with concentration; the 1074cm-' band develops a shoulder on the low-frequency side, and its half-width increases very quickly. At 6.0 M NaH2P04,there is a symmetrical, very broad band centered at approximately 1040 cm-l. In general, it was found that integrated band intensities were linear with stoichiometric concentration for phosphoric acid and its salts, if corrections were made for changes in species distribution due to chemical equilibria where necessary. The only exceptions were the 874- and 1074-cm-' bands of NaH2P04 and KH2P04,whose intensities were linear up to about 2 M, and then decreased with increasing concentration (the intensities for the corresponding bands of NH4H2P04were linear up to 3 M, the highest concentration studied). Changes in temperature also produced changes in the strong bands. Table I11 shows changes in the half-widths and band maxima for 0.1 M Na- and KH2PO4from 4 to 60 "C,and for 1.0 M NaH2P04from 4 to 50 "C. As in the concentration study, there was no significant difference between the two salts. At both concentrations, the frequency of the 874-cm-l band decreased with increasing temperature, while that of the 1074-cm-l band increased slightly, and the half-width of the 1074-cm-l band increased. For the half-width of the 874-cm-l band, however, there was a difference in the temperature dependence at the two concentrations. At 1.0 M, the half-width increased

60MI I

1200

1000

I

I

I

800

I

600

I

I

I

400

I

zoo

crn-1

Flgure 2. Raman spectra of aqueous 0.1, 2.0, and 6.0 M K,HP04 25 "C from 200 to 1300 cm-' (exciting line 488.0 nm).

at

to about the same extent as the increase in the half-width of the 1074-cm-l band, while at 0.1 M, the half-width of the 874-cm-l band showed a very small increase. M2HP04. Table IV shows the frequencies, relative intensities, depolarization ratios, and assignments for the HP02- anion. The assignment and the limitations of the C3" model have been discussed p r e v i o ~ s l y . ~ Figure -~*~ 2 shows spectra of 0.1, 2.0, and 6.0 M aqueous K2HP04at 25 "C (the data for the sodium and potassium salts were essentially the same). As concentration increases, the P(0H) stretching frequency appears to shift from approximately 850 to 870 cm-l, while the strong PO3 stretch at 987 cm-l develops a shoulder on the low-frequency side, broadens, and shifts to lower frequency. This behavior is similar to that of the POz symmetric stretch of HzPO4-



TAl3LE VI: Raman Bands of Aqueous PO,'- (Na, and K,) at 215 "C for 0.005-4.0 M Solutionsa depolrzn ratio

TABLE V: Concentration Dependence of urnax and AT, , 2 for t h e 850- and 987-cm-' Bands (P-OH and P o Symmetric Stretches) of Aqueous Na2and K.HPO, at 25 'Ca 987 cm-' [M,HPO,], 850 cm-' mol L-' urnax urnax AT,* slits

position of band max

-.

--

0 , O O 50 0,010

a

0.10 0.20 0.30 0.40 0.50 0.60 1.0

850 850 850 850 852 855 855

988 986 987 988 987 986 988 987 987

2.0 4.0 6.0

857 866 870

986 985 97 2

19.2 19.9 20.0 20.4 20.4 20.9 21.6 19.0 21.6 22.4 42.4 54.0

8 8 8 8 8 8 8 4 8 4 4 4

5145 nm

I J

08

M

w

-

Na3P04 .L

U L

1200

I000

w

1

I

I

800 cm-1

I

I

600

I

400

I

Figure 3. Raman spectra of aqueous 0.8 M Na3P04(supersaturated), 0.1 M Na3P04, and I0: M K3P04 at 25 OC from 300 to 1200 Cm-' (exciting line 514.5 nm).

(1074 cm-'), but the concentration effect is not as large. These concentration effects are summarized in Table V. The effect, of temperature was studied for 0.1 M Nazand KZHPO4solutions. As the temperature was increased from 4 to 60 "C, the P-OH stretching band shifted from approximately 860 to 844 cm-l; the PO3 stretch at 987 cm-' remained constant in frequency, and its half-width decreased slightly, from approximately 20.5 to 19.9 cm-'. &Pod. The Raman spectrum of PO:- shows four bands, at 412,550,934, and 1007 cm-' (Figure 3), and these have been previously assigned, based on a model of Td symmetry for the PO>The Raman data are shown in Table VI; again, the results are in general agreement with earlier work, and there were no significant differences between Na3P04and K3P04. In contrast with the H 2 P 0 4 and HP0:- spectra, none of the bands showed any significant concentra1,ion dependence. Both the frequency and half-width of the PO4 symmetric stretch at 934 cm-l remained constant over the whole concentration range studied (up to 4.0 M). Spectra of M3P04 are complicated by the hydrolysis reaction Pod3-1- HzO

assignment3-' u,(E) bending v4(F2) bending u,(A,) PO, symm str

412

b,m

dp?

0.85

550

b,m

dp?

0.85

934

s,sh

0.023

0.1

1007

b,w

0.93

IR56g4 9424,b 1007

v,(F2)

a Exciting lines 488.0 and 514.5 nm. in concentrated solutions only.

0 I M K3P04

25°C

ref 3

s49'

PO, asym str


7

this work

HP0d2- + OH-

At the lowest concentrations studied, only the 987-cm-l band of HP042- could be observed.29 While the Raman frequencies, relative intensities, half-widths, and depolarization ratios for the two salts were the same, the extent of hydrolysis was much greater for solutions of the potassium salt. Figure 3 shows spectra of 0.1 M Na3P04and K3P04,where the difference in the ratio of the intensities

Weak shoulder

TABLE VII: Concentration Quotient (Qh) for the Hydrolysis of Na,PO, and K,PO, Vs. Concentration at 25 'Ca Q h X 10' [M,PO, I, mol L-' - Na3P0, KW.4 0.005 5.6 7.9 0.0075 8.0 0.010 11 12 0.015 9.5 0.020 8.9 0.025 7.7 0.030 7.3 0.040 7.8 0.050 4.9 2.5 0.060 4.0 0.075 2.4 0.08 3.7 0.10 1.8 8.1 0.15 0.84 0.20 0.72 6.3 0.30 0.20 0.40 0.42 0.50 0.22 1.7 0.0077 0.60 0.75 1.4 1.0 2.3 2.0 0.0089

-

-

a Na,PO, exciting line 514.5 nm; K,PO, exciting lines 488.0 and 514.5 nm.

of the 934- and the 987-cm-' lines is apparent. It was also possible to measure Qh, the concentration quotient for the hydrolysis. For the hydrolysis equilibrium K h

=

~ H P O ~ Z - ~ O H[HP04'-]

-

apo43-

[Po:-]

[OH-] Y

~ ~ 0 ~ 2 - 7 0 ~ YPOp

=

Q,Q,

where aHzO= 1 and a, is the activity, [i] the concentration, and y1 the activity coefficient of species i. The species concentrations can be obtained from the Raman data; in this case, as the relative molar scattering factors (RMSF's) for the bands of HP0:- had been measured in the concentration studies of Naz- and K2HP04, the solution concentration of HPOd2-for each stoichiometric concentration of M3P04could be obtained from the integrated relative intensity at 987 cm-l. The solution concentration can then be obtained by difference, and the OHof Po43concentration is assumed to be equal to the solution concentration of HPOt-. The concentration quotient for the hydrolysis, Qh, can be obtained from these values. The values found for Qh are shown in Table VII; as concentration increases, Qh decreases more rapidly for the sodium salt than for the potassium one. This is presumably due to the greater tendency of Na+ than K+ to form ion pairs with Po43-.The limiting value of Q h at the lowest con-

818 1s



/

T

O.IM Na,PO, 514.5nm

1200

(aq.)

izucc...

1000

800

wavenumber /cm' 0

0

0

0.2

0.8

1

Figure 4. Plot of relative integrated band intensity (I,) at 934 ( 0 )and 1007 cm-' (0)vs. solution concentration of PO4%for Na3P04in aqueous solution at 25 OC, and least-squares fit lines. Stoichiometric concentrations were up to 0.8 M, and exciting line was 514.5 nm.

TABLE VIII: Variation of Hydrolysis Concentration Quotient ( Q h ) with Temperature for 0.1 M Aqueous Na,PO, and K,PO,a

Figure 5. Raman spectra (from 800 to 1200 cm-I) for 0.1 M Na,PO, in aqueous solution at 4, 25, and 50 OC (exciting line 514.5 nm). The decrease in intensity at 934 cm-' and increase at 987 cm-I correspond to a decrease in [PO:-] and an increase in [HPO?-].

0.1M Na,PO, (aq.) 25°C

w

514.5 nm

no NaCl

Q ~ 103 X

temp, "C 4 10 15 18 25 37 50 60 a

Na,PO, 1.0 1.8

KW, 3.2 6.1

2.6 3.2 6.1 10

14 16 29 35

Exciting line 514.5 nm.

centrations was approximately 0.0084 f 0.0013. At infinite dilution, Kh = Qh, and K3 = Kw/Kh.The Raman data then give an approximate value for the third dissociation of phosphoric acid of (1.2 f 0.2) X mol L-l. From the above analysis, it was also possible to estimate RMSF's for the 934- and 1 0 0 7 - ~ m bands -~ of Pod3-by plotting integrated band intensity vs. solution concentration of PO?- at each stoichiometric concentration of PO?-. Figure 4 shows the plots and the least-squares fit slope for Na3PO4 The lines pass through the origin within experimental error, indicating the validity of this data treatment. The relative molar scattering factor thus obtained for the 934-cm-l band of PO?- could then be used in the analysis of the temperature data. The effect of temperature was studied for 0.1 M K3P04 from 4 to 60 "C, and for 0.1 M Na3P04 from 4 to 50 "C. As the temperature increased, the spectra showed an increasing proportion of HP0:- in the solution (Figure 5), and an increase in Qh(Table VIII). The enthalpy change for the hydrolysis, AHh,was obtained from plots of Qh vs. 1 / T , and AH3 for the third dissociation from AH3 = AHw - m h , where AHw is the enthalpy change for the ionization of water (+13.52 kcal m~l-l).~O The AH3 values were +5.8 f 0.8 kcal mol-l for and +4.8 f 0.3 kcal mol-l for Na3P04. Although the precision was good, systematic errors resulting from uncertainty in drawing the baselines, and neglect of activity coefficients, or in measuring the RMSF's may be higher, and an error limit of f20% would be more realistic. The change in temperature also produced minor changes in the frequencies and half-widths. For both salts,

1200

1000

800

wavenumber /ctri' Figure 6. Raman spectra from 800 to 1200 cm-' of aqueous 0.1 M Na3P04at 25 OC, with no NaCI, 1.0 M NaCI, and 3.0 M NaCI.

Av1I2(934)decreased with increasing temperature (-0.03 cm-l OC-l for Na3P04and 0.05 cm-l OC-l for K&&). For K3P04,where it was also possible to measure the halfwidth of Aa1,z(987), it also decreased with increasing temperature (-0.03 cm-l 'CY). A decrease in the halfwidth of this band with increasing temperature was also observed in solutions of Naz- and KZHPO4.The changes in band frequency were very small, and may not be significant. For the 0.1 M Na3P04solution, u,, for both the 934- and 987-cm-' bands appeared to increase slightly with increasing temperature (-0.03 cm-l OC-l for 934 cm-l and 0.02 cm-l OC-l for 987 cm--l). For the K3P04solution, the frequencies of both bands appeared to decrease slightly (0.02 at 934 cm-l and 0.003 cm-l OC-l at 987 cm-'). A few experiments were also carried out on 0.1 M Na3P04and K3P04solutions with added NaCl and KC1. In each case, the added salt reduced the extent of hydrolysis, but there were no changes in band parameters. NaCl caused a larger shift in the hydrolysis equilibrium than the same amount of KC1; this again probably reflects the difference in the extent of Na+ and K+ ion pairing with At 3.0 M NaC1, it was not possible to detect the 987-cm-l band of HP042-in the Raman spectrum of 0.1 M Na3P04, and the 1 0 0 7 - ~ m -band ~ of Po43-(PO4 assymetric stretch) was broadened (Figure 6 ) .

Discussion The infrared and Raman spectra of the orthophosphates have been assigned p r e v i ~ u s l y , using ~ - ~ ~models ~ of Td,C3", CZu,and CSusymmetry for Po43-, HPOC-, HzPO4-, and



H3P04,although with the exception of PO?-, it has been necessary to assunie accidental coincidences of the deformation and bending vibrations, as the expected number are not observed. In addition, the OH vibrations have not been treated fully. While the strong concentration dependence of the frequency of the “890-cm-1” band of phosphoric acid had been previously observed, the effects of concentration and temperature on the frequencies and half-widths of the imion bands had not been documented, most of the early work having been done a t fixed and relatively high concentrations. Our observations of numbers of bands, relative intensities, frequencies, and depolarization ratios are in general agreement with previous work, and differences are largely due to concentration effects; the two exceptions are noted below. Herzog arid Steger4observed a band at 1030 cm-’ (not resolved from the 11074-~m-~ band) in solutions of Na-, K-, and NH4H2P04,and tentatively assigned it to an OH vibration. This “band” probably corresponds to the broadening we have observed on the low-frequency side of the 1074-cm-’ band of H2P04- with increasing concentrations; the band is symmetrical at low concentrations, and the total intensity of the band plus shoulder is linear with concentration up to 3 M NH4H2P04and up to about 2 M Na- and KH,P04. The “1030-~m-~” band is most likely the PO, vibration of H2P04- which has been perturbed, possibly by hydrogen bonding. Herzog and Steger4 also observed a band at 930-940 cm-’ in solutions of HP042- (not resolved from the band at 987 cm-l), which they assigned as a PO4 stretching vibration, occurring in HP0,2- because proton exchange in solution results in a temporary equivalence of the phosphate bonds. Again, this band may be the broadening of the 987-cm-l band which we observe in Na2- and K2HP04solutions with increasing concentration; the 987-cm-l band is symmetrical at low concentrations, and the total band intensity is linear up to 6 M K,HPO4. (These bands at 1030 and 930 cm-I are also noted by Mathieu and J a c q u e ~ . ) ~ At least four processes should be considered in using the Raman data as probes of solution structure. The phosphate ions may be solvated by interaction with water through the oxygen (type I hydration). It has also been

’0‘

I1

I

suggested, from studies of the infrared overtone and combination bands of water in phosphate solutions, that hydration also occurs a t the phosphate OH group (type II).9d331This type of hydration would be less favorable on electrostatic grounds. A number of hydrogen-bonded phosphate dimers have been p r o p o ~ e d , ’ ~for - ~ example, ~ H3P04.H2P04-with one, two, or three hydrogen bonds (A-C). By analogy with the behavior of other systems, including carboxylic acids, it would be expected that hydrogen bonding, whether to solvent water or to other phosphate moieties, would result in an increase in P-OH stretching frequencies, and a decrease in P-0 frequenciesa3%%Support for this comes from a study of phosphoric acid in some nonaqueous solvents in which the hydrogen bonding would be broken It was found that there was a very large increase in the P-0 frequency, and a small decrease in the P-OH frequency in going from water to

A

‘I

B

O--- H--- 0

L=

HO -P-O---H---

0 -P -OH

O--- H---O

C

/

acetonitrile. It has also been found that the P-0 frequencies of P1s043-(symmetric and antisymmetric stretching) are appreciably higher than those of P1602-.37 This increase, rather than the decrease expected because of the increase in oxygen mass, has been attributed to decreased hydrogen bonding of Pls0 to water, compared to P-l60. We have also observed that the P-OH frequency of aqueous phosphoric acid increases from 890 cm-l at 0.2 M to 910 cm-l at 15 M,7and to 915 cm-l in an anhydrous crystal of H3P04,38in which the hydrogen bonding is very strong.39 Finally, the influence of the cations should be considered, and the possibility of forming solvent-separated anion-cation pairs. (There was no evidence for contact-ion pairs and, at the highest concentrations studied, the ratio of water to solute molecules was still approximately six for NaH2P04and K2HP04,and nine for K3P04.) Considering first H,P04-, at the lowest concentrations, it seems reasonable that the ions are extensively hydrated, both through P-0 and P-OH. This is supported by the low limiting conductance12J3and self-diffusion coefficientll of H2P04-. The broadening of the P-OH band in dilute solution is consistent with hydrogen-bonding interactions with water over a range of energies.40 In dilute solution, the cations would also be solvated, and have negligible influence on the phosphate anions. As the concentration increases, the half-width of the P-OH band decreases. This could result from a decrease in the extent of type I1 hydration, or a decrease in the range of hydrogen-bond energies. As the ratio of water to solute molecules decreases, the number of possible configurations of water about a P--OH bond should also decrease; a t the very highest concentrations, the extent of type I1 hydration must become less, as water molecules which are hydrogen bonded to P-OH are unable to solvate cations, while water hydrogen bonded to P-0 can still be shared with a cation. At the same time, as the concentration increases, the concentration of phosphate dimers should increase, and more cations will begin to be separated from the phosphate oxygen by only a single H20. It seems plausible that the growth of the low-frequency component of the 1074-cm-’ band, and the increase in frequency of the 874-cm-l band with increasing concentration, indicate the increase in hydrogen-bonded phosphate dimers or polymers, as an increasing proportion of hydrogen bonds to water are broken and replaced by hydrogen bonds among phosphates. The shift of -30 cm-l (1074 to 1040 cm-l) is consistent with a small change in hydrogen-bond strength. The results obtained from band resolution provide some support for this interpretation. The 1074-cm-l band of Na-, K-, and NH4H2P04was resolved into two components, a sharp band a t 1074 cm-l, and a broader band at 1045 f 5 cm-l. These were assumed to correspond to the P-0 vibrations of “free” and “hydrogen-bonded” phosphate, respectively, regardless of whether the phosphate dimer was formed with one, two, or three hydrogen bonds; it was also assumed that the RMSFs of the monomer and dimer species are the same, and the model does not

820


TABLE IX: Concentration Quotient Qd ( L mol") Vs. Stoichiometric Concentration for the Formation of H,P,O,'- and H,P,0,4- for MH,PO, and M,HPO, Solutions at 25 "Ca Qd,Lrnol-'

concn, mol L-' 0.1 0.2 0.5 0.6 1.0 1.5 2.0 2.5 3.0 4.0 6.0 a

NaH,PO, 0.23

KH,PO, 1.7

0.30

1.2

0.30

0.43 0.78 1.2 0.53

NH,H,PO, 0.59 0.33 0.31

K,HPO, 0.64

0.19 0.65 0.10

0.31

Na,HPO,

0.18 0.17

0.44

0.11

0.33 0.92 0.23

0.16 0.53


consider the possible formation of higher polymers a t high concentrations. Using this simple model, [H,P04-] = (I1O74/lJcs, and [H4P20a^]= 0.5(Z1046/It~c,, where It is the total band intensity and c, the stoichiometric concentration of MH2P04. The concentration quotient for dimer forThe values mation is given by Qd = [H4P20~-]/[H2P04-]? found for Qd are shown in Table IX, and the average value is 0.6 f 0.3 L mol-'. The results obtained using this simple model are in good agreement with literature estimates of Kd. Potentiometric titrations at 25 "C have given 0.73 f 0.17,170.42 f 0.04,15and 5.6 f 2.0 (at 37 O C ) I 9 L mol-', and an isopiestic study has given 0.25 f 0.1 kg mol-' at 25 O C . I 6 It seems unlikely that these large changes in the H2P04spectra can be attributed to the cations only. First, the changes in both frequency and half-width are nonspecific up to about 3 M Na-, K-, or NH4H2P04.The changes are clearly apparent at concentrations far below those which would force contact-ion pairs, or even solvent-separated pairs. At 1 M NaH2P04,where the assymetry is quite clear (Figure l), the ratio of water to NaH2P04 is still 54. Further, there is no evidence for strong association between phosphate and sodium or potassium. It would also be expected that ammonium would have less effect on the frequencies and half-widths than sodium or potassium, because the ammonium ion fits into the water lattice with little disruption.sa Studies of nitrate solutions showed that the frequency and half-width of the vl(A1') band at 1049 cm-' increased with increasing concentration, except for ammonium nitrate solutions, where the half-width remained constant, and the frequency decreased We have also observed that addition of salts to 0.1 M NaH2P04causes only a small increase in the half-widths of the 874- and 1074-cm bands, and the bands remain symmetric. Addition of 1 M NaCl to 1 M NaH2P04again causes both bands to broaden slightly, but no increase in the asymmetry. Again, if the cations were largely responsible for the broadening and shifting, then the effects should be a t least as large in the M2HP04and M3P04 solutions, where the ratio of cations is larger for a given phosphate molarity. Finally, it is also noteworthy that the crystal frequencies of the P-0 stretch in anhydrous NaH2P04and Na2HP04,which are extensively hydrogen bonded, are lower than in aqueous solution. For nitrates, however (except for ammonium nitrate), the crystal frequencies are higher, as they are determined largely by the polarizing power of the cation.8a The Raman data for H 2 P 0 c solutions are then consistent with extensive hydration in dilute solution, both through P-0 and P-OH, and a t higher concentrations, formation of phosphate dimers or polymers. These can


still have hydrogen bonding to water, depending on the niimber of interphosphate bonds; the extent of type I1 hydration, however, must decrease a t high concentration so that water may be free to solvate the cations. The temperature data are also consistent with this model. As temperature increases, the frequency of the P-OH stretch decreases, and the P-0 stretch increases, for both the 0.1 and 1.0 M solutions. These changes are opposite to those found with increase in concentration, and are consistent with a decrease in the number or strength of hydrogen bonds of phosphate. Na2HP04 and K z H P 0 4also show an increase in the P-OH frequency with concentration, while the P-0 band becomes broadened on the low-frequency side. The effect is not as large as for HzP04-; certainly electrostatic considerations argue against extensive dimer formation. It has been suggested that H P O t - can also undergo type I1 hydration, which must decrease a t the highest concentrations. Again, the effects do not seem to be due to any great extent to the cations, and the most plausible explanation is the existence of phosphate dimers a t the higher concentrations. Band resolution was also carried out on the P-0 band of HP04'- at 987 cm-', to give components at 987 and 960 f 5 cm-', and Qd values for dimerization were obtained as before (Table 1x1. The average value, 0.28 f 0.12 L mol-', is in good agreement with a literature estimate of 0.17 f 0.02, obtained from potentiometric titration a t 25 O C . 1 5 The changes with temperature cannot be easily explained. As with H2PO4- a t 0.1 M, the frequency of the P-OH band decreases with increasing temperature, which may indicate a decrease in type I1 hydration. The frequency of the P-0 stretching band remains constant (or possibly decreases slightly; the change is within experimental error), and its half-width also decreases. The concentration of phosphate dimers a t 0.1 M must be very low, so that changes in the bands with temperature must largely reflect changes in phosphate solvation. For K3P04and Na3P04,there appear to be no changes in the frequency or half-width of the PO4 stretching band up to 4 M K3P04; the band is still symmetric a t this concentration, where there are only nine H,O's per K3P04, or about 2.3 per ion for complete dissociation into K+ and Po43-.If solvent-separated ion pairs exist a t the high concentrations, they do not appear to affect the Raman spectrum. Like the PlSO,3-study previously mentioned,37 the Raman data suggest that PO-: is extensively hydrated at all concentrations, and that the nature of the hydration shell remains unchanged. Water molecules hydrating Po43-are still free to solvate cations via the second OH dipole. At 0.1 M, the half-width of the PO4 symmetric stretch decreased with increasing temperature. Po43cannot undergo type I1 hydration, or form dimers by hydrogen bonding, and at 0.1 M, cation effects should be negligible. The temperature effect may indicate a decrease in hydration; that is, simply an expansion of the solvation shell. The effect is large enough that the observed half-width decreases, whereas an increase would be expected as the viscosity of the solution decreases with increasing temperature. The Raman study of the hydrolysis equilibrium gave a limiting value at low concentrations (ca. 0.01 M) of 0.0084 for the hydrolysis concentration quotient, or 1.2 X 10-l' mol L-l for the third dissociation of phosphoric acid. The thermodynamic dissociation constant K3 is 4.8 X 10-13,41 although a wide range of values, up to ten times higher, have been reported. It is not surprising that the Raman value is approximately twice the thermodynamic one. It


The Journal of Physical Chemistry, Vol. 83,

No. 7, 1979 821

(6) A. C. Chapman, D. A. Long, and D. T. L. Jones, Spectrocbem. Acta, was not possible to obtain sufficiently good Raman data 21, 633 (1965). (See ref 3-6 for references to other early work.) below ca. 0.02 M in order to extrapolate reliably to infi(7) C. M. Preston and W. A. Adams, Can. J. Spectrosc., 22, 125 (1977). nitely dilute solution, and the Raman method measures (8) (a) P. M. Vollmar, J. Chem. Pbys., 39,2236 (1963); (b) D. E. Irish concentrations rather than activities. We had previously and G. W. Walrafen, ibid. 46, 378 (1967); (c) D. E. Irish and A. R. Davis, Can. J . Cbem., 46, 943 (1968); (d) D. W. James and R. L. found Q, for the first dissociation to be approximately Frost, Can. J . Spectrosc., 23, 5 (1978); (e) T. G. Chang and D. 0.011 mol L-' at the concentration limits of our meaE. Irish, J . Pbys. Chem., 77, 52 (1973); (f) J . Sol. Cbem., 3, 175 surements,' whereas K1 is 0.0071 mol L-1.41r42As Raman (1974); (9) D. E. Irish and M. H. Brooker in "Infrared and Raman Spectroscopy", Vol. 2, R. J. H. Clark and R. E. Hester, Ed., Heyden, intensity data can be used to obtain solution concentraNew York, 1976, Chapter 6, pp 212-31 1. tions, rather than activities, acid dissociation constants (9) (a) D. E. Irish and H. Chen, J . Phys. Chem., 74, 3796 (1970); (b) obtained from Raman spectroscopy may be larger than 75, 2672 (1971); (c) 75, 2681 (1971); (d) D. J. Turner, J . Chem. Soc., Faraday Trans. 2,68,643 (1972); (e) J. Chem. Soc., Fara&y thermodynamic values, unless activity coefficients are Trans. 7, 70, 1346 (1974); (f) A. R. Davids and B. G. Oliver, J. Phys. known, or enough data can be acquired at low concenChem., 77, 1315 (1973). trations to extrapolate reliably to infinite d i l ~ t i o n . ~ ~ (10) ~ ~G.~ E.~Walrafen, ~ ~ , ~J .~Chem. Phys., 52, 4176 (1970). (1 1) 0. W. Edwards and E. 0. Huffman, J. Phys. Chem., 63, 1830 (1959). We measured AH3 values for the third dissociation of (12) C. M. Mason and J. B. Culvern, J. Am. Chem. Soc., 71, 2387 (1949). phosphoric acid of +5.8 kcal mol-I for 0.1 M K3P04and (13) M. Kerker and W. F. Espenscheid, J . Am. Chem. SOC.,80, 776 +4.8 kcal mol-l for 0.1 M Na3P04;the literature value is (1958). (14) K. S. Pitzer and L. F. Silvester, J. Sol. Chem., 5, 269 (1976). +3.Eie41In view of the many sources of error in obtaining (15) G. Ferroni, Electrochim. Acta, 21, 283 (1976). AH3, the discrepancies may not be significant. (16) R. H. Wood and R. F. Platford, J . Sol. Chem., 4 , 977 (1975).

Conclusions The Raman spectra of orthophosphate salts have been studied over ranges of temperature and concentration. In general, the data are consistent with earlier work, but two previously reported bands have been shown to be perturbations of the P-0 bands of H2P04-and HPO?-. The concentration and temperature dependences of bands have been documented, and these suggest extensive hydration of phosphate anions in solution, and formation of hydrogen-bonded phosphate dimers or polymers in H2P04and HPO?' solutions at higher concentrations. Within the concentration ranges studied (0.005-6 M), there was no evidence for specific cation effects. From the hydrolysis of Na3- and K3P04solutions, the third dissociation constant of phosphoric acid was estimated to be 1.2 X mol L-l, and AH3 was -+5 kcal mol-l. These are higher than the literature values, and most likely reflect the effect of measuring concentrations rather than activities. These studies indicate that Raman spectroscopy is of considerable utility in studying the nature of solvation, hydrogen bonding, and ion pairing in phosphate solutions, especially if computer time averaging could be employed to obtain reliable data down to 0.001 M or less. At the higher concentration end, studies to the limits of solubility and over wider temperature ranges, and then into molten salts should be able to provide information on the nature of the phosphate complexes and the concentration regions where specific cation effects might be observed. Acknowledgment. It is a pleasure to thank Dr. D. E. Irish, Department of Chemistry, Waterloo University, Waterloo, Ontario, for helpful discussions.

References and Notes (1) NRCC Postdoctorate Fellow (1976-1978); Chemistry and Biology Research Institute, Agriculture Canada, Carling Ave., Ottawa, Ontario, Canada, K I A OC6. (2) Defence Research IEstablishment Ottawa, Department of National Defence, Ottawa, Ontario, Canada K1A 024. (3) J. Mathieu and J. Jacques, C. R. Acad. Sci., 215, 346 (1942). (4) E. Steger and K. Herzog, Z. Anorg. Allg. Chem., 331, 169 (1964). (5) A. C. Chapman and L. E. Thirlwell, Specfrocbim. Acta, 20,937 (1964).

(17) A. A. Ivakin and E. M. Voronova, Russ. J . Inorg. Cbem., 18, 465 (1973). (18) C. W. Childs, Inorg. Cbem., 9, 2465 (1970). (19) C. W. Childs, J. Phys. Chem., 73, 2956 (1969). (20) K. L. Emore, J. D. Hatfield, R. L. Dunn, and A. D. Jones, J . Pbys. Cbem., 89, 3520 (1965). (21) M. Selvaratnam and M. Spiro, Trans. Faraday Soc., 61, 360 (1965). (22) L. W. Green, P. Kruus, and M. J. McGuire, Can. J. Cbem., 54, 3152 (1976). (23) (a) H. S. Kielman and J. C. Leyete, Ber. Busenges. Phys. Chem., 79, 1201 (1975); (b) R E. Lenkinski, C. H. Francis Chang, and J. E. Glickson, J . Am. Cbem. Soc., 100, 5383 (1978). (24) D. Schioberg, K. P. Hofmann, and G. Zundel, Z. Pbys. Chem. (Frankfurt am Main), 90, 181 (1974). (25) E. Philippot and 0. Lindqvist, Acta Cbem. Scand., 25, 512 (1971). (26) W. G. Baldwin and L. G. Sillgn, Ark. Kemi, 31, 391 (1968). (27) R. E. Mesmer and C. F. Baes, Jr., J . Sol. Chem., 3, 307 (1974). (28) J. R. Allkins and E. R. Lippincott, Spectrocbim. Acta, Part A , 25, 761 (1969). (29) Several literature reports of PO -: frequencies are incorrect, as the frequencies quoted appear to have been confused with those of HPO?-: see G. Herzberg, "Molecular Spectra and Molecular Structure", Vol. 11, Van Nostrand, New York, 1945, p 167, Table 39; K. Nakamoto, "Infrared Spectra of Inorganic and Coordination Compounds", Wiley, New York, 1963, p 107, Table 11-24; E. A. Robinson, Can. J. Chem., 41, 173 (1963); S. F. Baldwin and C. W. Brown, Water Res., 6, 1601 (1972). (30) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions", Butterworths, London, 1959, p 363. (31) E. R. Nightingale, Jr., in "Chemical Physics of Ionic Solutions", B. E. Conway and R. G. Barradas, Ed., Wiley, New York, 1966, p 87, Chapter 7. (32) G. C. Pimentel and A. L. McClellan, "The Hydrogen Bond", W. H. Freeman, San Francisco, 1960, p 135. (33) P. G. Puranik, J . Chem. Phys., 26, 601 (1957). (34) U. Haldna and R. Aroca, Org. React., 13, 523 (1976). (35) J. A. Faniran, K. S. Patel, and L. 0. Nelson, J . Pbys. Cbem., 82, 1018 (1978). (36) R. J. Levine, D. B. Powell, and D. Steele, Spectrochim. Acta, 22, 2033 (1966). (37) S. Pinchas and D. Sadeh, J . Inorg. Nucl. Cbem., 30, 1785 (1968). (38) Provided by P. Kruus and M. Farrington, Department of Chemistry, Carleton University, Ottawa, Ontario, Canada. (39) (a) S. Furberg, Acta Chem. Scand. 9, 1557 (1955); (b) J. P. Smith, W. E. Brown, and J. R. Lehr, J. Am. Cbem. Soc., 77, 2728 (1955). (40) J. J. Fox and A. E. Martin, Proc. R. SOC.London, Ser. A , 162, 419 ( 1937). (41) J. R. Van Wazer, "Phosphorus and Its Compounds", Vol. I,Interscience, New York, 1958, p 481. (42) R. G. Bates, J. Res. Natl. Bur. Stand., 47, 127 (1951). (43) A. K. Covington, J. G. Freeman, and T. H. Lilley, J . Pbys. Cbem., 74. 3773 (1970) (44) A.'K. C0vi;lgton: M. L. Hassall, and D. E. Irish, J . sol. Chem., 3, 629 (1974).

A laser Raman spectroscopic study of aqueous orthophosphate salts

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