P R O C E E D I N G S OF

T H E R O Y A L SOCIETY.

S e c t io n A .— M a t h e m a t ic a l an d P h y s ic a l S cien ces .

Spectrometric Determinations o f the Effect o f a Neutral Salt on the Dissociation o f Acetic A cid .

By N. Y. Sidgwick, F.R.S., and L. A. Woodward.

(Received July 30, 1930.)

This paper gives an account of an extension of the work contained in the preceding paper (Sidgwick, Worboys and Woodward). For the first part the simple photoelectric colorimeter described in that paper was used. For the second part a new type of flicker photometer was constructed. The principle of both instruments is the same, and has been given in the previous paper together with the theory of the colour changes of methyl orange, the indicator used throughout.

The colour measurements allow us to determine the value of the apparent dissociation constant K of methyl orange in presence of various concentrations of neutral salt. At a given salt concentration therefore the use of the appro­priate K value will enable us to calculate the true hydrogen ion concentration of such a solution from its colour. In this way the degree of dissociation of acetic acid has been investigated in presence of different amounts of the neutral salt potassium bromide.

Part I.—Preliminary Measurements with the Simple Photometer.

Determination> of the Dissociation Constant of Acetic Acid in Absence of NeutralSalt.

The solutions used contained N/40,000 methyl orange and N/500 sodium acetate, together with a range of concentrations of acetic acid. At N/500 the sodium acetate represses the ionisation of the acetic acid considerably, but its neutral salt effect on the activity coefficients of the substances present must be negligibly small.

vol. cxxx .—A. B

2 N. V. Sidgw ick and L. A. W oodward.

The acetic acid was purified as described by Bousfield and Lowry,* by repeated distillation from potassium permanganate with an efficient still- head. The purity of the product and its freedom from formic acid were tested by determination of the maximum conductivity in water. The sodium acetate was the purest available B.D.H. trihydrate ; it was recrystallised from water with the aid of a centrifuge, and then carefully dehydrated below 120°.f In preparing the solutions conductivity water was always used, and the precautions of the previous paper were observed.

The wave-length of the spectrum band used was selected, as before, so as to give values of cx (the ratio of the acid to the alkaline colour) lying between 2*5 and 3*0. Three sets of measurements were made, each with a series of acid concentrations. The value of c± was determined separately for each s e t ; its small variations, due to a slight difference in the setting of the apparatus, do not affect the validity of the results. The temperature was 18° ± 1°. The results are given in Table I. The first column contains the total con­centration of acetic acid ; the second the observed relative colour (as defined in the previous paper) ; the third the values of [Hfree] calculated from the equation

[Hfree] = K . i i ^ i )(ci ~ c)

The value of K used was 3-0 x 10~4, as determined at 18° with this apparatus. The fourth gives the concentration of hydrogen ions combined with indicator anions, according to the equation

[H b o u n d ] -1 1

cx — 1 ' 40,000'The acetanion concentrations [A] in the fifth column are obtained by the relation

c

[A] — [Hbound] “h [Hfree] -|~ [NaA],assuming complete ionisation of the sodium acetate at N/500. The concen­trations of the undissociated acetic acid, [HA] of the sixth column, are givenby

[HA] = [total acetic acid] — [H].The values of K Ha (last column) are calculated from the ordinary mass-action equation

Kha [Hfree] • [A] [HA]

* ‘ J. Chem. Soc.,’ vol. 99, p. 1432 (1911). t See Green, ‘ J. Phys. Chem.,’ vol. 12, p. 655 (1908).

Dissociation of Acetic Acid.

Table I.—Acetic Acid + N/500 Sodium Acetate.

3

[Acetic acid]

X 104.c

obs.[Hfree] X 104.

[Hbound] X 104. [A] X 104. [HA]

X 101.k ha

X 105.

r 1327 2-45 8-53 0-18 28-71 1318 1-86Set 1. 925-5 2-34 6-48 0-17 26-65 898-9 1-92

ct = 2*96 *< 617-0 2-19 4-63 0-15 24-78 592-2 1-94462-7 2-04 3-39 0-13 23-52 439-2 1-81

* 370-2 1-94 2-76 0-12 22-88 347-3 1-82

1r 1234 2-34 7-88 0-18 28-06 1226 1-81Set 2. J1 740-4 2-17 5-16 0-16 25-32 735-1 1-78

Ci = 2 • 85 | 370-2 1-89 2-78 0-12 22-90 367-3 1-73L 185-1 1-61 1-48 0-08 21-56 183-5 1-74

1481 2-23 9-30 0-19 29-49 1472 1-86Set 3.

Ci = 2-62 “1111 2-15 7-33 0-18 27-52 1103 1-83789-8 2-06 5-68 0-16 25-84 784-0 1-87493-6 1-90 3-75 0-14 23-89 489-7 1-83

- 296-2 1-71 2-33 0-11 22-44 293-8 1-78

They are satisfactorily constant, and the mean value 1*83 X 10"“5 at 18° is in complete agreement with the accepted value from conductivity measurements.

I t is to be noted that the form of the mathematical relationships involved is such as to magnify experimental errors. The sodium acetate diminishes this, providing a large and constant amount of acetanions, which makes the percentage variation of [A] due to an error in colour measurement small. Slight variations in temperature will have a considerable effect, owing to the large temperature coefficient of the indicator K.

Effect of 2N Potassium Bromide on the Colour of Methyl Orange.I t had been found (previous paper) that the absorption of the yellow and red

forms of methyl orange was slightly increased by the presence of neutral salts, but to the same extent, so that the value of c1 was unaltered. This effect was remeasured with slightly different results, which were shown, however, not to affect the conclusions. Solutions of methyl orange (N/40,000) were used, one being slightly alkaline (100 per cent, yellow form) and the other having an excess of hydrochloric acid (100 per cent, red form). The absorptions were measured in absence and presence of 2N potassium bromide. The salt was recrystallised from water with the aid of a centrifuge. I t was found that the absorption of the yellow (alkaline) form was increased by about 10 per cent., and that of the red (acid) form only by about 1 per cent., so that cx is somewhat

4

decreased by the presence of the salt. In one experiment, for example, a mean value of ct = 2-89 in absence of salt fell to 2-65 in presence of 2N KBr.

To discover whether this discrepancy affected the results, we redetermined the apparent dissociation constant of methyl orange in presence of 2N KBr, for comparison with the value given in the previous paper. In the previous measurement a range of concentrations of salt and only one of acid were used ; we therefore now used a range of acid strengths and only one of salt. This further served to test the dependence of the neutral salt effect upon the hydrogen ion concentration.

The solutions contained N/40,000 methyl orange and 2N potassium bromide. The measurements were made as before ; temperature 18°. Two sets were made, and the results are given in Table II.

N. V. Sidgwick and L. A. W oodw ard.

Table II.—Hydrochloric Acid and 2N Potassium Bromide.

[HCltotal] X 10*.

cobserved.

[Hbound] X 104.

[Hfree] X 104. K X 104.

Set 1. r 3*82 2-25 0-20 3-62 0-98cx = 2-59 212 2 0 6 017 1-95 0-97

1*70 1-99 0 1 6 1-54 0-931-27 1-89 0-14 1-13 0-89

- 0-848 1-72 0-113 0-735 0-89r 3-82 2-35 0-20 3-62 0-93

Set 2. 2-76 2-25 0-18 2-58 0-92cx = 2 • 695 *< 1-91 2-12 0-17 1-74 0-89

1-48 2 0 0 0-15 1-33 0-93- 106 1-84 0 1 2 0-94 0-96

The values in the third, fourth, and fifth columns are obtained from the relations

[ H bo„nd] = ~ ~ ~. 4 0 0 0 0 >

[Hfree] - [HCltofcal] - [Hbound],

K = [Hfrce] . £ i_n£.C — 1

An error of 1 per cent, in observed colour will cause errors in K of 4 per cent, in the lowest and 8 per cent, in the highest acid concentrations. The values of K obtained are reasonably constant, and the mean value, 0-93 x 10-4 at 18°, in 2N potassium bromide, is not seriously different from that (0-59 X 10~4) given in the previous paper.

Dissociation of Acetic Acid . 5

Determination of K Ha in Presence of Neutral Salt.

This value, 0*93 X 1CT4 of K for methyl orange in 2N KBr, was used to investigate the dissociation of acetic acid under the same conditions. The solutions contained N/40,000 methyl orange, 2N KBr, and N/500 sodium acetate. As mentioned above, the sodium acetate has a negligible neutral salt effect, but increases the accuracy of the deductions by giving an excess of acetanions. The results are given in Table III, which is analogous to Table I.

Table III.—HA + N/500 NaA + 2N KBr.

[Acetic acid] X 104.

cobs.

[Hfree] X 104.

[Htonnd]X 104. [A] x 104. [HA]

X 104.K ha

X 105.

r 388*7 2*30 3*06 0*19 23*25 385*5 1*85Set 1. 259*1 2*18 2*13 0*17 22*40 256*7 1*85

Cj = 2-695< 172*8 2*035 1*46 0*15 21*61 171*2 1*84129*5 1*93 1*13 0*14 21*27 128*2 1*8886*38 1*77 0*775 0*113 20*89 85*49 1*90

r 518*2 2 ’37 4*11 0*20 24*31 513*9 1*94Set 2. 388*7 2*31 3*29 0*20 23*49 385*2 2*00

C x = 2*68^ 276*4 2*21 2*40 0*18 22*58 273*2 1*98215*9 2*13 1*92 0*17 22*09 213*8 1*98

- 155*5 2*01 1*40 0*15 21*55 154*0 1*96

The mean value of KHa at 18° is 1 • 92 X 10”5, as compared with 1 • 83 X 10“5 in absence of neutral salt, so that the salt causes an increase of only about 5 per cent. Recent work on the variation of activity coefficient with ionic strength would, however, lead us to expect that the neutral salt effect would be in general much larger than this, and that the dissociation would increase at low salt concentrations, pass through a maximum, and then decrease. Thus at a certain concentration for each salt the effect must be zero ; and it was thought that the small change observed in KHa in 2N KBr was due to an accidental choice of a salt concentration near this point. We therefore decided to examine a range of salt concentrations, and for this purpose constructed the flicker photometer described in the next section.

Part II.—The F licker Photometer.

The principle of this apparatus is the same as that of the simple photometer described in the previous paper, but it is far more accurate and convenient to use. In its construction we have had the advantage of the continual assistance and advice of Dr. G. M. B. Dobson, to whom we are very grateful.

6

By means of a suitable optical arrangement (described below) a beam of monochromatic light of known wave-length can be made to enter the same photoelectric cell by one or other of two routes, either through the compart­ment in which the cell containing the solution under investigation may be placed, or through an optical wedge. The colour of a given solution is then obtained as follows. Before introducing the cell with the solution, the photo­electric effect of the beam after passing through the empty chamber is noted. The beam is then deflected so as to pass through the wedge, and the wedge position corresponding to the same photoelectric effect as before is observed. This may be called the “ zero position.55 Then the absorption cell with the coloured solution is placed in the chamber and the light sent normally through it. The electrometer reading is observed, and the beam deflected through the wedge, which is then shifted so as to give the same reading. As shown in the previous paper the lateral shift of the optical wedge from its “ zero position 55 gives a direct measure of the absorption of the solution together with the cell containing it.

Thus each colour measurement involves the observation of two wedge positions, each of which involves the balancing by a null-point method of two photoelectric effects which are produced by the beam after travelling respec­tively two different paths. I t is essential for accuracy that the change over from one path to the other should be as rapid as possible, and accompanied at the null-point by the minimum transient diminution of the intensity of light, i.e., the minimum flicker of the electrometer needle. With our apparatus it is possible, when the wedge is correctly adjusted, to change over rapidly from one light path to the other with no observable flicker.

A diagrammatical representation of the apparatus is shown (only roughly to scale) in fig. 1. The source of light L is a 500-watt, gas-filled filament lamp, mounted to allow of focusing and lit directly from the laboratory mains. Owing to the heat generated this must be surrounded by a double-walled metallic jacket J through which water circulates. The light is focused on the slit of a Tutton monochromator by Hilger, a constant deviation instrument in which the wave-length can be read off directly from the drum which moves the prism (M). The monochromatic beam is made parallel by the lens S. The arrange­ment for changing the path of the beam consists of two totally reflecting prisms, P^ P 2, carried on a horizontal metal table which can be moved vertically by hand. When the table is depressed, the beam passes over the top o£ the prism Pl5 through the absorption chamber A, and is focused on the photoelectric cell C. When the table is raised, the beam suffers total reflection at Px, passes

N. V. Sidgw ick and L. A. W oodw ard.

Dissociation of Acetic Acid. 7

normally through the optical wedge W, is reflected at P 2, and finally focused again upon C. While it is being raised or depressed, part of the light goes one

i h.xTff

To electrometer

F ig. 1.—Apparatus (roughly to scale of 1 /20th inch — 1 inch).

way and part the other ; thus no “ flicker ” is produced in the photoelectric effect if the wedge is correctly adjusted at the null-point. Owing to the loss of intensity in passing through the prisms, it is necessary to insert an absorbing screen It of suitable density in the absorbing chamber ; otherwise the “ zero position ” cannot be realised. The optical wedge is held by an arm attached to a brass carriage running accurately on parallel steel bars. The carriage position can be set roughly by hand, and final adjustment is by a micrometer movement, the position being read off on a vernier scale. The solution to be investigated is contained in the rectangular glass cell X, the liquid layer being 1 cm. thick, and the whole cell holding only about 6 c.c. The electrical con­nections to the photoelectric cell C are similar to those described in the previous paper, the xylene leak, two-way switch, etc., being all contained along with C in a compartment B, which is completely lined with earthed copper sheet, The current is measured as before with a Lindemann-Keeley electrometer. The whole apparatus is carried on a single base of multiple-ply wood to avoid warping, and, with the exception of the monochromator, all is contained in two mahogany boxes fitted with levelling screws.

The apparatus can be made practically light-tight, and so need not be used in a dark room. The accuracy of the results is not affected by variations in the light source or in the photoelectric apparatus, etc., if these are sufficiently slow not to be mistaken for genuine “ flickers ” of the needle. In practice no difficulty is found in obtaining good null-points.

For experiments with methyl orange it is desirable to control the temperature.

8

To this end the cell with the solution (protected by a cover-slip) was placed for some time in an air-bath kept at 18° by immersion in the water of a thermostat at a slightly higher temperature. I t was then transferred to the absorption chamber, the temperature of which was regulated by blowing into it a stream of air previously heated by passage over an electrically heated resistance wire. By suitable hand regulation the chamber could be kept at 18 i t 0*2 , and the solution during measurement was well between these limits.

N. V. Sidgwick and L. A. W oodw ard.

Part III.—Measurements wtith the Flicker Photometer.

Test of the Colour Theory for Methyl Orange over the Range of the OpticalSpectrum.

It had been found in the previous work that satisfactory results could be obtained by using only a certain empirically selected range of wave-lengths. The present measurements were undertaken in order to test the applicability of the Tizard equation at other wave-lengths.

Five solutions were made up, each containing N/40,000 methyl orange. One was made slightly alkaline (2 drops of N potassium hydroxide to 100 c.c.), and one contained N/10 hydrochloric acid ; the other three contained inter­mediate concentrations of this acid. The absorptions were measured at 18° for a series of 10 wave-lengths from 4500 to 5625 A.U., a rubidium photo­electric cell being used. Every measurement was repeated at least twice with fresh solutions, and the agreement was satisfactory. The mean results are given in Table IV.

Table IV.—Methyl Orange + Hydrochloric Acid.

Ain A.U.

Dobs.

Lobs.

Acid I. Acid II. Acid III.

X obs. Per cent, red. X obs. Per cent,

red. X obs. Per cent, red-

5625 2-66 0-66 2-27 (80-5) 2-06 (70-0) 1-62 (48-0)5500 6-25 0-88 5-10 78-6 4-56 68-5 3-42 47-35375 9-95 1-39 8*11 78*5 7-30 69-0 5-33 46-05250 11-37 2-20 9-46 79-2 8-54 69-1 6-44 46-25125 12-07 3-40 10-26 79-1 9-37 68-9 7-36 45-95000 12-02 ' 4-64 10-47 79-0 9-76 69-4 8-06 46-34875 10-63 5-97 9*60 77-9 9-10 67-2 8-10 45-74750 8-23 6-82 7-96 (80-8) 7-76 (66-7) 7-49 (47*5)4625 5-84 6-94 6-15 (71-8) 6-23 (64-6) 6-52 (39-7)4500 4-03 6-57 4-59 78-0 4-86 67-3 5-43 . 46-4

Mean .... 78-6 Mean .... 68-5 Mean .... 46-3

Dissociation of Acetic Acid . 9

The first column gives the wave-lengths in A.U. ; the second and third the observed wedge shifts in centimetres for the excess acid solution (D) and the slightly alkaline solution (L). The rest of the table gives for each of the three intermediate acid concentrations X, the observed wedge shift, and the per­centage of the red form present. These shifts are not corrected for the absorption of the glass cell and the water ; this correction is constant through­out, and since in the calculations we deal only with the differences of wedge shifts, it vanishes. In the previous treatment of results use has been made of relative colours, but the results with the flicker apparatus will always be given in terms of observed wedge shifts. The following relations hold :

c = (X — w)/(L — w) and = (D — w)/(L — w),

where w = absorption of cell + water. The Tizard equation (equation (3), previous paper) becomes

K = [H ]. (D — X)/(X - L),

which is seen to be independent of w.The percentage of indicator present in the red form at each acid concentration

is calculated according to TizardJs additive law from the equation

Percentage red = (X — L)/(D — L).

With the exception of certain bracketed values (see below) concordant results are obtained over the whole spectrum.

The results are shown graphically in fig. 2, in which observed wedge shifts are plotted against wave-lengths. The curves for the excess acid solution (100 per cent, red) and for the alkaline solution (100 per cent, yellow) intersect a t about X = 4685 A.U. Since at this point the absorptions of the two forms are equal, any mixture of the two at the same total concentration should give the same value ; and this is proved by the fact that the curves for the three intermediate solutions all pass through this point.

In calculating the percentage of the red form present, the accuracy depends on the magnitude of the difference terms (X — L) and (D — L). When X = 4625, 4750 and 5625 A.U. (the bracketed values in Table IV), the measure­ments cannot be expected to yield accurate results, in the first two because the absorptions of the two forms are so nearly equal, and in the last because the whole absorption is so small; in reckoning the means these have been omitted.

The value of K for the indicator acid from the mean results in Table IV is given in Table V.

10 N. V. Sidgwiak and L. A. W oodw ard.

Excess

5000 5250Wave-lengths in A.U.

F ig. 2.

Table V.

Solution. • [HCltotal]X 104.

[Hbound] X 104.

[Hfree]X 104. K X 104.

Acid I ................................. 11-8 0-190*170-17

11.6 3*16Acid II ................................. 7-39

2-957*22 3*32

Acid III ............................. 2-83 3-28

The third column is obtained from the relation

[H bound]X - L 1 D - L ‘ 40,000

taking the mean values of the term (X — L)/(D — L). The Tizard equationwas used to calculate K, taking the mean values of (D — X )/(X L). Thevalues of K show fair agreement, but point to a higher figure than that previously obtained (3-03 X 10”4) with the simpler apparatus.

Determination of K for Methyl Orange at Optimum Wave-length.The optimum wave-length is that showing the greatest difference of absorp­

tion between the two forms. For all subsequent measurements the wave­length 5125 A.U. was selected, and a rubidium photoelectric cell, having its

Dissociation of Acetic Acid. 11

maximum sensitivity in this region, was used. The temperature was regulated to 18° ± 0 -2 ° , as described above. The indicator was N/40,000. The means of a number of concordant determinations are given in Table VI, which is similar to Table V.

Table VI.—Values of K for Methyl Orange at 18°.

[HCltotal] X 10*. X observed. [Hbound] X 104. [Hfree] X 104. K X 104.

7 0 3 9-11 0*17 6-86 3-426 0 3 8*79 0 1 6 5*87 3*414-74 8-39 0*15 4-59 3-254-06 8-00 0-13 3-93 3-343-29 7-56 0*12 3-17 3-302-22 6-70 0-10 2-12 3-31

Mean .... 3-34

The mean of a large number of determinations at this wave-length gave for the two forms the values D = 11-98 and L = 3-32 cm. Observational errors are magnified in the calculation of K ; the figures in the last column of Table VI show that the error in the absorption measurements is always less than 1 per cent. The mean value of K, 3-34 X 10”4, at 18°, is very near to that given by Giintelberg and Schiodt,* which is 3-23 X 10~4 at the same temperature.

Determination of K in Presence of Neutral Salt.Analogous determinations were then made in presence of potassium bromide.

I t has already been shown (Table II) that the salt effect is independent of the acid concentration. For these experiments four concentrations of acid were used, and four of the salt, the latter being approximately N/10, N/2, N, and 2N. The materials were purified as before. Temperature 18° dz 0-2°, wave­length 5125 A.U. The results are given in Table VII, the mean of two independent concordant determinations being quoted in each case.

The table is in four parts, each of which is analogous to Table VI, and beside each are given the salt concentration and the mean observed values of D and L. For each part the appropriate values have been used in the calculation of K. The agreement of the calculated K-values at each salt concentration shows that the error in the absorption measurements is always less than 1 per cent. Since the value of K in absence of salt is 3-34 X 104, it follows that with increasing salt concentration K passes through a maximum.

* 4 Z. Phys. Chem.,’ vol. 135, p. 393 (1928).

12 N. Y. Sidgw ick and L. A. W oodw ard

Table V II—Methyl Orange + HC1 + KBr.

[HCltotal]X 104.

Xobserved.

[Hbound]X io«.

[Hfree] X 104.

K X 104. Mean K X 104

[KBr] = 0-0916N f 2-213-29

6- 337- 14

0-080-11

2- 133- 18

4-194-19

D = 12-03 J. 4-06 7-60 0-12 3-94 4-19L = 3-43 4-74 8-02 0-13 4-61 4-03 4-15

[KBr] = 0-458N f 2-213-29

7-057-87

0-100-13

2-11316

3-0230 7

D = 12-08 < 4-06 8-28 0-14 3-92 3-14L = 3 * 53 4-74 8-55 0-15 4-59 3-21 3-11

[KBr] = 0-916 N f 2-213-29

7- 668- 57

0-120-15

2- 093- 14

2-282-23

D = 12-12 < 4-06 9-00 0-16 3-90 2-25L = 3 * 58 4-74 9-35 0-17 4-57 2-19 2-24

[KBr] = 1-832 N f 2-213-29

9-109-89

0-160-18

2-05311

1-211-21D = 12-31 4-06 10-30 0-19 3-87 1-17L = 3-68 4-74 10-52 0-20 4-53 1-18 1-19

Determination of the Dissociation Constant of Acetic Acid in Absence of NeutralSalt.

This was done with N/40,000 methyl orange and pure acetic acid, but without sodium acetate. Temperature 18°, wave-length 5125 A.U., D = 11*98, L = 3*32 cm. The results are given in Table VIII, which is analogous to Table I.

Table VIII.—Acetic Acid.

[Aceticacid]X 104.

Xobserved.

[Hfree]X 104.

[Hbound] X 104. [A] x 104. [HA]

X 104. Kha X 105.

999-3 10-28 13-7 0-20 13-9 975-4 1-95582-6 9-84 10-19 0-19 10-38 572-2 1-85272-4 9-18 6-99 0-17 7-16 265-2 1-89124-7 8-36 4-65 0-145 4-795 119-9 1-86101-6 8-06 4-04 0-14 4-18 97-4 1-7372-69 7-74 3-48 0-13 3-61 69-08 1-8261-95 7-53 3-16 0-12 3-28 58-68 1-7750-58 7-37 2-93 0-12 3-05 47-53 1-8833-98 6-90 2-35 0-10 2-45 31-53 1-8325-13 6-66 2-10 0-09 2-19 23-12 1 -99

Mean .... 1-86

The mean value, 1*86 X 10 5, agrees with that found in the previous experiments (Table I : 1*83 X 10~5).

Dissociation of Acetic Acid. 13

Determination of KHa in Presence of Potassium Bromide.

This was carried out in the same way as in the measurement of K (Table VII), with four concentrations of acetic acid, and four of potassium bromide (the latter the same as before). The same temperature and wave-length were used. The results are given in Table IX, which is arranged like Table VII.

Table IX.—Acetic Acid and Potassium Bromide.

[A ceticacid ]X 104.

X [Hfree] [Hbound] [A ] [H A ] K„a Mean Kha

X 106.o b s. X 104. X 104. X 104. X 104. x 10s.

[KBr] = 0-0916 N f D = 12-03 1L = 3-43

33-9850-58

6- 947- 39

2-863-54

0-100-12

2- 963- 66

31-0246-92

2-732-76

72-69124*7

7-798*37

4- 275- 60

0-130*14

4- 405- 75

68-29119*0

2-752*70 2*74

[KBr] = 0-458 N f D = 12-08 <T O KO

33-9850-58

7- 698- 10

2- 953- 57

0-120-13

3-073-70

30-9146-88

2-932-82

72-69 8-48 4-28 0-14 4-42 68-27 2-77Li = 5-05 124-7 9-10 5-81 0-16 5-97 118-7 2-92 2-86

[KBr] = 0-916 N fn io . io J33-98 8-24 2-69 0-14 2-83 31-15 2-4450-58 8-66 3-29 0-15 3-44 47*14 2*40D = 1J * l Z <

L = 3-58 72-69 9-07 4-03 0-16 4-19 68-50 2-47124-7 9-64 5-47 0-18 5-65 119-0 2-60 2*48

[KBr] = 1-832N f D = 12-31 L = 3-68

33-98 9-44 2-39 0-17 2-56 31-42 1-9450-58 9-77 2-85 0-18 3-03 47*53 1*8272-69 10-05 3-35 0*19 3-54 69*15 1*72

124-7 10-62 4-89 0-20 5-09 119-6 2-08 1*89

For the calculation of [Hfree] by the Tizard equation, the proper value of the indicator K has been used at each salt concentration (i.e., the mean values from Table VII). The agreement in KHA-values shows that the experimental error is always less than 1 per cent. The value of KHa in absence of neutral salt being 1 • 86 X 10“5 these results show that with increasing salt concen­tration it passes through a maximum.

P art IV.—D iscussion of R esu lts .

Comparison of Results from the Simple and Flicker Photometers.The simple apparatus gave a value 3*0 X 10-4 of K for methyl orange at

the room temperature of 18°, and this was used in the calculation of Kha from the experiments in Part I of this paper, for which the same apparatus was employed. The new flicker colorimeter, however, has given the higher value 3*34 X 10~4 at a controlled temperature of 18°. This may be due, at least in

14

part, to the solutions in the earlier work not having attained the temperature of the room, since Tizard and Whiston have shown* * * § that K for methyl orange increases by about 4 per cent, per degree. This explanation is supported by the fact that for the dissociation constant of acetic acid, which is little affected by temperature, both instruments have given practically the same values (1*83 and 1-86 X 10“5), although the two different values of K were used in the two calculations. So, too, the values of Ka/Kc in presence of potassium bromide obtained by the simple apparatus (previous paper, Table IV) were, at salt concentrations of 0 • 5, 1 • 0, 2 • 0 N : 1 • 06, 1 • 48, 3 • 06 ; while interpolation from the values obtained with the new apparatus (this paper, Table VII) gives 1-10, 1-56, 3 • 12. In general it seems that reliable results are obtained under given conditions if we use values of K determined under the same conditions. The recent determination of K for methyl orange by Giintelberg and Schiodtf is 3-23 X 10"4 at about 18°, which is in better agreement with our later value than with our earlier one, or with the value 3*0 X 10-4 got by interpolation from the earlier work of Tizard.i

Theoretical Significance of Results.The fundamental thermodynamic equation for a weak acid (see previous

paper, equation (6)) is

Tr a n ■ a A __ fa ./ a ch . cA _ / H . / a vr * 7 *

®HA /HA ChA /HA

The results of the measurements with the flicker colorimeter are given in fig. 3. The acetic acid curve is got by plotting the values of K0/Ke - / a / / ha

against the square root of the volume normality of the potassium bromide (Ka is the value in absence of salt). We should expect the variation of / A to be relatively small, and this has been approximately verified for acetic acid by the calculations of Randall and Failey,§ which are based on the experiments of Sugden|| upon partition between aqueous salt solutions and amyl alcohol at 25°. I t is therefore interesting to compare the acetic acid curve with that for a strong acid, where the concentration of the undissociated part is zero. This is given in the HBr curve on fig. 3, which is taken from the electrometric

* ‘ J. Chem. Soc.,’ vol. 117, p. 154 (1920).f Loc. cit.J 6 J. Chem. Soc,,’ vol. 117, p. 150 (1920). -§ ‘ Chem. Reviews,’ vol. 4, p. 291 (1927).|| c J . Chem. Soc.,’ vol. 129, p. 177 (1926).

N. V. Sidgwick and L. A. W oodw ard.

Dissociation of Acetic Acid . 15

results of Harned and James* for centinormal hydrobromic acid in potassium bromide solutions. Their units are slightly different from ours, but this does

not affect the general shape of the curves (see previous paper). Their values for water (yH . ycm against the square root of the molality) are added ; the lowest (dotted) curve gives the theoretical values for a uni-univalent electrolyte in dilute salt solutions according to the theory of Debye and Hlickel (see previous paper).

I t will be seen that all these curves, colorimetric and electrometric, are of the same form. In very dilute solutions all approximate to the theoretical limiting slope ; each passes through a minimum at about the same salt con­centration, and ultimately rises in concentrated salt solutions (> 3N) above its initial value. To the same class belong the later colorimetric measurements of Giintelberg and Schiodt (loc. cit.), and the approximate calculations of Harnedf for formic acid, based on the rate of hydrolysis of methyl formate.

On the other hand, a sharp contrast is provided by the corresponding curve for methyl orange (Ka/Kc against the square root of the concentration : see Tables VI and VII). This shows a more marked deviation from the theoretical curve in very dilute solutions; the minimum occurs at a lower salt concentration (about 0-05 N) ; and the curve, after passing through the unit ordinate at a concentration of only about N/3, rises to much higher values in the strong

* ‘ J . Phys. Chem.,’ vol. 30, p. 1060 (1926). t ‘ J. Amer. Chem. Soc.,’ vol. 49, p. 1 (1927).

16 B. A. F isher.

solutions. The measurements of Giintelberg and Schiodt (loc. cit., plotted in fig. 1 of the previous paper) confirm these conclusions. This difference must be due to the fact that with the indicator we have in addition to the equilibria ruling in a partly ionised solution of a weak electrolyte, another, the tautomeric equilibrium between the two structurally different forms. The more rapid rise of the curve for the indicator seems to show that this equilibrium is con­siderably shifted with increasing salt concentration towards the side of the non-dissociated (red) form.

We wish to express our thanks again to Dr. C. M. B. Dobson for his kind help, and also to Imperial Chemical Industries for a grant towards the cost of the work.

The Moments of the Distribution for Normal Samples of Measures ofDeparture from Normality.

By R. A. Fisher, Sc.D., F.R.S., Statistical Department, Rothamsted Experimental Station, Harpenden, Herts.

(Received September 1, 1930.)

1. The Appropriate Symmetric Functions of the Observations.

If *1 ••• the values of a variate observed in a sample of v , from anypopulation, we may evaluate a series of statistics ( ) such that the mean value of kpwill be the pth cumulative moment function of the sampled population ;the first three of these are defined by the equations :

^ = » s (*),

*2 = , 7 ~ j ; s (* -

kz = (n - 1) (n - 2) S (x ~~ *l)3 ;

then it has been shown (Fisher, 1929)* that the cumulative moment functions* R. A. Fisher, Moments and Product Moments of Sampling Distributions,” ‘ Proc.

Lond. Math. Society,’ Series 2, vol. 30, pp. 199-238 (1929).