YAPOR PRESSURES OF SOLUTIOKS AND T H E RAMSAY-YOUXG RULE. APPLICATION TO THE COMPLETE SYSTEM WATERAMMONIA BY F. C. KRACEK
Aside from approximation methods based on the laws of dilute solutions, there exists no method that will deal comprehensively with the relation between the vapor pressure and composition for concentrated solutions, whether they be saturated, unsaturated in the ordinary sense, or liquid mixtures, Le., solutions a t temperatures above the highest melting point in the system, It has early been recognized that the laws of ideal or dilute solutions do not apply to concentrated solutions. Repeated attempts t o derive a satisfactory expression for their behavior by modifying the dilute solution laws have to date resulted in failure; in other directions, attempts to account for the abnormal behavior of concentrated solutions on the basis of association or of compound formation in solution have likewise added little that is useful. I n view of these facts it remains necessary to treat the effect of composition in an empirical manner, and to seek to eliminate the effect of temperature by evolving a rational method that will reduce all experimental data to a common basis (common isotherm or a common isobar) for which the empirical relation between composition and some thermodynamic function of vapor pressure can be established. The method described in the following pages is based on the RamsayYoung rule, and, as n’e shall see later, is thermodynamically sound. The method developed is not particularly simple, and while this may appear to be a serious objection, we may be reminded that no simple method will completely describe the behavior of solutions of all concentrations over a great range of temperature. I t is presented in the hope that it may prove to be useful in dealing with the effect of temperature and composition on the vapor pressure of solutions. The vapor pressure-temperature relationship a t constant composition offers no theoretical difficulties. Two methods in general are available for this purpose. One is the usual logarithmic vapor pressure formula originally proposed in a simple form by Kirchhoff; the other, less well known, consists in comparing the temperatures a t which the substance or solution under investigation and some other reference substance exert equal vapor pressures; as such, it is essentially a boiling point law. The logarithmic vapor pressure formula l o g p = A / T + B b g T + . . . . . . . . .. . . . . . . . . . . . . . . . . . . . + I (1) does not lend itself particularly well to the study of vapor pressures of solutions of varying compositions, for while it is comparatively easy to determine its constants for any one given composition, the change of these con-
F. C. XRACEX
500
stants with composition leads to such cumbersome computation that a simpler method is preferable. The simplest alternative is the boiling point relation proposed by Duhring,’ which states that the difference between the temperatures a t which a substance A exerts the vapor pressures pl and p2 is a constant multiple of the difference between the temperatures a t which a second substance B exerts the same vapor pressures, that is, (t2
- tl)A
or, in absolute temperatures,
=
m(t2
- tl)BJ
(2)
+
TA = To mTB. The usefulness and some of the limitations of this rule have been discussed a t length by von Rechenberg2 (who, incidentally, has been led by its use to propose the somewhat questionable concept of the zero-point of vaporization). The application of this rule to solutions has been studied by Badger and ~o-workers,~ Mollier,4 Wilson,6 and others. It is useful for small ranges of vapor pressure, particularly for chemically related substances. The linear relation of the Diihring rule fails to hold over extended ranges of vapor pressure; this shows that a higher power equation is needed. Such an equation is supplied by the Ramsay-Young rule. The relation proposed by Ramsay and Younga states that the ratio of the absolute boiling points of two substances A and B a t various vapor pressures varies linearly with temperature. This may be expressed by the equations
+
(TA/TE),= (TA/TB)~, c(T - TO)B or
R’
= R’o
+ c(T - To)B.
(3)
The thermodynamic basis of this generalization has been discussed among others by Porter’ and Johnston;* the rule can easily be shown to follow directly from the logarithmic vapor pressure formula. It is essentially a power series boiling point equation, with all powers beyond the second neglected.
The Ramsay-Young Rule for Solutions Consider a binary system composed of the substances A and B. To apply the Ramsay-Young rule, select one of these (B), as the reference substance. In the region of liquid mixtures, depending upon whether the boiling Diihring: “Neue Grundgesetse zur rationellen Physik und Chemie” (1878). apem in 2. physik. Chem., and the book, “Die einfache und fraktionierte Destillation in TEeorie und Praxis,” Leipzig (1923);t h s author has employed the Diihring rule exclusively in tabulating the vapor preeaures of nearly 500 substances. ‘Baker and Waite: Chem. Met. En 25, 1137,1174(1921); Badger: 27, 932 (1922); Carr, Townsend and Badger: Ind. Eng. &hem., 17,643;Leslie and Carr: 810 (1925). Mollier: Forschungsarbeiten a. d. Geb. Ingeniemessen, 63,85 (1909). Wilson: Eng. Expt. Sta., Univ. Illinois, Bull. 146 (192.5). 6Rarnsay and Young: Phil. Mag., 20, 515 (1885);21, 33, 135;22, 32,37 (1886). Porter: Phil. Mag., 13, 724 (1907). *Johnston: 2. physik. Chem., 62, 330 (1908).
* von Reohenberg: several
’
THE RAMBAY-YOUNG RULE
50'
points of the solutions under a given standard pressure gradually increase, decrease, pass thru a maximum or a minimum on passage from the boiling point of the reference substance t o the boiling point of the other component of the solution, the ratio of the two absolute boiling points will also correspondingly increase, decrease, or pass thru a maximum or a minimum. At other pressures the boiling point ratios of individual solutions of constant composition will alter by an amount dependent upon the slope c of each individual Ramsay-Young line for the particular composition. Hence the problem is resolved into the relatively simple procedure of determining (a) the value of the absolute boiling point ratio for some standard pressure a t various compositions, and (b) the change in the slope of the boiling point ratios with changes of composition. The advantage of the use of the RamsayYoung rule lies principally in the fact that as a two-constant formula it is capable of reproducing a much greater range of vapor pressure than any other equation of comparable simplicity. Application to the System Water-Ammonia To illustrate concretely the method briefly described above we have selected the system H20-NH3 as the most suitable. This system has been studied extensively from the experimental standpoint, in view of its undoubted theoretical as well as practical importance. The boiling points (or the vapor pressures) in the system vary gradually from one component to the other without passing thru either a maximum or a minimum, thus partly simplifying the calculations. Furthermore, the solubilities and vapor pressures of saturated solutions have been determined. These serve as a valuable check on the correctness of the values calculated for the liquid mixtures. The total pressures of aqueous solutions of ammonia have been studied by Carius,' Roscoe and Dittmar,* SimsI3 Watts,4 Wachsmuth,6 Raoult,6 Doyer,' and Permans at o°C and higher temperatures. NIalletg made a few measurements between -3.9' and - 40°C. More recently Smits and Postmalo made an extensive study of the system at low temperatures, measuring vapor pressures up to approximately I atm., including those of saturated solutions. Mollier" made measurements up t o about I O atm. over an extended range of composition. Further recent measurements of the vapor pressures of liquid Carius: Ann., 99, 129 (1856). Roscoe and Dittmar: Ann., 110, 140 (1859);112, 327 (1859). * Sims: Ann. 118,333 (1861). 'Watts: Ann. Suppl., 3, 227 (1864). Wachsmuth: Arch. Pharm., (3)8, 510 (1878). 6Raoult: Ann. Chim. Phys. (51, 1, 262 (1874). ' Doyer: Z.physik. Chem., 6,486 (1890). Perman: J. Chem. SOC.,79, 718 (1901); 83, 1168(1903). Mallet: Am. Chem. J., 19, 804 (1897). Smlts and Postma: Proc. Acad. Sci. Amsterdam, 17, 187 (1914);Postma: Rec. Trav. chim., 39, 515 (1920). l1 Mollier: Forschungsarbeiten a.d. Geb. Ingeniemeasen, 63, 85 (1909).
502
F. C . KRACEK
mixtures of water and ammonia are due to Wilson' whose data unfortunately do not agree a t all well with those of other investigators, especially in the region of lower pressures. Mittasch, Kuss and Schlueter2 have also made some measurements above o°C., of indifferent accuracy. The principal series of data of good mutual agreement are those of Perman, Smits and Postma, and of hlollier. Our calculations are based mainly on the work of the latter investigators. The other data quoted were used as confirmatory checks rather than as fundamental data. Beside the above-quoted series of measurements of total vapor pressures, partial vapor pressure data due to Gaus? Abegg and Rie~enfeld,~ Locke and ForssallJ5PermanJ6h'euhausen and Patrick,' and Wilson are available. Solubilities have been measured by Rudorff,* Guthrie, Pickering,*ORupert ,I1 Smits and Postma,12 and Elliot,13with the result that two compounds, zXH3. H20 and h'H,.H,O have been found to exist in the solid state. The vapor pressure curves for ammonia and water are known with great exactness.I4 This is of importance in that it lends security to the calculations on solutions. The correlation of the above mass of data by means of the Ramsay-Young rule is given in the subsequent pages. A critical test for its accuracy is found in the agreement of the derived and observed vapor pressure curves for the saturated solutions. It is necessary to adopt certain conventions in the numerical work to follow. These conventions are more or less arbitrary; they depend upon the nature and fundamental constants of the system under consideration. Ammonia has been selected as the reference substance B in the equation of the Ramsay-Young rule (equation 3 ) . Since HzO exerts lower vapor pressures than NH1, and the vapor pressures of the solutions are always intermediate between those of the two components, the value of the boiling point ratio R' in the above-mentioned equation, equal to one for pure " I , is always greater than one for the rest of the system. Subtracting one from R' we have R ' - I = R = (TA/TB) - I = (TA-TB)/TB, (4) Wilson: Eng. Expt. Sta., Univ. Illinois, Bull. 146 (1925). hlittasch, Kuss and Gchlueter: Z. anorg. allgem. Chem., 159, I (1926). Gaus: 2. anorg. Chem., 25, 236 (1900). Abegg and Riesenfeld: Z. physik. Chem., 40, 84 (1902);45,462 (1903). Locke and Forssall: Am. Chem. J., 31, 268 (1904). Perman: J. Chem. SOC.,83, 1168 (1903). ' Yeuhausen and Patrick: J. Phys. Chem., 25, 693 (1921). Rudorff: Pogg. Ann., 116, 55 (1862). Guthrie: Phil. Mag., 18, 22, 205 (1884). 'OPickering: J. Chem. Soc., 63, 141 (1891). I1 Rupert: J. Am. Chem. Soc., 31, 866 (1909); 32, 748 (1910). l 2 Smits and Postma: op. cit. Elliot: J. Phys. Chem., 28, 887 (1924). l4 Cragoe, Meyers and Taylor: Vapor Pressure of Ammonia, Bur. Standards Sci. Paper S o . 369 (1920); J. Am. Chem. SOC.,42, 206 (1920). The vapor pressure data on water were taken from the 5th ed. of Landolt-Bornstein Tabellen; compare Washburn's tabulation in the 3rd volume of the International Critical Tables.
THE RAMSAY-YOUNG RULE
so3
or, the symbol R has the significance of the relative boiling point elevation. As we shall see later, this is more useful for this particular case than the boiling point ratio. R, has been selected as the value of R a t the vapor pressure corresponding to that of pure NH3 a t zso°K (1241 mm Hg). This value lies approximately
FIQ.I Duhring type vapor pressure diagram for the Bystem NHs -HzO
midway of the logarithmic range of the vapor pressures covered by the experimental data, and the temperature 2 50°K rather than that corresponding to I atm. pressure (z3g.7s°K) has been selected purely for convenience in calculation. Compositions are expressed in mol fraction or mol per cent of water for theoretical reasons. Since the molecular weights of NHI and H10 are not
504
F. C. KRACEK
greatly different, this convention does not impair the use of the results for practical purposes.' Graphical representation of the system is given in Figs. I and 2 , by means of the Diihring rule and the Ramsay-Young rule, respectively. The construction of the diagrams is obvious, but to remove all possibilities of am-
-
.E
,
7
I P
.+
.A0
-
.Y)
L
.-.
.... 20
t -
-
%
-
3
Kl-
-
FIG.2 Ramsay-Young diagram for the system NHJ-HsO. 1 The conversion from mol to weight per cent in this case is greatly facilitated by constructing a plot of the difference between the two along the ordmate agamst mol per cent along the abscissa. This difference never exceeds 1.42per cent. For convenience in constructing the plot use may be made of the equation WA - XA = 0.05827 NA - 0.05827Na2 - 0.0034 NA' WAand Nh signifying the wei ht and mol fraction of water in solution, respectively. This approximation e uation can %e readily derived from the relation between compositions expreeaed in we& and mol fractions.
505
THE RAMSAY-YOUNG RULE
biguity in interpretation, a brief description of the procedure may not be amiss. Suppose that a given solution exerts a vapor pressure p at the temperature t",C = T".K. Let the temperature a t which pure NH3 exerts the same vapor pressure p be tBaC = TBOK. I n the Duhring diagram we simply plot the two temperatures against each other, Le., t. vs. t B . To establish the same point in the Ramsay-Young diagram, the ratio TJTB is calculated, and its value R', or the corresponding value of R = R ' - I is plotted against either t B or TB. Repeating this procedure for various values of the vapor pressure of a given solution of constant composition, the constant composition Diihring or Ramsay-Young line is established. As will be seen from Fig. 2 , the slopes of the Ramsay-Young lines vary with comI
Y O
LLLl
""
L 5
,,
,
, I
, ,, , ,' , 8
e
LO
FIG.3 Plot of the slopes of the Ramsay-Young lines for the system N H z - H 2 0 vs. composition.
position; the same is true, of course, of the Duhring lines, the latter, however, are curved quite noticeably, whereas the former are st,raight lines within experimental error. I n this system the Ramsay-Young line for H 2 0exhibits the greatest slope; the slopes of the lines for solutions vary considerably, and differ greatly from the ideal slopes, which necessarily should be directly proportional to t'he composition expressed in mol fractions. This abnormality in the values of the slopes is to be expected from the nature of the system, which is far from being ideal. It is interesting to note in anticipation that the change of slope with composition, dc/dX is zero a t about 36 mol per cent of 1120, corresponding roughly to the composition zXH3.H20instead of to NHs.H?O, the compound ordinarily assumed to exist in aqueous solutions of ammonia.
F. C. XRACEE
0
~ r o r o O ~ r o v i r o v i 0
. . . COW . . h . C .O e. h. d .'
v i N W
& r o eo
N
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m 3 m d u m
3
w
CO
roviovioomrovio o. m. r .- m . -.
. . v. i h. - .
NCC
w r o m N " O \ * O h m r
(
H
I I T
roroooorovirororo
9 dt"P?"??c??
h d ' C 3 N O N O W O L O W 3
k
i
' ?
roroo 0 rovirororoo
?c???Pdc?"??? 3
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-
O\rOOLO
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0 0 rornvio
10
q w
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d
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W
0.
rorovirnmrooovio m, W. L .O O N. mCC . . N. m. h. p
m
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1
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O 3
N c
0 0
i
CI
0
r - N
rob
3
roo
0 mrovi
9 ? 1 ? ? ? 1'909 9 ' 9 N
w r - 3 3
m m - h n c
3
3
C O N
507
THE RAMSAY-YOUNG RULE
Determination of the Slopes of the Ramsay-Young Lines From the various series of experimental data on the vapor pressures of aqueous ammonia solutions, the values of R were calculated and tabulated for each well established constant composition. To save space these tabulations are not reproduced; the calculations were carried out with considerable r
LyG-1
45
-
t
35
-
Jo-
o
1
z
1 3
4
5
e
7
a
J
s
u
2 250
io
FIG. 4 The standard boiling point curve for the system NHs-HsO at 1241mm. Hg (TN,,=2jo"K)
care, using the previously quoted Bureau of Standards vapor pressure data for NH3 as reference. The slope for each constant composition line was determined from a large scale graph of R against the temperature of NH3, yielding the value of c in the formula of the Ramsay-Young rule for that composition of solution. The various values of c = dR/dTB were then plotted against the composition expressed in mol fractions of HzO, as shown
508
F. C. KRACEK
in Fig. 3. The resulting smooth curve can not be expressed conveniently by a simple algebraic expression; the values of the slope were therefore read off from the smooth curve and tabulated in Table I for convenient reference. The value of c for H20 in terms of NH, temperatures (dc/dTB) varies slightly, but not sufficiently to introduce an appreciable error if it is assumed to be constant over the range of pressures covered by the data. We have assumed therefore that the slope for each constant composition of solution is constant. Variation of R, with Composition As has already been mentioned, the standard reference pressure corresponding to the vapor pressure of NH3 a t z jo'K has been selected for the calculation of R,. This gives us the expression for the Ramsay-Young rule in the form R = RO c(T - 2 5 0 ) ~ . (5)
+
Knowing the value of c in the above equation from Table I, we can calculate the value of Ro for each experimental point. When this is done for the various solutions the result is a series of values of Ro which, when plotted against composition of the solutions, yields a curve reproduced in Fig. 4. Since T, = R'TB, and Tg = 2 5 0 for Ro, this curve also represents the variation of the boiling points (at the standard reference pressure) of the solutions with composition; the curve may be termed the standard boiling point curve, or the standard isobar. The standard isobar of Fig. 4 can be expressed with good approximation by means of a fourth degree equation; a more usable expression is obtained, however, if we employ the simple device of plotting the log (Ro i k) against log NA(KA = mol fraction of H20 in solution), as shown in Fig. 5 . The equation of the straight line is log (Ro - 0.0070)ca~c.= 2.1394 log NA 9.73465 - IO (6) This equation brings out the advantage of using R instead of R' in the computations. Both R and NAare zero for pure S H 3 ,hence the logarithmic plot can be used to obtain a straight line that will a t least approximately represent the relation between these two quantities. The same result of course would be obtained by setting k = 1.0070 and using R'o, but the relationship then would not be quite so obvious. Inspection of Figs. 4 and 5 shows that the values of Ro - k for the experimental points equalized by equation ( j ) fall quite near the straight line in all cases; in order to prevent any actual departure from the straight line from being overlooked, a deviation curve of Fig. 6 has been obtained, and the values of the deviations tabulated in Table 11. These deviations are to be added to the calculated values of RO- k, that is, R o = (Ro - k)cs,o. deviation. (7)
+
+
The Complete Pressure-Temperature-Composition Diagram for the System The combined results of the above considerations enable us to calculate the vapor pressure of a solution of any composition a t any given temperature
so9
THE RAMSAY-YOUNG RULE
FIG.5 Logarithmic plot of the standard 1241 mm. Hg isobar
m . 0
I
2
3
4
5
6
7
8
0
FIG.6 Deviation curve for R, vs. composition (see equation 7 ) .
1
0
F. C. KRACEX
-
h W In \o I n w h\o b 0 O I - W O I W h N h O I d h b h I n d m N b a 0 -
. . . . . . . . . . " "
++
THE RAMSAY-YOUNG RULE
511
within the range of the experimental results considered, namely, up to approximately 10,000mm Hg. T o be more exact, we should say that we calculate directly the boiling points of the solutions corresponding to any given pressure. For a solution whose composition is given by NAwe have:
+
log (Ro - k)=iC. = 2.1394 log NA 9.73465 RO = (Ro - k)cale. deviation (Table 11) R = Ro c(T - 2 5 0 ) ~(Table I) R'=I+R T, = R' T B
+
+
-
IO
(6)
(7) (5) (4) (3)
Since the value of the vapor pressure corresponding to T. is the same as the vapor pressure of NH3 a t Tg, it can be directly located by reference to the already quoted Bureau of Standards table of the values of the vapor pressure of N H 3 upon which these calculations are based. The complete results for the liquid mixtures of HzO and N H 3 have been calculated and arranged in Tables I11 and IV for vapor pressures up to the neighborhood of 10,000 mm Hg. For technical purposes extrapolation can safely be extended to higher pressures. The Vapor Pressure Curve for Saturated Solutions Since the vapor pressure of the saturated solution must be equal to the vapor pressure of a solution of the same composition a t the same temperature even if the solid phase is not present (as in case of undercooling), the method outlined above must be able t o yield the complete vapor pressure curve of saturated solutions of the system from a knowledge of the vapor pressures of the liquid mixtures and the temperatures and compositions along the solubility curve. This expectation is fulfilled with a good agreement between the calculated values and those obtained by Smits and Postma.' The most reliable series of solubility data on this system are represented graphically in Fig. 7. The existence of two compounds in the solid state is whose melting points are indicated, namely, 2SH3.H20 and P I " 3 . & 0 , - 78.8 and - 79.2 respectively. The melting point of pure NH3 is - 77.6OC. The eutectic between S H 3 and z2;H3.H20is located a t -93.0°C, that between 2NH3.Hz0 and iYH3.H20 is a t -86.4'c. There is considerable uncertainty in the experimental results on the branch of the curve for the solubility of ice; the most probable temperature for the eutectic between NH3.HzO and ice appears to be that determined by Smits and Postma as -100.3~C. Rupert states that this eutectic must lie below -1rzoOC; the disagreement is most likely due to failure of the very viscous solutions to crystallize readily. The derived vapor pressure curve for the saturated solutions, together with the points directly determined by Smits and Postma will be found represented in Fig. 8, the lower left portion of Fig. I , and in the left half of Fig. 2. The numerical values of the vapor pressures and compositions of the saturated solutions are given in Table 5'. 1
Smits and Postma: op. cit.
F.
C.
KRACEK
F. C. K R A C E K
.
I
ru
0
L.
V
0
THE RAMSAY-YOUNG RULE
515
Lo 01
s
00 Lo
00 0
h Lo
.t 0
0 10
3
I 10 C
g-
0
0
OIW
0
0
ha
0 Vi
0 b
0 m
0 N
E Z - I I I I I I I I I
-
0
0
+
~ N
0 n)
0 b
0
0
via
0
0
h O O
0
516
F. C. KRACEK
The interesting feature of the saturated solution curve is the existence of several vapor pressure maxima in accordance with the thermodynamic theory of saturated solutions first outlined by van der Waals1 and Roozeboom.* Three pressure maxima occur in this system, for solutions saturated with zXH3.H20r ;PI;H~.HsO,and ice (solid H20) respectively, at temperatures
’, ‘
Mol fracCion H20 0
I
2
3
4
5
6
1
7
8
9
10
FIG 7 Solubility diagram for the system S H 8 - H 2 0
some distance below the melting point of each pure solid phase. Each of the saturated solutions exhibiting the maximum vapor pressure is richer in XH3, the more volatile component, than the corresponding solid phase with which it is in equilibrium, entirely in accord with the theory. Van der IVaals: “Lehrbuch der Thermodynamik,” 2 (1912). (1904).
* Roozeboom: “Die heterogenen Gleichgenichte,” 2
T H E RAMSAY-YOUNG RULE
517
Thermochemical Applications The evaluation of the heat of vaporization from vapor pressure is a t once a test for the accuracy of the data, as well as one of the important reasons for their experimental determination. The calculation is performed thru some modification of the Clapeyron-Clausius equation for the well-known thermodynamic relation between the temperature coefficient of vapor pressure and the volume coefficient of the entropy of vaporization.
If it can be assumed that the heat of vaporization varies linearly over a small range of temperature, the Clapeyron-Claueius equation dp/dT = H/(TAY) can be expressed by the very nearly exact integrated expression log p2 - log pi
=
H
____ 2.3026
R,
~
T2 - TI 11 T?T, AI7
where H and R, are t h e heat of vaporization and the gas constant, bot,h in callmol or in cal,'g, p? and PI arc the vapor pressures a t the temperatures T? and TI, and Yi;'AT- is the ratio of the ideal volume of vapor to the actual change of volume inrolved in the conversion of a unit mass of liquid into vapor a t t,he mean temperature between TI and T,. Equation (8) yields the heat of vaporization at the mean temperature (Tz Ti)/2; it is exact in so far as the assumption of the linear \-ariation of H with T is valid. If the temperature interval T? - TI is taken small, the
+
518
F. C. KRACEK
validity of this assumption is within the experimental error of the measurement of the heat of vaporization. An exactly similar expression for the heat involved in the formation of one mol of vapor from solution can be derived from Gibbs; since the vapor
TABLE v Saturated Solutions mol % H20 0.0
5
.O
IO .o
'8' p mcalmcd.Hg -77.60 -80.5
45.8 34.4
-84.4
23.3
-89.0 18.80 -93 .o 20.0 -91.2 25 . o -83.85 30.0 -79.7 33 *33 -78.8 35 . o -79.0 -83.85 40.0 41.45 -86.35 -82 .o 45 . O 50.0 -79.2 -81.85 55 .o 60.0 -89 .o 65 . o -99.9 65.40 -100.3 70.0 -68.7 -46.0 75 .o 80.0 -31.25 85 .o -20.1 90.0 -11.95 95 . o -5.35 I 5 .o
100.0
0
.oo
Pressure Maxima 31.0* -79.0 4 3 . 5 ~-83.0 8 7 . 0 ~-17.0
14.3 9.03
Solid Phaae
(triple point)
"3 1J ,1 11
"3
+
10.5
HsO
("312
(eutectic)
J1 11
17.7 J1
20.9
17
20.2
17.4 8.6 6.5 6.6 5.4
(triple point)
11 11
+
(XH3)H20 (NH3)2H20
(eutectic)
11 2,
(triple point)
11
2.7
0.67 0.09 0.083 I .6 6.4 11.4 14.1 13.5 10.3 4.579
7,
J1
(eutectic)
(triple point)
21.1
6.7 14.3
composition in general is not the same as the composition of the liquid from which it is formed, it is essential to remember that such an expression applies to the formation of one mol of vapor from an infinite quantity of solution of constant composition.
THE RAMSAY-YOUNG RULE
519
If the relation between the vapor pressure and temperature is expressed by means of the Ramsay-Young rule, and the heat of vaporization of the reference substance B is known at various temperatures, we have
and
Equating dp, and dpB a t pp =
PB
it follows that
or
Further, since according to the Ramsay-Young expression for R',
T,
=
=
R'
R' T B
+ CTB
so that on substitution,
Ha = H B R '
-
R +CTB
It should be noted that the heat of vaporization H. of the solution and the volume ratio of the vapor for the solution are taken at T., while the corresponding quantities for the reference substance B are taken at the temperature Tg a t which B exerts the same vapor pressure as the solution at T,. The only source of appreciable error in this equation lies in the estimation of the volume ratio for the vapor from solution, since no experimental data on this point are available. I n the case of the system NHI-HzO the specific volumes of the liquid and vapor of the components are known accurately; the volume ratio for the solutions can be approximated from these and the composition of the solutions. The expressions in equations (8) and ( I O ) are accurate enough to be used with confidence. The calculated values of the heats of vaporization of H20 and NH3 at z j ° C are 10494 and 4750.6 cal 'mol as compared with the experimental values 10490 and 4749.6, using equation (8) applied to the vapor pressure data of these substances over the temperature interval zoo to 3oOC. Equation (IO) yields 10490 cal/mol for the heat of vaporization of HzO at z j ° C in satisfactory agreement, taking the value of HB for NH, from Osborne and Van Dusen's work.' 'Osborne and Van Dusen: Bull. Bur. Standards, 14,439 (1918);J. Am. Chem. Soc., 40, 14 (1918).
F. C. KRACEK
520
The heats of vaporization, or, better stated, the heats of formation of a mol of vapor from an infinite quantity of solution have not yet been measured. In Table VI we give values a t 25OC calculated from the derived expressions for the Ramsay-Young rule by equation ( I O ) , and from the derived values of the vapor pressures in Table IT' by equation (8). It will be observed that
TABLE VI Heats of vaporization of solutions of NH3 and H 2 0 a t 2 5°C XA
KA 0.
0
0.10
0.00035
Ha
Ha
equation ( 8 : equation 4750.6 4797
(IO)
4750.6 4798 4892
XaH.4 SXBHB 4750.6 4752
AHr*
__
43
H theor
4750.6 4795 4927
.20
,0008
4888
.30 .40
,0014 ,0023
5060
5065
4755 4759
5337 5754 6299 693 5
5340
4i64
5750 6300
4775 4802
6949 7692
4887 5135
205 5
5452 5845 6347 6942
2570
7705
8585
5815
2750
.00415 .60
'70 .80 .90 I .oo
,00895 ,0238 ,0670
I854
7682 8579
172
376 688 IOjO
I545
5135
8565 __ 10490 I 0494 10494 10494 * - AHr = heat evolved when I mol of condensed vapor is dissolved in an infinite quantity of solution of equilibrium composition. ,
I .oooo
both methods yield substantially the same values, as they should. I n these calculations we have made no assumption regarding the state of the vapor arising from the solutions other than that the volume ratio (VilAT',)is directly proportional to concentration. Any further assumption does not enter, since obviously, if the vapor is associated to a certain extent, both Vi and AV will be affected to the same extent. V i is the ideal volume of unit mass of the vapor a t pressure p and represents the sum of the ideal partial volumes of whatever compounds may occur in the vapor. Theoretically, the heat of formation of one mol of vapor from a solution of a given composition is equivalent to the sum of the heat required to evaporrrte XAmols of A plus I - SAmols of B, minus the heat evolved when one mol of solution of the composition of the vapor is dissolved in an infinite quantity of solution of the given composition, represented by NA of A and I - NA of B.' The vapor compositions can be calculated from partial pressure data; the heat of solution referred to above can not be obtained directly, but a rough estimate can be derived for this system from the measurements of the heats of formation of aqueous ammonia solutions by Baud and Gay,2 and Vrewsky and S a ~ a r i t z k y . The ~ theoretical values of the heat' of vapori1 N and S are used in turn t o represent the mol fraction of a given component in the liquid and vapor. * B a u d and Gay: ;Inn. Chim. Phys., 17, 398 (1909). 3Vrewsky and Sawariteky: Z. physik. Chem., 112, 90 (1924).
THE RAMSAY-YOUNG RULE
521
zation of the various solutions are included in the last column of Table V I for comparison. I n view of the largely hypothetical basis of the theoretical values the agreement between these and the values given in columns 3 and 4 of this table must be assumed to be somewhat fortuitous.
Conclusion The detailed application of the Ramsay-Young rule to the system XH3H 2 0 given in the preceding pages is advanced in the hope of showing the comparative ease with which vapor pressure data can be correlated by means of this useful but almost forgotten device. The choice of the system has been fortunate in that experimental values for the entire system are available ; when data are available for a portion of a system only, the correlation of the various interlocking relationships (such as the change in the slopes of the Ramsay-Young lines with composition, etc.) is less certain than in the case under consideration, but the same objection applies to any other comprehensive method. Particularly important is the fact that the method is theoretically sound from the standpoint of thermodynamics, as evidenced by the development of equation ( I O ) for the heat of vaporization of solutions and the numerical check of this equation thru the calculation of the heat of vaporization of water from the value for ammonia. Of equal importance is the ability of the method to reproduce the vapor pressure curve for saturated solutions from data on unsaturated solutions and the melting point curve. Too often we find vapor pressures for saturated and unsaturated solutions treated as two distinct phenomena with no apparent connection between them. Concerning the actual data on the system KH3-H20,it is interesting to note that no conclusions can be drawn from them regarding the actual state of the solutions, that is, the method gives no information on the question whether conipouiids between the components occur in the solutions or not. This is evidenced by the apparent inconsistency between the occurrence of the maximum in the slope curve (p. j o j ) at approximately 36 mol per cent of water, and a t 5 2 . j mol per cent in the heat of formation curve as given by Baud and Gay.' summary A systematic method for the treatment of vapor pressure data on solutions by means of the Ramsay-Young rule has been developed and applied in detail to the complete system of aqueous ammonia solutions, over the whole range of compositions, and for vapor pressures up t o 10,000mm Hg. The vapor pressure curve for saturated solutions has been calculated. Thermodynamic expressions for the heat of vaporization in terms of the Ramsay-Toung rule have been worked out for solutions and applied to the calculation of the heatsof vaporizationof solutionsof water and ammonia at z j"C. Geopiiutzcal Ln'm nfory, Cm n p q z e Iiietzlulioir o j Ti-nshinglon.
Baud and G a y op. rit. Recalculation of their data. taking into account the more recent work of Tren-sky and i'aivaritzky 'op. cit.) makes it probable that the maximum in the heat of formation curve lies still further shifted toward the S H side of the system.
