H. A. Neidig, T. G. Tenter,' and R. T. YinglingZ Lebanon Valley College Annville, Pennsylvania
The Chemistry of Orthophosphoric
Acid and its Sodium Salts
Laboratory investigations of the chemistry of orthophosphoric acid and the sodium salts of orthophosphoric acid provide an unusual opportunity for discussing various aspects of the concepts of stoichiometry and thermodynamics, as well as the acidbase chemistry of these systems. When investigating the chemistry of orthophosphoric acid, there are three types of equilibria that should be considered. These equilibria are dissociation, hydrolysis, and disproportionation. The corresponding reactions are shown in the following equations. Dissociation Equilibria HaPO.(aq)
=
H+(aq)
+ HSOr-(aq)
+ HPO*"(aq) I I P O F ( a q ) = 1%+(aq) + POla-(sq)
H2P04-(aq) = H+(ttq)
(1)
(2) (3)
Hydrolysis Equilibria
Disproportionation Eguilibria
At the same time, the nature of the conversion of H3P04to H2P04- might be considered as a simple dissociation as shown in eqn. (1)or as the transfer of a proton to a water molecule as shown in eqn. (10). Gurney (1) discusses the transfer of protons in soluThis article is based on the laboratory work done during the 1965 Summer Institute of the Laboratory Experiments for Chemistry Courses Project at Lebanon Valley College. The authors wish to acknowledge NSF Grant GE-5507 under which this work was done. The authors wkh to express their appreciation to Richard C. Bell, Robert J. Cullen, Harold F. Emmit, William 0. Kuntz, Jr., Leroy H. Arnold, Darryl W. Brixius, and Stephen I f . Jacobs for doing the majority of t,he laboratory work on these experiments. The authors would also like to acknowledge the numerous comments and suggestions made during the investigation on which this paper was based by Professor Frank H. Verhoek of Ohio State University and by Professor R. E. Griswold of Lebanon Valley College. 'Present address: Longwood College, Farmville, Va. ¶Present address: The Ohio St,ate University, Columbus, Ohio.
tions in detail with a number of specific references to the phosphate system. The purpose of this article is to suggest a number of possible laboratory investigations of the chemistry of H 9 0 a and its sodium salts involving potentiometric titration studies and/or thermochemical studies. Investigations are described that would provide data that could be used to consider such concepts as stoichiometry, equilibria, or thermodynamic functions. By altering the degree of sophistication of the experimental procedure and the processing of the experimental data, some of the investigations could be used in conjunction with a firsbyear college chemistry course or in an advanced course such as physical chemistry. Literature Review A variety of experiments appear in the literature involving H3PO4or its sodium salts. Watt and Felsing (2) present an experiment in which the partial nentralization of H8P01 is studied by preparing Na2HP04. State (3) describes an experiment in which data from the titration of HsPOPwith sodium hydroxide solution are used to write the equation for the reaction, providing a way of considering the stoichiometry of the system. An experiment (4) is presented in which qualitative and semiquantitative data are obtained for the titration of hydrochloric acid, sulfuric acid, and orthophosphoric acid with sodium hydroxide solution. These data are used to compare the relative acid strengths of hromcresol green and bromthymol blue to those of HC1, H2S01, HS04-, H3POs HPPOP-, and HPOn2-. Brescia et al. (5) find the gram equivalent masses of H3P04by the titration of the acid with sodium hydroxide using methyl orange and phenolphthalein as indicators. I n an exper ment on acidimetry, Hendel (6) suggests using a potentiometric titration of H3POI3s a test of the validity of the indicator method. The experiment involves the study of the two inflection points corresponding to the neutralization of the first two hydrogens of the acid. Wilson et al. (7) present a study of potentiometric and indicator end-points using the titration of HaPOn with sodium hydroxide. The reaction is followed with three different indicators and with a pH meter. An experiment involving the use of a pH meter is described by Pecsok (8)in which mixtures of HsPOa and NaH;POa and of NaHzPOn and NapHP04 are analyzed. An article by Olsen (9) describes simple equipment for automatic potentiometric pH titrations. Data are given for the titration of H P 0 4 , of a mixture of HsPOa and HC1, and of H3P04 and KHzPOI with sodium hydroxide. Volume 45, Number I , January 1968
/
57
Reilley and Sawyer (10) describe an experiment in which data from the potentiometric titration of HaPo, with sodium hydroxide are used to calculate the primary, secondary, and tertiary dissociation equilibrium constants. Daniels et al. (11) describe the poteutiometric titration of H3P04 with sodium hydroxide to obtain data to calculate the second dissociation constant of the acid. An experiment is given by Hutton (18) in which data are obtained by measuring the emf of a cell using quinhydrone-platinum electrodes during the titration of H3POnwith sodium hydroxide. Hutton (1B) g'lves a second experiment which involves the analysis of an HsPO, solution by titrating with sodium hydroxide using a mixture of bromcresol green and thymolphthalein as indicators with appropriate color standards. A thermochemical study is described by Palmer (13a) in which enthalpies of reaction are calculated for the reaction of excess sodium hydroxide with HPO4, with Na2HP04, and with IIHJ'O,. Palmer (13b) also suggests the potentiometric titration of a standard solution of KHzPOnwith hydrochloric acid to confirm the evidence of the polybasicity of H3P01 obtained by the thermochemical method. Cooke (14) and Zajicek (16) each describe a computer program that can be used to obtain the concentration of various species of HQO, from pH 0 to 14. Nature of Investigations
Data are given for the potentiometric titrations and thermochemical studies of the reactions of solutions of H3P04,NaH2POp,Na2HP04,and NarPOa with a solution of sodium hydroxide and/or hydrochloric acid. These data can be used to calculate equilibrium constants and standard free energy, entropy, and enthalpy changes for the dissociation, hydrolysis, or disproportionation equilibria for various orthophosphate species. Experimental
Processing the Data
Potentimnetric Titration. A 25.00-ml aliquot of a stock solution of H3P0, or one of its sodium salts is mixed with 100.0 ml of distilled water and is titrated with a standardized solution of sodium hydroxide or hydrochloric acid. The reaction mixture is stirred with a magnetic stirrer. A pH meter is standardized with a standard buffer solution and is used to measure the pH of the reaction mixture after the addition of each portion of titrant. Th,m,ochemical Studu. The calorimeter constant " for a calorimeter is calculated from data obtained by mixing standardized solutions of sodium hydroxide and hydrochloric acid in the calorimeter. After the calorimeter constant is known, an aliquot of a standardized solution of sodium hydroxide or hydrochloric acid is transferred to the calorimeter. An aliquot of t,he stock solution of H3P04 or one of its sodium salts is transferred to a second container. The quantities of reactants are selected so that the number of moles of sodium hydroxide or hydrochloric acid is at least five times greater than the number of moles of the phosphate species being used. The temperatures of the two reactants are measured, with a thermometer graduated in ~~~
58
/
~
0.l0C units, every 30 sec while stirring for a 5-min prcmixing time period. The reactants are mixed in the calorimeter, and the temperature of the reaction mixture is measured every 30 see for a 10-min post-mixing time period. Themometn'e Titration. The following components are assembled and appropriately connected: calorimeter, thermistor probe, thermistor bridge, power supply, and recorder. The thermistor probe and an electric stirrer are clamped in position over the calorimeter so the stirrer blade and thermistor probe tip will he immersed in the liquid in the calorimeter. A constant flow buret is assembled and calibrated. The tip of the buret is placed just above the surface of the solution in the calorimeter. Several types of constant flow devices are described in the literature such as those by Brockett ( 1 G ) or van Swaay and Lolley (17). The recorder scale is calibrated by means of a titration using standard hydrochloric acid and standard sodium hydroxide solution. A 20.00-ml sample of 1.00 M hydrochloric acid is pipeted into the calorimeter and 100.00 ml of boiled distilled water is added to the calorimeter. The solution in the calorimeter is stirred to ensure thorough mixing and equilibration. The recorder and thermistor assembly are turned on and the flow of 1.00 M standard sodium hydroxide solution is started when the recorder pen crosses a time interval line on the recorder chart. The constant flow buret is turned off when the recorder pen has leveled off indicating that all of the acid has reacted. A 20.00-ml sample of 0.60 M H3POais pipeted into the clean, dry calorimeter, and 100.00 ml of recently boiled, distilled water is added to the acid. The acid solution is thoroughly stirred. The recorder is turned on and when the recorder pen crosses a time line on the recorder chart the stopcock on the constant flow buret is opened. The standard sodium hydroxide solution is allowed to flow into the calorimeter until a leveling off of the curve on the recorder chart indicates that the titration is comolete.
~
Journol o f Chemical Education
Potentimnetric Titration. The data obtained for each of the potentiometric titrations are used to prepare a graph by plotting the pH of the reaction mixture versus the volume of titrant added to the reaction mixture. The concentrations of the stock solutions of H31'04 and the sodium salts are calculated from thc volume of sodium hydroxide and hydrochloric acid required to produce the inflection points which occur in the regions of the potentiometric titration curves where the slope is a maximum. The potentiometric titration curves can also be used to calculate dissociation, hydrolysis, and disproportionation equilibrium constants. The equilibrium constants for the step-wise dissociation of H3POn are calculated from the potentiometric titration curves using the methods given in Reilley and Sawyer (10). The equilibrium constants for the hydrolysis and disproportionation equilibria are calculated from the equilibrium constants for the step-wise dissociation of H3P04and for the dissociation of water. The pH of each of the stock solutions of HPO, and its sodium salts is calculated from the appropriate cquilibrium
the extent of dissociation of H 9 0 r and of the sodium salts in the stock solutions. If the assumption is made that the enthalpies of dilution of the products are the same as the enthalpies of dilution of the reactants, then the calculated enthalpy changes are equal to the standard enthalpy changes for the equilibria. A more sophisticated procedure for processing the data could involve the enthalpies of dilution in the calculation. Thermometric Titration. For the recorder chart calibration, the number of moles of sodium hydroxide solution added to the calorimeter per minute of the titration is calculated. This calculation is based on the known concentration and volume of the hydrochloric acid used for the calibration, and the length of time the solution flowed. For the titration of HJ'O.. ., the number of moles of sodium hydroxide solution used to reach each inflection point on the titration curve is calculated, using the data obtained for the recorder chart calibration. Jordan (19) gives a detailed descriptiori of the processing of data from thermometric titrations. Stern et al. (20) describe an electric heater which can be used for calibration of the apparatus used in thermometric titrations. The calibration described by Stern
constants, assuming that only the dissociation, hydrolysis, or disproportionation equilibrium are important. The standard free energy changes for each of the three types of the equilibria can be calculated from the respective equilibrium constants following the procedure of Lewis and Randall (18). I n these calculations, the ratio of the activity coefficients of the products to the activity coefficients of the reactants can be assumed to be unity for each equilibrium. If a more rigorous treatment is desired, the effect of ionic strength on the calculated equilibrium constants should be considered. Thennochemical Study. The data obtained from the thermochemical studies are used to prepare graphs by plotting the temperatures of the reactants and the reaction mixture versus time. The curves obtained from the plotted points are extrapolated in order to find the temperatures of the reactants and the reaction mixture at the time of mixing. The temperature changes and the enthalpy changes are calculated for mixing each of the phosphate species with excess sodium hydroxide or excess hydrochloric acid. The enthalpy changes for each of the three types of equilibria can be calculated, taking into consideration Table 1.
-
"
p H and Dissociation Equilibrium Constants for Solutions of HaPOa and Its Sodium Solts
Phosphate Species
Cono. of Stock Solution (moles liter-')
HIPOI NhHSO, NxlHP04
0.612 0.984 0.408
----------pH Initial*
Caled*
Exp.
7.52 x IOP 6.22 X 10-8 4.79 x lo-=
8.56 X 2.11 X 10' 8.46 X lo-1z
1.55 3.69 6.08
1.68 4.60 9.04
Equilibriom Constant Litc
Measured pH of 25.00 ml of stock solution plus 100.0ml of distilled water. pH of 25.00 ml of stook solution plus 100.0 ml of distilled water oaloulated assuming only dissociation equilibria. ' Reference (11 ). AGO, AHo, and ASo for the Dissociotion Equilibria of Solutions of H 8 O i and Its Sodium Salts
Toble 2.
Phosphate Species
Conc. of Stock Solution (moles liter-')
Hap01 NaHPOl NaXPOn
0.612 0.984 0.408
AH"
AG"
(koal mole-') Exp. Lit
2.82 9.11 15.11
ASo
(kcal mole-') Exp. Lit -1.88O -1.27 0.80b 1.05 3.509 5.18
2.89. 9.83b 16.3OC
(cal mole-' Exp. -13.7 -27.0 -33.0
deg-I) Lit r: -16.0" ~30.3~ -43.0"
Reference (b2). Reference (23). "eference (24). b
Table 3.
Summary of Doto for the Hydrolysis Equilibria for Solutions of the Sodium Salts of HaPo, c n n r nf
~olution (moles liter1)
Phosphate Species
~
a
-CalculatedpHa
Kw
AG"
AHo
(kcd mole-1)
(kcal mole-')
AS"
(cal mole-'deg-I)
~
PIT of 25.00ml of stocksolution plus 100.0of distilled water calculated assuming only hydrolysis equilibria. Table 4.
Summary of Data for the Disproportionation Equilibria for Solutions of NaHtP04 and of NazHPO4
Cone. of -~ stock Solution (mole liter-') ~
Phosphate Species N~HxPO~ N ~~ , A-. P~. O -I -
a
0.984 0.408
-CalculatedpHa
4.37 8.87
K, 2.47 X 4.01 X
AG"
(kcal mole-')
6.29 6.00
AS'
AHo
(kcal mole-') (cal mole-ldeg-I)
2.32 4.13
-13.3 -6.3
pH of 25.00 ml of stock solution plus 100.0 ml of distilled water calculated assuming only disproportionation equilibria. Volume 45, Number I, lonuory 1968
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59
might be useful if quantitative enthalpy change data are to be obtained from the titration. The standard entropy changes for each of the three types of equilibria can be calculated from the standard free encrgy changes and the standard enthalpy changes for these processes. The equilibrium constants, pH, enthalpy changes, entropy changcs, and free energy changes are given for the dissociation equilibria in Tables 1 and 2, for the hydrolysis equilibria in Table 3 and for the disproportionation equilibria in Table 4 . Possible Investigations
The data presented in Tables 1-4 suggest a number of investigations that might be designed to study the chemistry of solutions of H 9 0 r and its sodium salts and to develop various theoretical concepts. Some of these invcstigations described below might be useful for a first-year college chemistry course or might be more appropriate if used in an advanced course such as physical chemistry. Investigation 1
Problem. Determine if there is a relationship between the observed pH of stock solution of HzPOa, NaH2P04, and NazHP04 and the corresponding dissociat,ion equilibrium constants. Laboratory Work. Complete potentiometric titratiou of solutions of HaPOa, of NaHzP04, and of N a r HP04with standard sodium hydroxide. Processing of Data. Plot titration curves and calculate dissociation equilibrium constants. Discussion of Data. Compare the observed pH of the dock solutions with the calculated dissociation equilibrium constants. In this elementary approach to the systems involved, the data in Table 1 can be used to compare the diierent systems and to develop the relationship between pH and dissociation equilibrium constants. lnvestigotion 2
Problem. Consider whether the dissociation, hydrolysis, or disproportionation equilibrium is more extensive for solutions of H3POa and for solutions of its sodium salts. Laboratory Work. Complete the potentiometric titration of solutions of H1P04, ~. of NaH2PO&, ~. and of Na2HP04 with standard sodium hydroxide, and of solutions of NaH2P04, of Na2HP04, and of Na8P04 with standard hydrochloric acid. Another approach is to titrate a solution of H3POa with standard sodium hydroxide and a solution of Na3PO4 wit,h standard hydrochloric acid. Processing of Data. Plot titration curves and calculate the dissociation, hydrolysis, and disproportionation equilibrium constants. Calculate the pH for each of the equilibria assuming only one of the equilibria is important. Calculate the standard free energy changes for each of the equilibria. If the investigation is to be used in first-year chemistry, the free energy calculations could be made assuming the ratios of t,he activity coefficients of the products to that of the reaction is unity. For a very sophisticated treatment of the data, the activities of the reactants and of 60
/
Journal of Chemical Educution
the products might be considered. I n either case, the significance of using the activity coefficients in the calculations should be discussed. Discussion. Compare the magnitudes of the three equilibrium constants for a given phosphate species to determine which of the equilibria is the most significant. Compare the observed pH with the calculated pH based on each equilibrium for each solution. Compare the magnitudes of AG" for the three different equilibria. Examination of the data in Tables 1, 3 , and 4 suggest that the equilibrium constants decrease in t,he order: NaaPOI: Hydrolysis NhHPO,: Disproportionation > Hydrolynk > Dissociation NaH9P04: Disproportionation > Dissociat,ion > Hydrolysis H.P04: Dissociation
The initial concentration of a species can affect the extent of the various equilibria. For concentrations less than 10-2M, the extent of dissociation of NaH2POI begins to exceed the extent of disproportionation of NaH2P04. Below 10-4M initial concentration of NaHzPOa,the extent of disproportionation is even less than the extent of hydrolysis. The extent of the hydrolysis equilibria at the concentrations studied increases from NaHlPOa to War HPOl to Na8P04as shown by the respective equilibrium constant,s of 1.18 X 4.75 X and 1.19 X lo-? At the same time, the extent of dissociation decreases from NaH2POa to Na2HP04 to NaaPOn as shown by the respective equilibrium constants of 8.56 X 2.11 X lo-', and 8.46 X 10-'2. Examination of eqns. (I), ( 2 ) ,and ( 3 ) indicates the dissociation equilibria would result in solutions of H3POa, of XaH, PO4, and of Na2HPOabeing acidic. From eqns. (4), ( 5 ) , and ( 6 ) , the hydrolysis equilibrium suggest that solutions of NaH2P04, of Na2HP04, and of Nad'Oh would be basic. Because there is no hydrolysis equilibrium for a solution of H3P04, only the dissociation equilibrium is involved and the solution will be acidic. For a solution of Na2HP04, disproportionation and hydrolysis occur to a greater extent than dissociation so that the solution is basic. In addition, these data could be compared with those obtained from a logarithmic concentration diagram constructed from literature data (%). Discussion of this diagram could be used to consider the concentration of various phosphate species as a function of pH. Thomas ($5) presents a graphical treatment for acid-base equilibria calculations and from the logarithmic concentration diagram for HaPOn obtains KI = 7.5 X 10Wa, KI = 6.2 X lo4, and K3 = 4.8 X For a solution of NaHZPOn,the observed pH is 4.60, but the calculated pH's for dissociation, hydrolysis, and disproportionation are 3.69, 7.68, and 4.37, respectively. These data suggest that for a solution of NaHJ'Oa the disproportionation equilibrium best describes the observed pH. For a solution of Na2HPOI,the AG" for dissociation, hydrolysis, and disproportionation are 15.11, 9.99, and 6.00 kcal mole-', respectively. On the basis of AGO, the disproportionation equilibrium appears to be the most extensive equilibrium for a solution of NazHPOa.
Investigation 3
Problem. Compare the extent of dissociation of the three hydrogen-to-oxygen bonds in H3P04in terms of enthalpi change. Laboratory Work. Complete thermochemical study of the reactions of standardized solutions of HIP04,of NaHzP04, and of Na2HP04 with excess sodium hydroxide solution. Processing of Data. Prepare temperature-time curves and calculate enthalpies of reaction. In a first-year chemistry course, the enthalpies of dilution could be neglected in calculating the enthalpy of reaction, but in an advanced course such as physical chemistry, the enthalpies of dilution could be included in the calculation. Hess' Law could be used to obtain the enthalpies corresponding to the removal of the individual hydrogens from H3PO1. Discussion. Consider the hydrogen-to-oxygen bonding in H&O ' a, in HzPOa-, and in HP02- in terms of the appropriate enthalpy changes. If the dissociation process is assumed to involve the transfer of a proton to a solvent molecule as shown in eqn. (9), the first dissociation of H3P04would require energy for the establishment of an electrostatic field around each of the ions formed and to overcome the binding energy of the proton in HJO ' 6. The solvation of the proton would release energy. Because the enthalpy change for the first dissociation is -1.27 kcal mole-', the solvation energy must exceed the other energy requirements. However, AHo for the second and third dissociation are 1.05 and 5.18 lccal mole-', respectively. These data suggest that the energy required for transferring the proton from H2P04-to a solvent molecule is greater than the energy required for the transfer from H 9 0 r to a solvent molecule. This difference in the energy required could be a result of a number of factors. There is a greater energy requirement for the dissociation of HIPOn- because of thc attraction between the doubly charged H P O P and the hydronium ion formed. Another factor is the marked difference in the proton binding energy in H3P04 and in H2PO1-. Also, the nature of the electrostatic fields created around the dissociated species will be' different. Thus, the data available do not indicate the cause of the energy difference but simply show that a difference exists. A similar argument could be developed involving the enthalpy of dissociation of H P O P in comparison to that of HzPOr- or of H3PO4. Another point of view is to consider the dissociation of H3POnin an infinitely dilute solution. The equation for this process can be expressed as: HaP04(aq)= Ht(aq)
+ H2PO4-(aq)
AHT
where AHT is the total enthalpy change. This dissociation in solution can be divided into the following steps: HaP04aq) = HsPOdg) HaPOdg) = H+(g) f H90,-(g) IIt(g) = Hf(aq) HPOI-(g)
=
H2PO4-(aq)
so that AH,
=
AH,
+ AH, + AH, + AH4
AH, AH, AHs AH4
where AH1 and AHz are endothermic and AH8 and AHn are exothermic. AH%is a measure of the bond energy. However, the data collected refer to AHT from which AHz cannot be calculated. Hence, the enthalpy data obtained for this investigation have this obvious limitation when being used to discuss the bond strength of the H-0 bond in HaPO4.
Problem. Obtain evidence for the neutralization of each of the hydrogens in H3POn. Laboratory Work. Complete a potentiometric titration and a thermometric titration of H3POneach with excess standard sodium hydroxide. Processing of Data. Prepare a potentiometric titration curve and a thermometric titration curve. Discussion. Compare the two titration curves in terms of the stoichiometry of the system. Although an inflection point corresponding to the neutralization of the third hydrogen of H3P04is not obtained using a potentiometric titration approach, this neutralization is shown by the thermometric titration approach. The third dissociation equilibrium constant (Ka = 8.46 X 10-12) shows HPOaZ- to be almost as weak an acid as water (K = 1 X lo-'"). Investigation 5
Problem. Compare the enthalpy changes for removing the three hydrogens from H 9 0 4 with those for adding the three hydrogens to Poda-. Laboratory Work. Same as for Investigation 3 including a thermochemical study of the reaction of standardized solutions of Na3POa,iYazHPOd,and iYaH2POa with excess hydrochloric acid. Processing of Data. Prepare temperature-time curves and calculate the enthalpies of reaction. By the use of Hess' Law, calculate the enthalpy changes for the appropriate related reactions. Discussion. Compare the enthalpy changes for removing each successive hydrogen from HaP04d h the corresponding enthalpy changes for the successive addition of each hydrogen to Pop3-. lnvesfigation 6
Problem. Consider the stepwise dissociation of HaPO4in terms of dissociation equilibrium constants and the standard free energy, enthalpy, and entropy changes. Laboratory Work. Same as for Investigations 2 and 3. Processing of Data. Same as for Investigation 3 including the calculation of the entropy changes. Discussion. Consider the trends in the dissociation equilibrium constant and in AGO, AH", and AS" for the stepwise dissociation of H3PO1. The data in Table 2 show that with the successive removal of hydrogens from H3POnthe AHo and AGO become more positive and that ASa becomes more negative. If the multistep nature of each dissociation is neglected, one explanation of the trend in AHo is that the energy required to remove a proton would increase as the negative charge increases on the dissociation species. The positive AG" for the first dissociation of H P 0 6 suggests that the process is not the simple Volume 45, Number 7, Januory 1968
/
61
cleavage of hydroge~i-to-oxygen bond. The energy requirement for the process indicates the possibility that the first dissociation could involve a proton transfer to a solvent molecule. Strictly speaking, however, the fact that AGO is positive only indicates that the reactiou is not spontaneous, and that the undissociated hypothetical 1 m H,POa is more stable than 1 m H + and 1 m H2POa-. The trend in ASo can be explained as a result of the effect of the charged species formed by dissociation on the structure of the solvent molecules. However, ASo is the sum of the entropy changes for stepwise reactions involving only solvation or dissociation so that the limitations of any explanation of trends in ASa must be recognized. These data show that AH" and ASo complement each other so that both AHo and AS0 cause AG" to change in the same direction. There is a trend in AHo to more positive values and a trend in AS" to more negative values which both c a w AGO to have a trend to more positive values.
Problem. Compare the equilibrium constants and the standard free energy, enthalpy, and entropy changes for the dissociation, hydrolysis, and disproportionation of HPOn2-and HPP04-to determine which equilibria is the most important. Laboratory Work. Same as for Investigations 2 and 3. Processing of Data. Same as for Investigations 2 arid 3. Calculate the entropy changes for each of the equilibrium processes. Discussion. Consider the magnitudes of the equilibrium constant and AGO, A H o , and ASo for each of the equilibria. The data in Tables 2 4 reveal that the AGO values for the processes increase in the order: NaH*P04: Disproportionation > Dissociation > I Hydrolysis > Dissociation
Any discussion of these thermodynamic functions should include a consideration of the effects of concentration on them and the difference between the functions having the superscripts and those not having the superscripts. In com~arinethe dissociation and hvdrolvsis eauilibria for a sokion of NaH;POI, the Ak"f& the tho equilibria are 1.05 and 15.10 kcal mole-', respectively. This difference is unexpected in terms of establishing electrostatic fields around the dissociation species. When the AS" of -27.0 cal mole-' deg-' for the dissociation equilibria and -4.0 cal mole-' deg-I for the hydrolysis equilibria are considered, the effect of t)he ionic field appears to become more significant.
tions of each of the salts with excess standard hydrochloric acid and sodium hydroxide. Processing of Data. Prepare temperature-time curves and calculate enthalpies of dissolution and of reaction. By use of Hess' Law, calculate the enthalpy changes for the appropriate processes. Discussion. Compare the enthalpies of dissolution of each of the three salts in the three solvents. Consider the relationship between the enthalpies of dissolution in water, acid, and base and the corresponding enthalpies of reaction for solutions of the salts. The enthalpy data can be used to advantage in raising a number of questions that emphasize various aspects of the acid-base chemistry of orthophosphoric acid and its salts. Why is the enthalpy of dissolution of sa3POn.12 H 2 0 in water 10.9 kcal mole-' but only 4.3 lccal mole-' in hydrochloric acid? What equations can be written to describe the reactions which occur when the salts of H3POIare dissolved in water, in excess acid, or in excess base? What insight do the enthalpy changes for the reactions of solutions of the salts of H3POrwith excess acid or base provide about t,he magnitudes of t,he enthalpies of dissolution? Literature Cited ( 1 ) GURNEY, R. W., "Ionic Processes in Solotion," Dover Publications, Ino., New York, 1962. ( 2 ) WATT,G. W., AND FELSING, W. A., J . CHEM.EDUC.,15, 543
1142Rl ,-""-,.
( 3 ) STATE,H. M., J. CHEM.EDUC.,39,297 (1962). ( 4 ) "Investigating Chemical Systems," Webster Division, X e Graw-Hill Book Co., Inc., St. Louis, hIo., 1963, p. 65. ( 5 ) BnEscrA, F., ARENTS,J.,MEISLICH,H., N D TURK, A.,
"Fundamentals of Chemistry: Laboratory Studies," Academic Press, New York, 1966, p. 141. ( 6 ) FIENDEL, J . M., J. CHEM.EDUC.,29, 148 (1052). ( 7 ) WILSON,J . M., NEWCOMRE, R. J., DEN-LEO, A. R., AND RICKETT,R. IM. W., "Experiments in Physical Chemistry," Pergamon Press, Macmillan Company, New York, 1962, p. 229. ( 8 ) PECSOK, R. L., J. CHEM.EDUC.,28,252 (1951). ( 9 ) OLSEN,E. D., J . CHEM.EDUC.,43,310 (1966). ( 1 0 ) REILLEY, C. N., AND SAWYER, D. T., "Experiments far InstrumentalMethods," McGraw-HillBoak Company, Inc., New York, 1961, p. 17. ( 1 1 ) DANIELS, F., WILLIAMS, J . W., BENDER, P., ALBERTY, R. A., AND CORNWELL, C. D., "Experimental Physical Chemistry," (6th ed.) McGraw-Hill Book Company, Inc., New York, 1962, p. 199. ( 1 2 ) HUTTON,W., "General Chemistry: A Laboratory Text," Charles E. Merrill Books, Ine., Columbus, Ohio, 1965, p. 139. ( 1 3 ) ( a ) PALMER,W. G., "Experimental Physical Chemistr.~," Cambridge Univeaity Press, London, 1954, p. 164. (b) ibid,, p. 228. (14) COOKE, JR.,S. L., J . CHEM.EDUC.,~Z, 620 (1965). (15) ZAJICEK, 0. T., J. CHEM.EDUC.,42,622 (1965). (16) BROCKETT, C. P., J . CHEM.EDUC.,43,207 (1966). ( 1 7 ) VAN S w a a ~ M., , AND LOLLEY, R. F., J . Ca~nr.EDWC.,42, :iRl --- (1- Qfi.5) . * - ,. ( 1 8 ) LEVIS, N. G., AND RANDALL, IM., "Thermodynamics," ~McGraw-HillBook Company, Inc., New York, 1961, p. \
Problem. Compare the enthalpies of dissolution of solid Na3POI.12 H20, Na2HP04.7 HzO and NaH2POa.H20in water, in excess hydrochloric acid, and in excess sodium hydroxide and relate these enthalpies of dissolution to the appropriate enthalpies of reaction of the corresponding solutions of the salts with excess hydrochloric acid and with excess sodium hydroxide. Laboratory Work. Complete thermochemical studies of the solution of eaoh of the three salts in eaoh of the three different solvents and of the corresponding solu62
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journal of Chemical Educofion
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