N.C. DEKOA N D R . 11-.T.\FT,JR.
244
Using these data thc absolute entropy of AlgCd:, a t 270" is found to be 16.12 e.u.!g. atom. The present measurements together with published Cp data'* for temperatures above 320°K. permit the calculation of S Z ;-~ 5'00~ for AIgCd,. The above room temperature data extend t o only 430°K. and must be extrapolated for about 110". Ordinarily such an extrapolation would be rather questionable. I n this case C, is almost constant for the upper 70" on the measured curve so the extrapolation is probably fairly reliable. S?ioa - S"OK. = 13.91 e.u./g. atom, of which approximately 1.2 e.u./g. atom is from the extrapolation above 480°K. Comparing the entropy gain between 0°K. and 270" with the absolute entropy a t 270°, one sees that &OK. = 0.21 e.u./g. atom. Similar calculations for 3igaCd were made, but existing heat capacity data above 50" are so divergent that no significance could be attached to the results obtained. (IS) I;. G. Khomyakov, 1 ' . A . Kholler and V. A . Troshkina, Vestnik Moskov Uniu., Yo. 6, Ser. Piz-Math. i Eslesl. Xnuk S o . 4, 6, 43
Vol. i f i
The residual entropy in SIgCtl can be accounted for if the number of Schottky defects observedlh a t 25" continue to exist a t the absolute zero and are randomly distributed over the lattice sites. The number of Schottky defects a t 25' is 1 . 7 C. The entropy associated with these defects when randomly distributed is simply the ideal entropy of mixing. This calculates to be 0.17 e.u.,g. atom. Experimentally, S ~ = K 0.21 e.u.jg. atom with a probable error of 0.OT e.u. l g . atom, neglecting error in A S for the extrapolated region between 4.70" and 333'K. Thus, the observed residual entropies agree within the limit of error with the value calculated as mentioned. This agreement, while interesting, must be viewed with caution until direct experimental verification is forthcoming t h a t : (1) the number of Schottky defects observed a t 25 O remain a t reduced teniperatures and (2) the composition of the superlattice is exactly 73 atomic per cent. cadmium, an assumption involved in arriving a t the number of lattice imperfections. PITTSBURGH 13, PEXXA.
(1R5Oi.
[COXTRIBUTION FROM THE SCHOOL O F CHEMISTRY AND PHYSICS,
THEPEXNSYLVANIA
STATE COLLEGE]
Concentrated Sulfuric Acid-Water BY N. C. DENOAND R. My.T.%FT, JR. RECEIVED MAY18. 1953 The HDfunction of Hammett can be precisely evaluated from 83-99.870 (wt.) sulfuric acid and the activity of water can be estimated to a reasonable agreement with experiment from 83 t o a t least 95yo acid. The method assumes t h a t the reaction HzO H ? S 0 4= H?O+ HSOa- is of primary importance in determining the properties of these solutions and a mole fraction equilibrium constant of 50 is shown t o be applicable for this reaction over the entire range 83 to 99.8yo sulfuric acid. These results are interpreted on the basis that the activity coefficients involved approach constancy in 83-99.8y0 sulfuric acid solutions. This ideal behavior is attributed t o the high dielectric constant and similarity of the medium to that of fused salts. Several applications to reaction rates studied in the H?SOa-HnO system are made. The rate data support the validitv of the conclusions reached.
+
+
I n Table I the observed values of Ho are compared with values calculated from eq. 1 assuming reaction 2 t o be complete (Brand's method') and values calculated from eq. 1 using K , = 50. HO(calcd.) = -8.36 log ;YHso~-/XH~SO~ (1) On the basis that observed Hovalues are accurate The ratio of the mole fractions XHSO~-/XH~SO,, are to 0.05 unit, the value 50 for K z is precise to + 10, obtained from the stoichiometric amounts of water since the Ho values calculated by eq. 1 do not fit and sulfuric acid assuming that reaction 2 is com- experimental values within this limit when larger Calculation of Ho.--Hrandl has shown that the Hammett acidity function,? Ho, in the region 9099.8xc.sulfuric acid can be calculated by eq. 1
+
plete. This assumption is in close agreement with the Raman spectra work of Young,3who found that H30
+ H?SO4
=
Hx0"
+ HSOI-
(2)
in this region, the addition of each mole of water gave one mole of bisulfate ion. Since equimolar water-sulfuric acid corresponds to 84.5Vo acid, it seemed surprising t o us that eq. 1 would fail from 85-90y0 acid unless reaction 2 was substantially incomplete. LVe have found that the calculation of the I& function by eq. 1 can be extended with excellent precision t o the region 89--83'30 sulfuric acid if a mole fraction equilibrium constant, AT2,of 50 is assumed to be valid for reaction 2 over this region. (1) J. C. D. Brand, J . Chern. Soc., 1002 (1950). (2) L. P. Hammett and -4. J. Deyrup, T H I S J O U R X A L , 54, 2721 (1932); L P. Hamrnett and 31. A. Paul, i b i d . , 66, 827 (1934). (3) T.F, Young, Rec. Chem. Progress, spring issiie (1951).
or smaller values of
K fare used t o calculate the
XH~SO~/XHSO~ratio. For example, a value of K? = 40 leads t o a deviation of 0.08 between calculated and observed Ho values for 84.5% acid, the acid concentration for which calculated values are most sensitive t o the value of K?used. The following alternate equation can be used for the computation of I10 Ho = -6.66
+ log
XH20/X11;o-
(3)
Equations 1 and 3 are equivalent by virtue of the mole fraction equilibrium constant for reaction 2 which can be written in the form
In a later section log f E I o is evaluated, where f is the activity coefficient. Reference t o Table I11
CONCENTRATED SULFWRIC ACID-WATER
Jan. 5 , 1934
245
tures in the region 150-280°an5were extrapolated to
TABLE I
COMPARISOS O F CALCULATED A N D OBSERVED VALUESOF HO 2.5' using the Clausius-Clapeyron equation. T o make this lengthy extrapolation as objective as -Ha Calcd.
HPSOL,.%
99.8 99.5 99.2 99.0 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 71.53
0bsd.a
10.27 9.91 9.76 9.61 9.26 8.97 8.89 8 76 8.64 8.54 8.41 8.31 8.19 8.08 7.94 7.84 7.69 7.60 7.48 7.32 7.17 7.01 6.85 6.71 6.56 6.43 6.29 6.16 6.03 5.67 Q. ref. 2.
Brand's method
10,32 9.91 9.70 9.60 9.27 9.05 8.90 8.76 8.64 8.52 8.41 8.29 8.18 8.05 7.90 7.72 7.46 6.97
Eq. 1 or 2 with Kx = 50
Eq.6
C c)
E,
v)
E
-e a
possible, the original data were fitted to linear functions by the method of least squares. Method I1 employed directly the data of Shankman and Gordon6 for activities of water a t 25' in sulfuric acids up to G8.9dYo. From 69-86y0 acid log aHZ0was obtained by an extrapolation using an empirical formula given by the above authors. TABLEI1 COMPARISON nF CALCULATED ASD OBSERVED I'ALUES nF L O G OHzO
Log aH20 c)
E,
v)
8.07 7.97 7.85 7.71 7.58 7.45 7.32 7.21 7.12 7.03 6.96 6.93 6.86 6.80 6.75 6.70 0.59
Calcd.
H2SO12 % Log XH,O+
98.06 -1.012 95.94 - ,727 95.06 - ,657 91.26 - ,465 91.01 - ,456 88.40 - .401 86.61 - ,371 85.14 - ,360 83.00 - ,364 81.15 - ,380" 78.50 - ,396' 77.26 - ,415" 74.36 - .460" 71.53 - ,500" 68.94 - ,538' 66.95 - .56iG
7.32
7.18 7.02 6.85 6.69 6.61 6.49 6.38 6.28 6.18 5.95
Hn
-9.30 -8.88 -8.76 -8.33 -8.30 -8.00 -7.78 -7.62 -7.34 -7.03 -6.60 -6.42 -6,08 -5.67 -5.40 -5.14
Measured
, -
Method I Method I I
-5.31
-4.G1 -4.42
-3.80 -3.76 -3.40 -3.15 -2.98 -2.70 -2.41" -2.00' -1.91" -1.58" -1.21" -0.98' -0.75"
- 5 ,m0 -4 85" -4 48"
-3.80" -3.6gh
-3.23b -3.19 -2.81b -2.95 -2.64 -2.56b -2.40 -2.04* -2.09 -1.9gb -1.96 -1.78* -1.69 -1.46 -1.27 -1.14
-3.12b
Vapor pressure data of Thomas and Barker (ref. 4 ) . Vapor pressure data of Burt (ref. 5). The calculation of these values by the method indicated is not strictly valid since K z appears to increase below 83% acid. However, the errors introduced are quite small since below 83% acid becomes increasingly less sensitive the calculation of XH~O+ to the value of K1 used.
b
will show the striking fact that the region in which logfH,O is constant (83--99y0 acid) is the same region that eq. 3 is valid. If eq. 3 is corrected for the rapidly changing value of log fH,O below 83y0 acid, eq. 5 is obtained
I n Table I the last column shows t h a t this equation accurately evaluates HOfrom 79-99.870 sulfuric acid. In addition i t is not in error by more than 0.1 Ha unit down to 75y0 acid. Calculation of the Activity of Water.-In Table I1 it is demonstrated that from 83-95% sulfuric acid, log aH,O can be calculated from the relation
+ + 5.00
log U H ~ O = log XH~O+H a
(6)
The constant, 5.00, is an empirical constant whose value was chosen t o give a best fit between observed values of log aHzo and values calculated by eq. 6. This equation is essentially a rearranged form of + be estimated eq. 5. I n using eq. 6, X H ~ Ocan simply from stoichiometric amounts of water and sulfuric acid for the region above 90%. Below 90%, this and K 2 = 50 are used. The experimental values for log U H ~ Oin Table TI were obtained by two methods. I n method I, applicable from 74-98y0 acid, the vapor pressure data of aqueous sulfuric acids measured at tempera-
The average deviation between calculated and measured values of log aHlo is 0.05 using the values by method IT whenever possible. If one point a t 88.4y0 acid is neglected, the average deviation becomes 0.03. However, the average deviation between the two experimental methods for log U H ~ Ois 0.09 in the region in which they overlap. It is thus evident t h a t eq. 6 cannot be given a precise test a t present. The deviations between observed and calculated values of log U H ~ Oare somewhat greater a t 96 and 98y0 sulfuric acid. However, this may not be significant because the experimental values are in greatest error in this region. A second independent method of determining K z can now be made from the constants 8.36 of eq. 1, 5.00 of eq. 6, and log f ~ ~ oThe . relationship between log K 2 and the above constants is obtained by combining eq. 1 and 6, so that
(4) J. S. Thomas and W. F. Barker, J. Chcm. Sac., 127, 2820 (1925). ( 5 ) B. C. Burt, ibid., 86, 1339 (1904). (6) S. Shankman and A, R. Gordon, Tars JOrrRNhTs, 61, 2370
(1939).
240
and thus log K 2 =
N.
;YHlo?%?oi:
~Ylilox8?so 1
=
c.DENOA N D R. w.T A F T , JR.
5.36 - 5.00 + l o g f H l o
Activity Coefficients.-By tionship~~
Yol. 76 virtue of the rela-
'l'he coilstants S.36 and 3.00 can be evaluated
0 ' ; sulfuric acid and are solely from data above 9 therefore not dependent on the value of log K 2 obtained originally. To obtain a value of logj"H,O which is independent of the previously selected value of log K 2 , the following procedure was used. Reaction S was provisionally assumed t o be complete in 83% sulfuric acid; this permits one to obtain a first approximation for log X H ~ Osimply from the stoichiometry. Together with the log ~ H value ~ O from Table I11 a first approximation of 1.43 can be obtained for log f H 2 0 . This value can be substituted in the above equation to obtain a first approximation for log K z . series of two successive approximations leads to limiting values of 1.66 for logfH,o and 1.69 for log IC2. The latter is in excellent agreement with the value 1-70, which was obtained originally from the best fit of observed 110values and those calculated by eq. 1 or 3 in the region S:3-89ch sulfuric acid. Freezing Poict of Water-Sulfuric Acid.-Kunzler and Giauclue' h a r e iriatlc accurate measurements of the freezing [mint of water-sulfuric acid solutions particularly in the equimolar region, I n this system the solvent may be considered to be hydronium bisulfate (H30---HSOa-) and the foreign solute t o be water and sulfuric acid. If we use the value of l
