The Specific Heats of Some Aqueous Sodium and Potassium Chloride

II. Chester M. White. J. Phys. Chem. , 1940, 44 (4), pp 494–512. DOI: 10.1021/j150400a013. Publication Date: April 1940. ACS Legacy Archive. Cite th...
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494

CHEBTER

M.

WHITE

SUMMARY

1. A modified twin calorimeter is described in some detail. 2. Specific heats are presented for sodium chloride and potassium chloride solutions a t four temperatures. The concentration of the solutions ranged from 0.01 to 1.0 molal.

This research was carried out at the suggestion of and under the direction of Professor Arthur A. Sunier; grateful acknowledgment is here made of his assistance. REFERENCES (1) GUCKER: J. Am. Chem. SOC. 60, 1005 (1928). (2) JOULE:Mem. Proc. Manchester Lit. Phil. Soc. (2) 559 (read 1845); Scientific Papers 1,192 (Taylor and Francis, London (1884)). (3) PFAUNDLER: Sitzsber. Akad. Wiss. Wien 59,2145 (1869). (4) RICHARDS AND GUCKER: J . Am. Chem. SOC.47, 1876 (1925). (5) RICHARDS AND HALL:J. Am. Chem. SOC.61,707 (1929). (6) WHITE,C. M.: J. Am. Chem. SOC.68, 1615, 1620 (1936). (7) WHITE,W . P.: J. Am. Chem. SOC.36, 2292 (1924).

T H E SPECIFIC HEATS O F SOME AQUEOUS SODIUM AND POTASSIUM CHLORIDE SOLUTIONS AT SEVERAL TEMPERATURES. I1 CHESTER M. WHITE

Department of Chemistry, University of Rochester, Rochester, New York Received May 10, 1989

I n recent years precise specific heats for aqueous salt solutions have been determined principally from 18' to 25'C., although results have been reported a t a few higher and lower temperatures. Apparently no attempt has been made to investigate thoroughly the region from 35' to 45'C. This temperature range is particularly interesting, since the specific heat of water is known to pass through a minimum at 38°C. Furthermore, earlier work (9) in this laboratory on sodium chloride solutions seemed to show a departure from the usual linear relation for @ a t 45'C., while the results a t 35°C. were definitely linear. It therefore seemed advisable to study the specific heat of dilute sodium chloride solutions a t several temperatures in this range. In this paper new measurements are reported a t 35', 38', 41', and 45'C. for sodium chloride solutions which varied in concentration from 0.01 to 0.20 molal, and the data of Hess and Gramkee (9) are 'discussed in considerable detail.

SPECIFIC HEATS O F AQUEOUS SALT SOLUTIONS.

49 5

I1

APPARATUS AND MATERIALS

The apparatus used previously (9) was set up in a more suitable laboratory and a few minor changes were made; somewhat better results were obtained under these conditions. The calorimeter stirrers were run a t a higher rate of speed (138 R.P.M.). Several coatings of Bakelite varnish were found to make the deKhotinsky seal between the annular ring and the Dewar jar more permanent a t 45OC. The top of the annular ring was coated with a thin layer of stopcock grease to insure a water-tight ground joint. The leakage constants ( k = degrees per minute per degree) and the heat of stirring (w = degrees per minute) were determined by obtaining the rate of heating under two thermal heads. With the larger value of k it was difficult to measure the small fraction of the total heat due to stirring. However, the heat of stirring is probably the same in the two units because of the method of operating the stirrers. The approximate heat capacity of a calorimeter unit was determined by the electrical method. The values, which are given in table 1, are the average of several experimen ts. TABLE 1 Constants of the apparatus TEMPEMTUBE RANGE

1

SOLUTION

k

k

0.0021

0.0013

~

Ty

I

‘0.

28-34

1

I

O.ooOo7

~

HEATCAPACITY

cnloriea p m d e p e e

102

The solutions were made from Baker’s C.P. sodium chloride, which was not further purified, but was dried for several days at 120OC. The solutions were prepared as described in the preceding paper. PROCEDURE

The only change in the method was to lengthen the “fore” and “aft” periods t o 14 min. The value of AG was determined graphically from a plot of the galvanometer deflections; this procedure was sufficiently precise in the present case. In the standardization of the calorimeter 700.00 g. of water was always placed in the tare, while the solution calorimeter contained 705, 710, and 715 g. (uncorrected) of water. Several determinations were made with each of these weights of water in the solution calorimeter. The averaged points are plotted for the four temperatures in figure 1. The radii of the circles are proportional to the average deviation of the runs. Probably the error of the standardization runs is about f0.01 per cent. The equivalent weights of water for the salt

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CHESTER M. WHITE

runs were obtained from this plot. At frequent intervals during the course of the research a standardization run was made to insure constancy of the apparatus. The Beckmann thermometer, which was used to measure,the temperature rise in all of the determinations, was carefully compared with a thermometer standardized by the Bureau of Standards, and suitable corrections were applied. The temperature rise was also corrected for the varying amounts of mercury in the bulb at the different temperatures; the magnitude of this correction is briefly discussed in the preceding paper.

FIQ.1. Plot of water standardization data RESULTS

In table 2 the data for the sodium chloride solutions are summarized at 35", 38', 41°, and 45%. The first column records the molality and also the weights (in vacuo) of the salt and water with which the solution calorimeter was charged. The second column gives the nominal temperature, since the specific heat changes only slightly with the temperature. The third and fourth columna record the AG values, which are the average of three determinations (except at 0.01 molal where four runs

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were averaged) and the average deviation, respectively. The average deviation for all runs is 0.06 cm., which is equivalent to a change of 0.01 per cent in the specific heat. The fifth column gives the specific heat in TABLE 2 Summary of results for sodium chloride solutions 'EYPERATURE

AQ

'C.

em.

cm.

35 38 41 45

1.19 0.85 1.22 1.49

0.07 0.08 0.04 0.07

0.9967 0.9966 0.9966

0.03283 (salt, 1.371 g.; water, 713.49 g.)

35 38 41 45

1.58 1.35 1.84 1.87

0.04994 (salt, 2.081 g.; water, 712.75 g.)

35 38 41 45

0.06993 (salt, 2.917 g.; water, 713.75 g.) 0.09989 (salt, 4.178 g.; water, 713.75 g.)

YOLALlTY

___

BPUxmC HEAT

0

%Yl.la- ptY lcqree p a

mm

0.9968

-12.8 -24.8 -22.8 -24.7

-17.5 -19.6 -19.7 -18.7

0.07 0.09 0.11 0.14

0.9950 0.9950 0.9950 0.9952

-14.6 -15.8 -14.3 -14.0

-16.7 -18.1 -17.9 -17.1

0.69 0.41 0.79 1.03

0.04 0.05 0.02 0.06

0.9935 0.9935 0.9936 0.9938

-19.2 -19.6 -18.4 -18.6

-16.2 -17.3 -16.9 -16.2

35 38 41 45

1.35 1.13 1.56 1.85

0.07 0.01 0.02 0.01

0.9923 0.9922

-14.4 -16.9 -15.6 -14.9

-15.8 -16.5 -15.9 -15.4

35 38 41 45

1.19 1.03 1.51 1.64

0.07 0.04 0.04 0.02

0.9904

0.9905

-12.7 -14.0 -11.8 -13.6

-15.2 -15.6 -14.8 -14.4

35 38

41 45

0.86 0.65 1.00 1.28

0.10 0.06 0.05 0.08

0.9879 0.9879 0.9879 0.9881

-15.6 -15.2 -15.5 -15.5

-14.7 -14.7 -13.7 -13.5

0.1598 (salt, 6.668g.; water, 713.75g.)

35 38 41 45

0.61 0.36 0.96 1.34

0.04 0.04 0.06 0.03

0.9858 0.9857 0.9861 0.9866

-15.1 -15.4 -12.9 -11.5

-14.3 -14.0 -12.8 -12.8

0.2OOo (salt, 8.347 g.; water, 714.75 9 . )

35 38 41 45

1.28 1.25 1.70 1.84

0.08 0.05 0.02 0.03

0.9832 0.9834 0.9836 0.9837

-13.4 -12.6 -11.3 -12.2

-13.8 -13.1 -11.7 -11.8

0.00999 (salt, 0.416 g.; water, 712.75 g.)

0.1299

(salt, 5.418 g.; water, 713.75g.)

0.9923 0.9925 0.9902 0.9904

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CHESTER M. WHITE

15OC. calories. The specific heat of water was taken as 0.9974 a t 35", 38", and 41"C., and as 0.9976 a t 45°C. The calculations of @ were based on the average specific heat values carried to five significant figures; they were then rounded to 0.1 calorie and are given in column six. This rounding process accounts for the occurrence in several instances of different values of @ when the specific heat is the same at the temperatures 35", 38", and 41°C. The calculated @ values given in the last column were obtained from empirical equations derived from the specific heats (carried to five significant figures), in turn obtained from the individual values of AG. TREATMENT AND DISCUSSION OF RESULTS

Empirical equations were derived for the apparent molal heat capacities by the method of least squares. A given error in the specific heat produces a large percentage error in @ in dilute solution, but the error rapidly diminishes as the concentration increases (see dotted lines in figure 2). For this reason it is advisable to weight the @ values in proportion to the concentration before the least squares procedure is applied. Since AC, is defined as ma, the weighting may be accomplished by fitting the data expressed as AC, to an empirical equation of the form: AC, = A'm

+ B'm3iz + . . .

I n order to test the procedure the precise results of Randall and Rossini (18) with sodium chloride a t 25°C. were treated by this method. Since their @ values when plotted against ml/*showed a slight but definite curvature, it seemed advisable to fit the data to a parabolic' as well as a linear equation. The following equations were obtained : @ = -23.36 @ = -23.95

+ 13.28m112+ 0.50m + 14.41m

The probable errors of a single observation from the empirical equations are approximately 0.005 per cent (parabolic) and 0.007 per cent (linear). A curve was constructed from the rounded values of Randall and Rossini, and the probable error of each observation from this curve was found to be about 0.01 per cent. The parabolic equation seems to fit the data Recently Gucker, Ford, and Moser (3) have found that a parabolic equation is necessary t o represent adequately their apparent heat capacity data on aqueous solutions of glycine and glycolamide; the form of their equation is = 90 am bm2 the constants being obtained by a least squares procedure. A similar form of equation was used by Gucker, Pickard, and Planck (4) in connection with heat capacities of sucrose solutions.

+

+

SPECIFIC HEATS O F AQUEOUS SALT SOLUTIONS.

11

499

more closely than the curve which Randall and Rossini drew. Thus the slope becomes a function of the concentration. Other investigators (5, 27) have shown from heats of dilution that the slope of the curve for sodium chloride is not constant but varies with the concentration. The present results (table 2) were fitted to linear equations. The constants for the equations are summarized in table 3 for the four tem-

CM FIG.2. Plot6 of the apparent molal heat capacities for sodium chloride solutions TABLE 3 Constants for the heat capacity equations

'C.

35 38 41 45

-18.61 -21.42 -22.01 -20.67

$10.83 f18.56 +22.96 +19.81

$16.26 +27.84

$34.44 +29.72

peratures. Also the slopes (B,) of the corresponding partial molal heat capacity equations are given in the last column of table 3. The two slopes differ by a factor of 3/2. The intercepts for both equations are identical. Plots of the individual runs show no deviations from these equations which are substantially greater than lfO.01 per cent. Also the probable error of a single determination for each equation calculates to lf0.01 per cent.

500

CHESTER M. WHITE

Therefore the equations adequately represent the data. At 45OC. and in the range of concentration up to 0.30 molal the results of Hess and Gramkee indicate a minimum in the @ versus m1I2curve (see figure 3). The present results give a linear equation throughout the range of concentration studied; it has not been possible to ascertain, with certainty, the reason for this discrepancy. Since the uncertainty in the standardization runs is estimated at f 0 . 0 1 per cent, the precision of the heat capacities is placed at f 0 . 0 2 per cent. In figure 2 the average values of the apparent molal heat capacities are plotted at the four temperatures. The dotted lines indicate an error of f 0 . 0 2 per cent from the 41°C. curve. From this plot it is evident that the four equations as well as the averaged points are almost entirely contained within the dotted lines. These results tend to prove that the apparent molal heat capacities for these dilute solutions remain constant TABLE 4 Constants for the heat capacity equations* Derived from Hess and Gramkee's data PmABSIUY CELORIDE SOLUTION8

BODIUY CHLORIDE BOLURONB

TEYPEBATUBE

Probable error

c$¶

B BI Probable dcpldmlla lCp,/dmll¶ error

per cent

'C.

15 25 35 45

A

w or

-27.19 -21.46 -19.76

+13.48 $11.80 $12.28

$20.22 4-17.77 +18.42

0.02 0.02 0.01

pa

-34.18 -29.14 -24.91 -24.39

+12.08 $9.85 $7.53 $7.64

+18.12 4-14.77 $11.30 +11.46

0.02 0.02 0.03 0.02

* The author wishes to thank Mr. Joseph T. Anderson for the valuable aid which he rendered in connection with the least squares calculations. from 35" to 45°C. The precision of the apparatus is not sufficient to resolve the individual @ curves (if linear) in this range. If there were a transition from a linear curve to one with a minimum, the precision should be sufficht to indicate it. TREATMENT AND DISCUSSION OF THE RESULTS OF THE PRECEDING PAPER

In the preceding paper, Hess and Gramkee presented specific heats for sodium chloride and potassium chloride solutions at several temperatures. Their results (except those for sodium chloride at 45°C.) were treated in the same manner as described above. The constants for the empirical (linear) equations for both the apparent and partial molal heat capacities are found in table 4. The probable error of a single determination is given for each temperature. Plots of the @ values for sodium chloride and potassium chloride at

SPECIFIC HEATS O F AQUEOUS SALT SOLUTIONS.

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50 1

1 5 O , 35O, and 45°C. are shown with the corresponding linear equations in figures 3 and 4, respectively, while in figure 5 the 25°C. results for both salts are plotted along with the linear equations. Two runs a t 0.01 molal sodium chloride and 25°C.do not appear on figure 5, since they fall off the plot. In figures 4 and 5 results of other investigators are also shown. Omitting the data for sodium chloride at 45"C., there are in all three determinations which deviate from the linear equations by more than 0.04 per cent, while in the case of potassium chloride there are twelve such deviations. The probable errors, recorded in table 4, show on the average about 0.02 per cent. In view of the precision claimed for the

FIG.3. Plot of Hess and Gyamkee's values for sodium chloride solutions a t 15", 35", and 45°C.

specific heat measurements the linear equations adequately represent the data. After considering the heat capacity data of the various workers on sodium chloride solutions, it was thought that the @ - @O values which Young and Machin (27) obtained from dilution work constituted the most precise values of the slope a t the present time, and that the results of Randall and Rossini (18) based on direct measurements offered the most precise values of @ itself. By combining the results of these two investigations in a suitable manner, it has been possible t o arrive a t a series of precise values of 9 with which to compare the present results a t 25°C.

502

CHESTER M. WHITE

In dilute solution Young and Machin have employed the empirical equations of Young and Groenier (26), which were based entirely on the precise dilution work of Gulbransen and Robinson (5). The latter investigators believed that the probable error in their @ - O0 values amounted to 10 per cent. Since Young and Machin's results in dilute solution were dependent on their data, it would seem reasonable to as-

0

0.2

0.6

cn

0.8

LO

FIG.4. Plot of Hess and Gramkee's 9 values for potassium chloride solutions at, 15", 35", and 45OC. and the values of Lange and Monheim a t 15°C.

sume the same magnitude of error in their @ - a0values up to m1/2= 0.46. A constant percentage error in Ip - a0implies a corresponding percentage error in the specific heat which varies with the concentration; thus a 10 per cent error in @ - a0 changes the specific heat by 0.00011 per cent a t 0.01 molal, while a t 0.25 molal a change of 0.026 per cent is produced. Randall and Rossini claim a precision of 0.01 per cent over the entire

SPECIFIC HEATS OF AQUEOUS SALT SOLUTIONS.

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I1

concentration range. To combine these two pieces of data a value of @ - @O was selected from Young and Machin’s data at which the precision was believed to be equal to 0.01 per cent. This value (4.40) of @ - @O was equated to the value of 4, computed from the empirical linear equation of Randall and Rossini’s data a t the same concentration; the resulting value of Q o when combined with the @ - Qo values computed from Young and Machin’s data leads to the values of @ given in table 5 and plotted in figure 5, and in this section will be referred to as reference data and curve, respectively. A definite degree of curvatuve is exhibited in the plot of these % values. The dotted lines on either side of the curve correspond to a 10 per cent error in the 9 values. Randall and Rossini’s = 0.6, linear equation, given above, is also plotted in figure 5 up to d 2 and 0.01 per cent error curves are drawn on either side of this straight line. It will be noted that the two sets of dotted lines either cross or become tangent a t milZ = 0.457, a t which concentration the precision of the direct and indirect measurements is thought to be the same.

dl,

cp

ml/,

cp

ml/n

cp

0.0 0.1 0.2 0.3

-21.76 -20.98 -20.10 -19.12

0.4 0.457 0.5 0.6

-18.03 -17.36 -16.84 -15.57

0.7 0.8 0.9 1.0

-14.19 -12.73 -11.20 -9.63

Possibly the @ values of table 5 may require a slight temperature correction to make them strictly comparable with 25OC. data, since the 4, - @O values computed from Young and Machin’s data apply a t 18.75”C. It is generally believed that d@/dm1/2either is independent of or changes but slightly with the temperature. Theoretical considerations indicate that the slope of the reference curve a t 1.0 molal, for example, would be altered by 0.4 calorie in correcting the data to 25°C. The Q values of table 5 were recalculated with this correction applied, and the D curve in figure 5 shows the percentage difference on the specific heat basis between the corrected and the uncorrected curves. The R curve indicates the difference in specific heat between the original reference curve and a second curve whose intercept has been decreased by 0.2 calorie; this curve also indicates the difference between any two @ curves differing by 0.2 of a calorie throughout. The Q curve in figure 5 shows the percentage difference on the specific heat basis between the curve of Randall and Rossini and the reference curve, and it is quite clear that the results by these two methods agree

504

CHESTER M. WHITE

excellently. It should be noted that the two intercepts and the @ values at 1.0 molal are in very good agreement. When this agreement is considered in connection with the R and D curves, further assurance is obtained that d@/drn1/*is either independent cf or changes but slightly with temperature. If the difference between Randall and Rossini’s and the corrected reference curves is desired, the algebraic sum of the D and Q curves must be used. The effect of lowering the reference curve intercept by 0.2 of a calorie is shown by curve &’. The parabolic equation given above for Randall and Rossini’s data developed by the method of least squares (yielding a probable error of 0.005 per cent) when combined with the dilution data according to the precedure outlined above gave a I

I

I

b

0.7,

0.4

I

I

I

I

m w

I

I

01

I

I

1

’

ID

FIQ.5. Comparison of Hess and Gramkee’s Q values for sodium chloride and potassium chloride solutions a t 25°C. with those of some other investigators. Go value of -21.81 and the percentage difference curve falls slightly above curve Q; this agreement gives added weight to the correctness of the method outlined above. In figure 5 the data of Hess and Gramkee a t 25°C. are plotted except for the two values of 9, -66.8 and +12.8, a t 0.01 molal which did not fall on the plot. The linear empirical equation is also graphed in figure 5. The V curve indicates the difference between the reference curve and the linear equation of Hess and Gramkee. The agreement between the two curves is about that indicated by the probable error given in table 4. It should be noted that the intercept and the 1.0 molal value of @ agree vel1 with the results of other investigators. The V‘ curve shows the

SPECIFIC HEATS OF AQUEOUS SALT SOLUTIONS.

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difference between the corrected reference curve and that of Hess and Gramkee, or the sum of curves V and D. Gulbransen and Robinson have derived a linear equation for 4, by combining their own results with the heat capacity of the solid salt and heat of solution data; their equation is 4, =

-21.90

+ 10.5m''2

Combining their value of the slope with the appropriate 4, value from Randall and Rossini in the same manner as described in connection with Young and Machin's work, the following equation was obtained : 4,

= -22.19

+ 10.5m'/*

Both intercepts are in good agreement with those of Randall and Rossini and the reference work. These equations, valid only to 0.4 molal, deviate a t the highest concentration by 0.002 per cent and 0.01 per cent from the reference values, respectively. Lipsett, Johnson, and Maas (16) have reported specific heats a t 20" and 25°C. from their integral heat of solution data and the heat capacity of the solid salt. A linear equation was obtained by the least squares procedure for their 25OC. data.(to 1.09 molal); the equation is 4, =

-19.59

+ 10.72~~'/*

The probable error of a single observation from the equation is 0.005 per cent. The average deviation of this equation from the reference 4, values is 0.06 per cent. By means of E.M.F.measurements, Harned and Nims (8) have arrived at 4, values which are in fair agreement with results of other methods up to 0.2 molal but deviate considerably a t higher concentrations. In figure 5 the data of Hess and Gramkee for potassium chloride are plotted along with a straight line through Randall and Rossini's rounded values. The average deviation of the empirical equation from Randall and Rossini's rounded values amounts to 0.036 per cent. Since the determinations a t the two highest concentrations show rather large deviations from Randall and Rossini, four linear equations were calculated by the least squares procedure in which the heat capacities a t the two highest concentrations were eliminated. The modified equation a t 25°C. shows a deviation of only 0.008 per cent from Randall and Rossini's data. The constants for these limited equations (valid to 0.3 molal) are given in table 6, and the equations are plotted in figures 4 and 5. The potassium chloride equations (table 4) a t 35" and 45OC. differ by 0.02 per cent a t 0.25 molal, while the limited equations differ by less than 0.01 per cent. These results tend to prove that the 4, values for the potassium chloride solu-

506

CHESTER M. WHITE

sions, like the results for sodium chloride solutions, remain constant over this temperature and concentration range. Lange and Monheim (13, 14) have reported @ values a t 18.75"C. for potassium chloride solutions from a combination of the temperature coefficient of the integral heat of dilution and the heat capacity of solid salt. Their most recent @ values were corrected to 15OC. by the temperature coefficient of table 4; the resulting @ values are plotted in figure 4. The precision of their data is considered to be better than that of Hess and Gramkee. The average deviations of the limited and complete equations from Lange and Monheim's data are 0.008 per cent and 0.02 per cent, respectively. Other data which did not seem to be sufficiently precise to be discussed here are as follows: the earlier work on sodium chloride and potassium chloride solutions given in the International Critical Tables (lo), the work of Urban (23), the results of Clews (1) on potassium chloride solutions a t several temperatures, and the results of D'Ans and Tollert (2) on sodium TABLE 6 Constants for the potassium chloride apparent heat capacrty equations valid to 0.3 molal TEMPERATURE

I

A

B

-34.07 -30.59 -24.31 -23.91

f15.30 +15.01 +9.07 +8.89

"C.

15 25 35 45

chloride and potassium chloride solutions a t various temperatures and concentrations above 1 molal. THEORETICAL SLOPE AND OTHER CONSIDERATIONS

It is generally recognized that dilution data yield the most precise value of the limiting slope (dC,,/dm*/2), but since such data are available only a t 15" and 25°C. it was thought desirable to calculate the theoretical slopes for a uni-univalent electrolyte from the Debye-Huckel theory at the higher temperatures and compare them with those given in tables 3 and 4, which apparently are the only values in the literature. Values of dV/dT were computed from data given in the International Critical Tables, while the Wyman equation (25) supplied the values of dD/dT and dzD/dT2. These calculations, carried out by the procedure of La Mer and Cowperthwaite (ll),yielded the following results: 15, 16, 17, and 18 at 35", 38", 41", and 45"C., respectively. Any differences between the experimental and theoretical slopes may be accounted for by the probable errors of the experimental results. At 15" and 25°C. the calculations

SPECIFIC HEATS O F AQUEOUS SALT SOLUTIONS.

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yielded, for the values of the slope, 14 and 13, respectively, which are recorded here for the sake of completeness. a t 25°C. for the individual ions K+, Na+, and C1The values of were calculated (assuming the value for K+ equals that of C1-) and found to be -14.6, -6.9, and -14.6, respectively. These values are in good agreement with those giren by Pitzer (17) and Rossini (21). The value of for B a f f , computed from earlier data (24), was found to be -44.3. The temperature coefficient d@/dTa t or near room temperature has been assumed by Rossini (21) to be constant for all uni-univalent electrolytes from the most dilute solution to 2.5 molal, and the value employed by him is 0.3 calorie per mole per degree per degree Centigrade. The present results for a 20°C. interval (15" to 35°C.) lead to the value of d@/dT for sodium chloride of 0.3 calorie from 0.1 to 1.0 molal, while for potassium chloride the value was 0.3 calorie, with a variation of f O . l calorie. Both sodium chloride and potassium chloride show a zero temperature coefficient from 35" to 45°C. This statement may not be strictly true above 0.2 molal. By inspection of table 4 it is seen that d V / d T is positive and of such a magnitude as to be in line with the discussion just given for d+/dT. RELATIVE PARTIAL MOLAL HEAT CONTENTS FOR SODIUM CHLORIDE AND POTASSIUM CHLORIDE SOLUTIONS

Since values of C,, - Ci, may easily be calculated from data given in table 4 a t several temperatures, the Person-Kirchoff relation has been used to compute the relative partial molal heat contents (E,) of sodium chloride and potassium chloride solutions a t several temperatures from a t 25" and 18"C., respectively. For sodium chloride known values of solutions at 25°C. Robinson (19), Young and Vogel (29), and Gulbransen and Robinson have reported values of E t . Recently Young and hfachin have presented data from which values can be obtained. They coupled their experimental data in concentrated solutions with the very precise results of Gulbransen arid Robinson in dilute solution. In order to calculate the S values were plotted against m"* and the resulting curve was integrated graphically to provide the integral heats of dilution (AH,). Below 0.15 molal the empirical equation of Young and Groenier (26) was integrated analytically to give the A H , values. The EZvalues at 25°C. were calculated by Rossini's equation (20) :

The 25'C. curve in figure 6 was constructed from these values. ' The values a t the other temperatures were calculated from these results a t 25°C. and the heat capacity data in table 4 by means of the PersonKirchoff relation.

508

CHESTER M. WHITE

The necessary heat capacity data were calculated a t various concentrations from the linear least squares equations. The average value of - c:2 was used in the calculations. For the 45OC. values the empirical equation of Hess and Gramkee a t 35°C. was used, since it has been shown that the 9 values are independent of temperature to 0.2 molal. The values above 0.2 molal have been enclosed in brackets, since there may be some doubt as to their precision. The results of these calculations are summarized in table 7 and shown graphically in figure 6.

c,,

a FIG.6. Curves of calculated values for sodium chloride at several temperatures compared with the results of other investigators.

The same procedure which was applied to the results of Young and Machin a t 25°C. was employed on their data a t 12.5"C. Tnese values a t 12.5"C. were corrected to 15°C. by their temperature coefficients; they are given in table 7 and are plotted in figure 6. The values of Gulbransen and Robinson a t 15°C. are also plotted in figure 6. The calculated values of a t 15°C. are in good agreement with the work of Young and Machin and Gulbransen and Robinson, showing an average deviation of 11 and 8 calories, respectively. The results of Harned and Nims as recalculated by Harned and Hecker

SPECIFIC HEATS OF AQUEOUS SALT SOLUTIONS.

509

I1

(7) are not shown in figure 6. They are in satisfactory agreement with the other data below 0.2 molal; but differences of more than 150 calories are found a t 35" and 40°C. (not shown in table 7). An error of 35 calories may exist in their Ez values a t 1.0 molal because of the uncertainty in dE/dT. Errors of this magnitude are not unusual in comparing E.M.F. and calorimetric data (15). Recently the results of Harned and Nims have been subjected to a second calculation by Harned and Cook (6). The precision of their Ezvalues does not appear to be sufficiently improved t o warrant inclusion in table 7 and figure 6. Rossini (20) has made a critical study of heat of dilution da,a published for sodium chloride and potassium prior to 1930 and has presented chloride a t 18°C. in 18" calories. His values for sodium chloride solutions have been calculated to 15°C. by the linear equations of Hess and Gramkce. These results may be said to be in satisfactory agreement with the corresponding data in table 7 . Also the E2 values a t 25"C., which Saxton

zz

TABLE 7

L values for aqueous sodium chloride solutions at several ~~

25%

Reference' data

0.01 0.05 0.10 0.20 0.36 0.50 1 .oo

45.5 64.1 54.9 14.1 -65.8 - 138 -387

38.6 51.6 40.0 -1.3 -77.4 - 144 -375

57.6 94.0 100 83.5 36.4 -10.4 - 185

1

temperatures

350c.

45'C.

75.7 134 157 164 145 118 -4.4

and Smith (22) computed from Rossini's values a t 18"C., are in good agreement with the corresponding values in table 7. These results have not been plotted, since it was felt that they would complicate figure 6. E 2 values could also be obtained from the data of Lipsett, Johnson, and Maas a t 20" and 25°C.; however, these calculations were not made, as it seemed desirable to compare their results on the @ basis. Values of ZZfor potassium chloride solutions a t 15", 25", 35", and 45°C. were calculated from Rossini's values a t 18"C., using the partial molal heat capacity equations of Hess and Gramkee and the Person-Kirchoff relation. No attempt mas made to correct the results to 15" calories, since the magnitude of the correction was so small. The calculated values and the reference data a t 18°C. are recorded in table 8 and plotted in figure 7. Some difficulty was experienced in drawing a smooth curve through the reference data a t HOC., since the values of z2a t 0.20, 0.36, and 0.50molal fell on a straight line.

510

CHESTER M. WHITE

Recently Young and Seligman (28) have presented empirical S equations a t 12.5' and 25OC. for potassium chloride solutions. These equations

TABLE 8 & values for aqueous potassium chloride solutions at several temperatures

yo-

0.01 0.05 0.10 0.20 0.36 0.50 1.00

1

16%.

44 53 46 16 -74 - 140 -355

18%.

Referenoa data

26'C.

49 64 62 38 -44 -105 -306

61 90 98 90 25 -24 -191

(3H.LG.

35°C.

-~ 74 119 139 148 103 68 -61

U'C.

85 144 175 199 171 149 53

15'

0lw.DATA

ta

QH.&6.

Is'

+M FIG.7. Curves of calculated h values for potassium chloride at several temperatures

are valid to about 0.1 mole per liter and were derived from the experimental data of Lange and Leighton (12). Following the same procedure which was used above to calculate & values from the data of Young and

SPECIFIC HEATS OF AQUEOUS SALT SOLUTIONS.

I1

51 1

Machin, Ezvalues a t 12.5' and 25°C. were obtained from the S equations. The results a t 12.5"C. were brought to 15°C. in the usual way. At 15°C. the calculated values a t 0.01 and 0.05 mole per liter are 41.4 and 51.6 calories, respectively. At 25°C. the ZZvalues a t 0.01, 0.05, and 0.10 moles per liter are 52.9, 85.4, and 89.0 calories, respectively. The results a t 15°C. seem to be in slightly better agreement with the data of table 8 than the values a t 25OC. The data of Lange and Monheim would also yield values of ZZat 12.5" and 25°C. for potassium chloride solutions; however, the necessary calculations were not performed, since it seemed desirable to compare the results on the @ basis (see figure 4). A comparison of figures 6 and 7 will show that the sodium chloride and potassium chloride family of & curves are quite similar in shape. An inspection of tables 7 and 8 will show that the corresponding values of for the two salts show fairly close agreement in dilute solution but deviate considerably a t higher concentrations. The differences increase as the temperature is raised. The deviations in the two series of curves can be - ci2for the two salts, as shown traced to differences in the values of by the values of d@/dm'" given in table 4.

zz

c,,

SUMMARY

1. The twin adiabatic calorimeter method was used to investigate the heat capacities of aqueous sodium chloride solutions a t 35", 38", 41", and 45°C. from 0.01 to 0.2 molal with a precision of 0.02 per cent. 2. The apparent mold heat capacities follow a linear relation a t the four temperatures when plotted against m"'. It is shown that the earlier results of Hess and Gramkee a t 15", 25"' and 35°C. for sodium chloride solutions and a t 15", 25", 35", and 45°C. for potassium chloride solutions follow the same relationship from 0.01 to 1.0 molal. Empirical equations, derived by the method of least squares, are presented for all data. 3. Agreement of the present results and those of Hess and Gramkee with earlier specific heats (where compsable) is found to be satisfactory. Hess and Gramkee's data for sodium chloride at 25°C. are compared with a reference @ curve constructed (by an apparently new method) from indirect dilution measurements and direct specific heats, and satisfactory agreement is obtained. 4. The experimental slopes are compared with the Debye-Huckel slopes and some other theoretical considerations are given. 5. The Person-Kirchoff equation is used to calculate relative partial molal heat contents for sodium chloride and potassium chloride solutions a t several temperatures; where comparable, there is fair agreement among the various sets of data.

512

CHESTER M. WHITE

The author is very grateful to Professor Arthur A. Sunier for his helpful advice during the investigation and for his assistance in the preparation of the paper. REFERENCES

(1) CLEWS:Proc. Phys. SOC.(London) 48, 95 (1936). 2. Elektrochem. 43,81 (1937). (2) D’ANs AND TOLLERT: (3) GUCKER, FORD, A N D MOSER:J. Phys. Chem. 43, 153 (1939). AND PLANCK: J. Am. Chem. SOC.61, 459 (1939). (4) GUCKER,PICKARD, A N D ROBINSON: J. Am. Chem. SOC.66, 2637 (1934). (5) GULBRANSEN (6) HARNEDA N D COOK:J. Am. Chem. SOC.61, 495 (1939). A N D HECKER:J. Am. Chem. SOC. 66, 4838 (1933). (7) HARNED (8) HARNED A N D NIMS: J. Am. Chem. SOC.64,423 (1932). (9) HESSA N D GRAMKEE:J. Phys. Chem. 44,483 (1940). (10) International Critical Tables. McGraw-Hill Book Co., New York (1928). (11) LAMERA N D COWPERTHWAITE: J. Am. Chem. SOC.66,1004 (1933). (12) LANGEAND LEIGHTON:Z. Elektrochem. 34, 566 (1928). (13) LANGEA N D MONHEIM:Z. Elektrochem. 35, 29 (1929). (14) LANGEAND MONHEIM:2. physik. Chem. A160, 349 (1930). J. Am. Chem. SOC.66, 4733 (1933). (15) LANGE,MONHEIM,AND ROBINSON: AND MAAS: J. Am. Chem. SOC.49,1940 (1927). (16) LIPSETT,JOHNSON, (17) PITZER, J. Am. Chem.Soc. 69, 2365 (1937). A N D ROSSINI:J. Am. Chem. SOC.61, 323 (1929). (18) RANDALL (19) ROBINSON: J. Am. Chem. SOC.64,1311 (1932). (20) ROSSINI:Bur. Standards J. Research 6, 791 (1931). (21) ROSSINI:Bur. Standards J. Research 7, 47 (1931). AND SMITH:J. Am. Chem. SOC.64, 2626 (1932). (22) SAXTON (23) URBAN:J. Phys. Chem. 36, 1108 (1932). (24) WHITE: J. Am. Chem. SOC. 68, 1615 (1936). (25) WYMAN:Phys. Rev. 36, 623 (1930). (26) YOUNGAND GROENIER:J. Am. Chem. SOC.68, 187 (1936). (27) YOIJNGA N D MACHIN:J. Am. Chem. SOC.68, 2254 (1936). (28) YOIJNGAND SELIGMAN: J. Am. Chem. SOC.60,2379 (1938). (29) YOUNG. ~ N DVOGEL:J. Am. Chem. soc. 64,3030 (1932).