DECOMPOSITION OF PEKSULPHURIC ACID, ETC. 2083CCXIX.- The Dynamics of the Decomposition o f Per.-sulphuric Acid and its S d t s in Aqueous Solutiori,.By LEILA GREEN and ORME MASSON.LEVI AND MIGLIORINI (Gazzetta, 1906, 36, ii, 599) have shownthat potassium and sodium persulphates decompose in aqueoussolution unimolecularly, and that the action is much acceleratedby the addition of acids. Our own experiments confirm both ofthese results. It is, however, somewhat difficult to reconcile themwith one another, for the act,ion itself produces acid sulphate, andcan, indeed, be followed throughout its course by the increasin2084 GREEN AND MASSON : DYNAMICS OF THE DECOMPOSITION OFacidity, so that t’he curve should exhibit the features of an aut+accelerated, rather than those of an unmodified, unimolecular action.The difficulty, however, disappears if the acid sulphate product beassumed to ionise only into metal and HS04’, and to provide prac-tically no H’ ions, or if, in other words, sulphuric acid be regardedas a monobasic acid under the conditions of the experiments.Theaction may then be formulated by the equation:S20s” + H20 = 2HSO4’ + &02,which makes it strictly unimolecular in form. On general groundsthe assumption may be objected to, but it does not appear possibleto explain without it the behaviour of persulphuric acid and itssalts, and it will be shown that one can, by its aid, co-ordinate thevarious results obtained with the acid, its potassium and sodiumsalts, its barium salt, and mixtures of these with each other, withother salts, and with acids.One or two unexplained difficultiesremain, which will be dealt with in the sequel.The persulphate solutions employed by us were obtained fromsolutions of the barium salt, prepared from commercial ammoniumpersulphate by treatment with excess of barium hydroxide in itvacuum and subsequent neutralisation with dilute sulphuric acid.The initial strength of each persulphate solution was determinedby measuring the final acidity produced by boiling a measuredvolume, the titrations being carried out with standard sodiumhydroxide, using methyl-orange as indicator. Comparative testswere made in some cases by the ferrous sulphate and permanganatemethod, and also by gravimetric determinations of the metal assulphate.The results in all cases agreed fairly well, but theacidimetric method was found to be the most accurate, besideshaving the advantage of rapidity. The progress of the decom-posit.ion in each experiment was also followed by acidimetry. I nall cases the temperature of the thermostat was 80*0°, which wasfound to give a convenient rate of action, except in the experimentsconducted at 70° and 90° for the purpose of fixing a, temperature-coefficient. The solution was always divided at the outset into anumber of 5 C.C. samples, and these were heated in closed tubes,according to the method described in it previous research on cyanates(Masson and Masson, Zeksch. physikal. Chern., 1910, 70,290).The persulphates which we have examined may be divided, forthe present purpose, into three classes.The first contains those ofsodium, potassium, and ammonium, which are neutral salts con-vertible into soluble acid sulphates. The magnesium salt properlybelongs to this class, but differs somewhat in its behaviour fromthe other members. The second class contains pemulphuric aciditself, which doubles its acidity by conversion into sulphuric acidPERSULPHURIC ACID AND ITS SALTS IN AQUEOUS SOLUTION. 2085The third class contains barium persulphate, which, originallyneutral, produces persulphuric acid and insoluble barium sulphate.The course of the action is quite different in each of these classes,and they therefore require separate consideration.I n the sequel we have thought it desirable to economise space bysuppressing most of the numerical details of our work, and havetherefore given only the essential results, except where fuller treat-ment appeared necessary.Class I.-Neutral Persulpha.tes which form Soluble Acid Sulphates.These cases conform to the equation for simple unimolecularaction :1 A - x !@ = k,(A - x), 01' k, = -10&-1, cl t t, - t, A - x2where A is the initial concentration of persulphate, and A --z is itsvalue at any subsequent time, t .To avoid some slight uncertaintydue to the time required to raise the tubes to the bath temperature,the time at which the first sample was taken from the bath wasselected, rather than the moment of immersion, as t,. The valuesof k, given in table I are averages calculated in each case fromseveral points in a curve covering nearly the whole course of theaction. Separate values in any one experiment were found to agreewell.It is evident that li, is but slightly dependent on the initialconcentration, or even on the nature of the metallic radicle.I n this and subsequent tables, the concentrations are expressed ingram-molecules of persulphate per litre, and the times are measuredin minutes:TABLE I.Na,S,08 ............... 0 *226 0'00641Na 29208 ............... 0 '1 25 0.00577Na,S,08 ............... 0.127 0.00533(NH,),S,OB ............ 0 '229 0.0061The curve for the ammonium salt showed rather more irregularitythan the others, and its mean velocity-coefficient was, as shown,perceptibly higher.This is perhaps explained by the formation oftraces of nitric acid by oxidation, with consequent acceleration, butthe divergence from the normal course is only slight.Experiments with sodium persulphate solution containing addedsodium nitrate (selected as a typical neutral salt of the same metal)have proved that the only effect of such addition is to raise slightlythe unimolecular constant. Thus, in a test with 0'1283-sodium per-sulphate and 0'25-sodium nitrate solution, with twelve experimentalSalt. A . 4-K,S,08 ................. 0.108 0'00542086 GREEN AND MASSON : DYNAMICS OF THE DECOMPOSITION OFpoints covering a range of 85 per cent. decomposition, k, was foundto vary irregularly between the extreme values 0-0062 and 0.0068,with a mean value of 0.0065.On the ot'her hand, it will be shownthat acids largely accelerate the action, and the special influences ofadded sulphates will also be dealt with later.The magnesium salt, in contrast to those of the alkali metals,shows distinctly the effect of auto-acceleration, which, in this case,is probably to be explained by the formation of some non-ionisedmagnesium sulphate and free hydrogen ions, according to theequation :Thus, in an experiment in which the initial concentration ofmagnesium persulphate was 0.2414, the unimolecu1a.r coefficient,calculated in the usual way, was found t o increase steadily fromabout 0.0055 (appreciably equal to that of the sodium or potassiumsalt) at the start to 0.0066 when the action was half completed,and 0.0092 when less than 10 per cent.remained undecomposed.A similar, but much more pronounced, auto-acceleration will beshown to occur in the case of the barium salt, where the precipitationof the insoluble sulphate necessarily adds hydrogen ions to thesolution. But the case of persulphuric acid itself must be discussedfirst.ME" + HSO,' MgSO, + Ha.Class Zl.-Persulphum'c Acid.In this case the curves obtained are again of the simple uni-molecular form, with no sign of acceleration by increase of hydrogenions; but it differs in two respects from that of the persulphates ofthe alkali metals. In the first place, the velocity is considerablygreater, and, in the second place, the value of its coefficient isdependent on the initial concentration, so as t o vary in differentexperiments while constant in any one.These facts are inaccordance with the hypothesis already put forward, that the actionproceeds practically tccording to the equation :S20," + " H Z 0 =2HSO4' + 402,and that it 'is accelerated by the hydrogen ions which are initiallypresent and remain unchanged in concentration. Such a hypothesisleads to the differential equation := (k2 + kA)(A - x),dtwhere k,+ kA is necessarily a constant ( K ) in any given experiment,and1 A - x hr= k, + kA =----log,-----'.t, - t, A - x2A simple explanation suggests itself for this accelerative actioPERSIJLPHURIC ACID AND ITS SALTS IN AQUEOUS SOLUTION. 2087of hydrogen ions. It may be assumed that, at the dilutionsemployed, the great bulk of the persulphuric acid is completelyionised into 2H' and S2081', while a small proportion is convertedinto H' and HS,O,'.I f this proportion be small enough, thetotal H' concentration may be taken as constant and equal to 2A,whilst that of the S20,// is appreciably equal to A -5, and that ofthe HS,O,' itself is therefore proportional to A ( A - x). If, further,the HS,O,' has a sufficiently high rate of reaction as compared withthe S208//, it will make itself felt in spite of its small concentration,and the total velocity of the action will be the sum of two velocities,k,(A -x) and kA(A -z), in accordance with the equation alreadygiven.By comparison of experiments with different A values, it is easyto evaluate k , and k ; and it has been found in this way thatk,=0'010 and k=O*163. These figures are illustrated by a com-parison of the found and calculated velocity coefficients in table 11.The fact that k, is nearly twice as great as the k, of sodium orpotassium persulphate is difficult to explain on any hypothesis, f o rit implies some influence of the hydrogen ions other than thatrepresented by the term kA(A - x) and independent of their con-centration. It is a fact, however, that, whilst d x / d t = 0*0055(A - x)holds for the sodium and potassium salts, the equation for per-sulphuric acid is~=(0*010+0*1638)(A -x)=K(A -x).dtTABLE 11.Persulphuric A cid.0.2566 0-0527 0.051 80,1251 0'0304 0'03040.1237 0-0302 0'03020.0923 0'0258 0-02500'0644 0'0210 0.02050'0416 0.0184 0.0168A.K (found). K (calculated).The solutions used in the first, third, and fourth of these testswere prepared from barium persulphate by adding the calculatedquantity of sulphuric acid, and were filtered from the bariumsulphate; while those used in the second, fifth, and sixth wereobtained by allowing barium persulphab solution t o decomposeautomatically at 80°, and contained the precipitated sulphate insuspension. These cases will be discussed later2088 GREEN AND MASSON : DYNAMICS OF THE DECOMPOSITION OFPersdphum'c Acid with Added Nitric Acid.In this case there is a permanent increase of the hydrogen ions,and, if the initial concentrations of the two acids (both reckoned asdibasic, that is, as H2S2O, and H,N,O,) be respectively A and B,the course of the action should be expressed by the equation :e= (k2 + k ( A + B)}(A - z),dtwhere k, + k(A + B ) appears as a unimolecular constant in any givenexperiment, andThis w&s confirmed by the experiments summarised in table 111.The first of these tests was made with an original mixture ofpersulphuric acid and nitric acid, while the other three were thelat.er parts of experiments, in which barium persulphate, mixedwith nitric acid, was allowed to decompose at 80° until thereremained only persulphuric acid and nitric acid in solution, andthe subsequent decomposition was then studied.These tests will bereferred to later. The figures in the last column of the table showthe value which IK would have if the nitric acid were absent(compare table II), and are given to indicate clearly its effect.TABLE 111.Persu2phuric Acid with Added Nitria Acid.0.1248 0'1542 Om0500 0-0506 0.03040.0635 om15 0.0508 0 yo504 0.02040.0628 0.1255 0'0414 0.0407 0.02020,0630 0'0634 0.0315 0.0306 0.0203A.B. K (found). H (calculated). K (original).Mixed PersuZphuric Acid and Sodium Persulphate.The theory for such a case may be given on the assumption thatthe k, and k, constants are active approximately in proportion tothe unchanging relative quantities of Na' and H', and that the latteralso contributes its special accelerative effect. Thus, if the initialH,S206 be A , and the initial N+S@, be B, whilst x represents thetotal S,O, destroyed, A and B will also represent at any time ths(H')2 and the (Na')2 respectively, anPERStJLPHURlC ACID AND ITS SALTS IN AQt'EOVS SOLUTION, 2089In any given experiment therefore a unimolecular constantshould be obtained, andI n one test, in which A =0.1285 and B=0*1234, a mean valueof 0.0276 was found for K in place of the calculated value 0.0288.In another, in which A =0-0625 and B=0*1250, the found andcalculated values were respectively 0.0183 and 0.0172.The agree-ment is thus fairly satisfactory in both cases.Persulpliuric Acid with Added Sodium Nitrate.This case is similar to the last, except that, the permanent con-and (Na'), being respectively A and B, thatThe constantcentrations of theof the Sz08" at any time is A - x instead of A + B - x.is here thereforeA B + kA = -loge----4 1 A - xK = hAX + "Ax t2 - t , A - x2I n the only test carried out, A = 0.1377 and B =0.0625, givingthe calculated value of the constant as 0-0311.The mean experi-mental value was 0.0325, which is identical with that calculatedon the assumption that the sodium nitrate is quite without effect.The difference is in any case too small t o be significant, but itmay be pointed out that a similar discrepancy was exhibited bythe mixture of sodium persulphate and sodium nitrate, indicatingthat the latter has a small accelerative effect, not included in thetheory, which may, in the present case, compensate for the expectedsmall lowering of the E value.Class IZI.-Barium Persutphate.This case differs from the others in the precipitation of theproduct barium sulphate, and it differs also in the form of thecurve in which x is plotted against t ; for this, being at first concavetowards the x axis, at once points to strong auteacceleration.Thetotal change affecting the barium salt is represented by the equation :2BaS20s + H20 = H2S,0s + 2BaS0, + 302,and it must occur in two steps, nameIy:(1) S,O," + H,O = 2HS04' + BO,,( 2 ) 2Ba" + 2HS04' = 2BaS0, + 28'.The first of these is a relatively slow action, and the second keepspace with it.. Thus 2Ba" disappear from the solution for oneS208" destroyed; and if the latter be x, as in previous cases, it isevident that x also represents the persulphuric acid (or acidity)produced, and A - 2x represents the barium persulphate remaining.VOL. XCVII.6 2090 GREEN AND MASSON : DYNAMICS OF THE DECOMPOSITION OFThis holds until A - z = x = Q A , when the precipitation of thebarium is complete, and subsequent action is concerned only withpersulphuric acid. The whole action may thus be divided into twoconsecutive stages, the characters of which are shown in the follow-ing summary:First stage A --z A -- 2~ x AutocatalyticSecond stage A - x 0 A - x Simple unimolecularThree of the six experiments with persulphuric acid solutionssummarised in table I1 were, in fact, the second stages of experi-ments with barium persulphate, which will now be dealt with ingreater detail, Comparison of these with the others shows thatthe presence of precipitated barium sulphate (since there was noother real difference) does not appreciably affect the velocity ofpersulphate decomposition by any kind of contact catalysis.Asimilar conclusion may be drawn from the sodium persulphate solu-tions of table I, one of which (the third) was mixed with theprecipitate beforehand in order to test this question. It maytherefore be concluded safely that the formation of this producthas no such direct effect on the decomposition of barium persulphateitself in the first stage of the action.In table 11, which referred only to persulphuric acid, A and zwere given the corresponding significance, and were equal respec-tively to $A and x - ~ A , where the symbols are used in referenceto the original barium persulphate contents, as in the abovesummary.But they must now be used in this latter sense, andthe equation for the curve, after the complete precipitation of thebarium, must be written dx/dt = (A, -t k A / 2 ) ( A - x).Now, since the whole curve is continuous, it is evident that theequation for the first, or autocatalytic, stage must be such as tobecome identical with that just given at the half-way point, wherex=&A. But it has been shown already that the Ic, of persulphuricacid and the k1 of sodium or potassium persulphates have verydifferent values, so that it might fairly be expected that theconstant (k,) for barium persulphate should differ from k2, andperhaps also from k,. Such proves to be the case, forit can be shown by a graphic method that the initial velocityof the decomposition of the pure barium salt solution, whenit is as yet unmixed with persulphuric acid (when x=O),approximates to dx/dt = 0.0040A.We thus have k3 = 0.0040, whilstk, = 0.0055 and k2 = 0.010, and the catalytic constant k: = 0.163. Itmust therefore be assumed that, in any mixture of two of thesesalts, the appropriate constants will be operative in proportion toTotal S,OB. BaS,08. H,S,Oa. Form of curve.Half-way point x = 3 A = A - x 0 +A PgRSULPHURTC ACID AND ITS SALTS IN AQUEOUS SOLUTION. 2091the amounts present, and that, consequently, the equation for thefirst stage of the barium persulphate action is:dg- A - ~ x X dt - (k3 ~- + k2- + h)( A - w). A - x A - xThis conforms t o the requirements, for the contents of the firstbracket are equal to k, at the starting point, where z=O, and tok, + k A 12 at the half-way point, where x = A 12. It will be shown,also, tha.t it expresses the whole of the experimental results withconsiderable accuracy.It is, perhaps, not superfluous to pointout that, if hydrogen and barium persulphates had the same velocityconstant (if k,=k2), the equation would be the ordinary oneexpressing an autocatalysed unimolecular action, for it would thenbecome d x / d t = (k,+ k z ) ( A - x).By integration of the above differential equat,ion, we obtain anequation which may be writben :1 M(N+x) k( M + N ) = -log, --___t N(M- x)'where M and N are constants in any given experiment, but varywith the initial concentration, and have the values :Such an equation is of but little use for theoretical purposes unlessM and N can be evaluated by independent measurements of thefundamental constants from which they are derived; but we areable to do this in the present case, having'found already E , and kfrom the study of persulphuric acid, and k, from the initial velocityof pure barium persulphate solutions.We are thus enabled tocompare the results calculated from the integrated equation withthose obtained by experiment.The details of one complete experiment with initially neutralbarium persulphate solution are shown in table IV. The valuesof M and N , given at the head of the table, were calculated fromthose of A ; ic, k,, and k,; and the theory of the first stage of theaction may be tested by the constancy of at different 1t N ( h 1 - z )values of t , and also by its agreement with the calculatedvalue of Om4343k(M+N). Also the time is noted (as read fromthe curve) at which x = $ A , that is, the time of the complete pre-cipitation of the barium mlphate.The simple unimolecularcharacter of the decomposition of the persulphuric acid in the second6 x 2092 GREEN AND MASSON DYNAMICS OF THE DECOMPOSITION OPstage is shown by the pract.ica1 constancy of the normal logarithmicfunction, calculated from the observed values of x and t , and thetheory of its dependence on A by a comparison of its mean valuewith that of k,+ k A 12 (compare table 11).TABLE IV.Barium Persulphate. A = 0.2502,First Stage.M = 0.2840, N = 0.0216.t.10"253545505.0.01310.03980.06630.09740'1160M( N + x) l / t log,,-----N( M - x)'0.02260.02080 -02070 *02050.0206Mean constant found .................. = 0.021 0.Calculated value of 0'4343 k(M+N) = 0.0216.Second Stage, after complete precipitation of Ba a t t = 52.5O.t.60"70551001151351552.0.15580.17960.20680-22210.23360'24110-2441l f t - 60 l0g,~~?01558A - x * -0'01260.01350'01320 01370.01350.0125Mean constant found ..................... = 0.0132.Calculated value of 0'4343(rC, +kA/2) = 0-0132.The details of two tests with smaller concentrations of bariumpersulphate may be given more briefly. I n one of these tho valueof A was 0.1288, whence 0*4343k(M + N ) =0*0128 by calculation,and during the first stage of the action (sixty-five minutes) thevalues found for -loglo7 M ( N + 2 ) ranged from 0*0130 t o 0.0134(mean = 0'0132).During the second stage of the same experiment,tho mean uniinolecular constant found was 0*0091 in place of thecalculated value 0.0089. I n the other case, A was 0.0832, whence0*4343k(M + N ) = 0.0093, and the constant found during the firststage (seventy minutes) ranged from 0.0103 t o 0.0112 (mean,0.0109), while the calculated and found unimolecular constants ofthe second stage were 0.0073 and 0*0080. In this case thereforethe numerical agreement was not quite so goad its in those of thestronger solutions.It seems worth while to call attention here to a striking contrastt h(A4-xPERSULPHURIC ACID AND ITS SALTS IN AQIJEOUS SOLTTTION.2093between the persulphate case and that of the decomposition ofcyanates in aqueous solution, which in some respects is very similar(Masson and Masson, Zoc. cit.). Barium cyanate, which precipitatesbarium carbonate, gives a simple unimolecular curve, whilst thecyanates of sodium and potassium, which yield soluble ammoniumcarbonate, give strongly auto-accelerated unimolecular curves.Barium persulphate, which precipitates barium sulphate, givesstrongly auto-accelerated unimolecular curves, whilst the per-sulphates of sodium and potassium, which yield soluble acidsulphates, give simple unimolecular curves. In the former case, itwas proved that ammonium carbonate accelerates the action, whilstin the latter case soluble acid sulphates have no such influence, buttheir hydrogen ions have, when liberated by the precipitation ofinsoluble sulphate.Mixed Ba&m Persulphate and Barium Nitrate.If the latter be added in quantity equivalent to the former (ormore), the barium ions cannot become exhausted by precipitation asbarium sulphate so long as persulphate ions remain, and the wholeaction can be written:BaS,O, + BaN,O, + H,O = 2BaS0, + 2HN0, + SO,.The action therefore does not divide into two distinct stages as inthe case of initially pure barium persulphate, but is markedthroughout its course by continuous precipitation and increase ofhydrogen ion concentration. Hence the auto-catalytic charactermust be also continuous, and this is found to be the case.If A represent the initial concentration of the barium persulphateand B that of the barium nitrate, the composition of the solutionat any subsequent time is such that it contains barium and hydrogenpersulphates and nitrates with the following concentrations :S,O,”=A - x , (NO,’),=B, Ba”=A +B-2x, and (H*)2=z.Thetotal cations or anions (considered as bivalent) are thus alwaysequal to A + B - x.If, as in the case of initially pure barium persulphate, it beassumed that the barium and hydrogen ions are operative in p r sportion to their relative concentrations, while the latter also producetheir special catalytic effect, we have the following diff erentidequation to express the course of the action:+ kx}(A -x), dx- A + B - ~ x X --dt ‘k3 A + B - L& + k2 A + €3 - xwhich, by integration, gives :BIog,A(N+ -- X) M - A - B log,----N ( A - x ) M - d M ( A - 2 2094 GREEN AND MASSON : DYNAMICS OF THE DECOMPOSITION OFwhere M and N are constants in any given experiment, and havethe values:An obvious simplification of the formula results where, as in theactual experiment (table V), the barium persulphate and nitrate aregiven the same initial concent'ration, or B = A .The values ofM and N given a t the head of the table were calculated from thatof A and those of k,, k,, and k , as already determined. In the thirdcolumn are given the found values of the constant:which may be compared with each other as to constancy and alsowith the calculated value of 0*4343k(M+N), given at the end ofthe table.The agreement is fairly satisfactory.TABLE V.Barium Persulphat e and Barium Nitrate in Equimolecular Mixture.B = A =0*1253. M=0-2845. N=0*0217.t. X. K.10" 0 '0062 0.024020 0.0147 0.025530 I 0.0223 0.023945 0.0355 0.022860 0'0457 0.020870 0.0577 0'022975 0-0643 0-021990 0.0791 0.0220105 0,0926 0.0223120 0.101 9 0'0220135 0.1105 0'022.3160 0 -1 200 0.0238195 0,1236 0*0238Mean value of K found ... ... .. , ,. . ... = 0.0229.Calculated value of 0.4343k(V+N) = 0'0217.Barium Persulphate with Added Nitric Acid.Here, as in the case of pure barium persulphate, the action maybe expected to divide itself into two stages, since the barium must betotally precipitated when x = A - x = QA.If B stand for the addednitric acid (reckoned it9 dibasic) or for the initial (H*j2, thequantity of the latter must steadily increase by production ofpersulphuric acid during the first stage, where its vdue is B + x;but from the middle point onwards through the second stage iPERSULPEIURIC ACID AND ITS SALTS IN AQUEOUS SOLUTION. 2095must retain the value B + i A . As in the simple case, the Ba"must have the value A -2x until this becomes nil at the middlepoint, whilst the S,O,// must have the value A - x from first to last.The first stage should therefore show an autocatalytic curve merginginto the simple unimolecular one of the second stage, and therespective differential equations should be :(11.) !!? = {k, + k( B + &A)>( A - x),dtwhich are identical when x = IA.These equations, indeed, follow logically from those already con-firmed for the case of a mixture of barium persulphate and bariumnitrate, for it is obvious that such a mixture, if it initially containsexcess of the former ingredient, must, at a certain point in iBhistory, become converted into a solution of barium persulphate andnitric acid, and subsequently into one of persulphuric acid andnitric acid.There are thus three distinct stages in such an action,and i t seems an unavoidable conclusion that the theory which isquantitatively applicable to the mixtures of the first stage (table V)and also to those of the third (table 111) must apply equally wellto those of the second.Nevertheless, it has been found in a seriesof experiments with barium persulphate and nitric acid in differentproportions that the nitric acid produces initially only about halfthe acceleration indicated in equation I, although it graduallyincreases its effect its the action proceeds, and attains full value asan accelerator when the barium is completely precipitated, afterwhich equation I1 holds well. Without further investigation, itdoes not seem possible to reconcile these observations.The Zn@uence of Sulphates, Produced or Added.As already pointed out, sulphuric acid or acid sulphate is anecessary product of the decomposition of persulphuric acid orpersulphates of the sodium class of metals, and yet there is in thesecases an entire absence of that autocatalysis which is so marked afeature in t,he case of barium persulphate, where the growingacidity is due to persulphuric acid formed by the precipitation ofbarium sulphate.The explanation already suggested is that thenegative ions produced are in reality HSO,' (not SO,"), so thatthere is no appreciable increase in the concentration of H' ions(the true accelerator) unless the conditions are disturbed by pre-cipitation or, to a smaller extent, by the process mentioned in th2096 GREEN AND MASSON : DYNAMICS OF THE DECOMPOSITION OFcase of the magnesium salt,. Briefly, the hypothesis is thatsulphuric acid acts practically as a monobasic acid in these solutions,while persulphuric acid itself acts as a dibasic one.The most direct test of this view, apart from the evidence alreadygiven in support of it, is obtained by studying the velocity of thedecomposition of persulphuric acid and sodium persulphate solu-tions, to which have been added beforehand known quantities ofsulphuric acid, sodium hydrogen sulphate (that is, sodium sulphateand sulphuric acid), or sodium sulphate.According t,o thehypothesis, the velocity coefficient should not be affected by addingeither sodium sulphate or sodium hydrogen sulphate to sodium per-sulphate; sodium hydrogen sulphate should produce but a slightlowering of the coefficient of persulphuric acid by adding Na' ionsto the solution without altering the H' concentration; sodiumsulphate should largely reduce this coefficient by converting free H'into HSO,'; and added sulphuric acid should accelerate in bothcases, but only to the extent due to it as a monobasic acid, or halfas much as the equivalent quantity of nitric acid or of persulphuricacid itself.In all cases the numerical results predicted by thehypothesis can be calculated from a knowledge of the fundamentalcomtants already given, namely, kl = 0.0055 for (Na')2, k,= 0*010for (H'j2, and k = 0.163 forThe results of the experiments performed confirm theseexpectations, with one rather notable exception in the case of theaddition of sodium sulphate to sodium persulphate. Here the uni-molecular constant, although it has at first the normal and expectedvalue of about 0.0055, quickly diminishes until it reaches a steadyvalue, considerably smaller and dependent on the amount of addedneutral su1phat.e.Four tests were made with approximately4-molar-sodium persulphate, conta.ining respectively 0.060, 0.125,O"128, and 0.255 molecule of sodium sulphate. I n each case thecurve showed a similar retardation until about one-fifth of thepersulphate was decomposed, and thereafter, and reckoned fromthis point, a good unimolecular constant was obtained, the respectivevalues being 0-0035, 0.0025, 0.0025, and 0.0020. These resultspoint to some complication, which, as will be shown, is never metwith except in the presence of mixed neutral and acid sulphate, andwhich is perhaps due to a reverse action in which the dissolvedoxygen plays a part'; for this product is the only substance presentwhose quantity is initially nil, and tends, on account of its limitedsolubility, to increase quickly to a maximum.In all the other cases the curves showed steady unimolecularactions, and the found velocity coefficients agreed fairly well withthose calculated in accordance with the hypothesis.Although theaccelerationPERSULPHCTRIC ACID AND ITS SALTS IN AQUEOUS SOLUTION. 2097agreement is not quantitatively exact, it is noteworthy that theresults fully establish the following facts :(1) Addition of sodium hydrogen sulphate produces no markedacceleration, showing that i t does not add H' ions; (2) additionof sodium sulphate to persulphuric acid prodyces a large retardation,which points to a suppression of H' ions; (3) addition of sulphuricacid produces such acceleration as points to the ionisation of abouthalf its hydrogen.The results are summarised in table VI.I n the first columnare given the nature and concentration of the persulphate used. I nthe second, the added sulphate is similarly specified. I n the third,under K (found), is given the experimental unimolecular constant,this being, as in previous cases, the mean of several concordant valuesfound over a large range of action. In the fourth column, underR (calculated), is given the value of k -. + 7c-- + k(H'),,where the ionic symbols refer to the corresponding concentrationsafter allowance for the conversion of all SO, into HS04/ ions. I nthe fifth column, under K (original), is given, for comparison, thevalue the constant would have if the added sulphate produced noeffect whatever.TABLE VI.Tlbe Effects of Added Sulphates.N%' H*' N a + H Na'+H'Sulphate.0 *1338NaHSO,0*1332H,SO,0-3767H,SO40 *1 250Na2S0,0 '1366NaHS0,0 * 0 5 0 8 H,S 0,0 *1194H,SO,0 '1544H,SO,Kfound.C0'00600.01610.03720'01510.03040.03700 04210.0425K:alculated.0.00550.01790-03890'01600.02880'03430.04050-0435Koriginal.0-00550.00550 00550'02930-03030'03010'03080'0309The Effects of Added Alkali.Levi and Migliorini found that alkalis accelerate the persulphatedecomposition, but to a smaller extent than acids. Our experi-ments, however, with persulphates of the first class do not confirmthis.When sodium or potassium persulphate is mixed with thecorresponding alkali in equivalent, or greater, amount, a regularunimolecular curve is obt'ained with a constant which is almostidentical with that characteristic of the pure salt solution. It is,indeed, very slight,ly smaller, which is probably accounted for bythe physical effect of the extra dissolved substance, but there is noevidence of positive or negative acceleration by hydroxyl ions.These, of course, become destroyed as the action proceeds, for the2098 DECOMPOSITION OF PERSULPHURIC ACID, ET C.necessarily neutralise the acid sulphate product, and any suchcatalytic effect would thus continuously diminish, and the curvewould not be that of a simple unimolecular action. It is noteworthythat the normal sulphate which results from this neutralisationdoes not produce any such marked retardation as was observed whenthe same salt was added beforehand to sodium persulphate, so thatit may be concluded that the reaction responsible for that com-plication can occur only in the presence of both normal and acidsulphate, as already mentioned.The results of four experiments are summarised in table VII.The k, values here may be compared with those cited for the puresalts in table I.TABLE VII.Effects of Added AIkaZi.Persulphate.Alkali. k, found.0.1 192Na,S,08 0 -21 92NaOH 0.00510*1185Na,S,O, 0'2236NxOH 0.00510 '1214Na28,0, 0.3434NaOH 0-00490 -0797 K,S,08 0.2040KOH 0-0050The behaviour of barium persulphate when mixed with bariumhydroxide is quite different, and is difficult to reconcile with anygeneral theory. The autocatalytic curve of the pure salt solutionhas been fully explained by the production of persulphuric acid,but here it is evident that neutralisation must occur continuously,and that the precipitation of barium sulphate is accompanied by aprogressive diminution of alkali instead of an increase of acidity.Indeed, the course of the action is followed in practice by alkalimetryinstead of the usual acidimetry. Now, as it has been proved thakhydroxyl ions exert no appreciable catalytic effect in the case ofthe salts of the alkali metals, it seems inevitable that barium per-sulphate, when mixed with sufficient barium hydroxide, should givea continuous simple unimolecular curve with its own velocityconstant (k3). Nevertheless, the curves obtained show a muchhigher initial velocity than corresponds with k,, that is, an initialacceleration by the added alkali, and they also give evidence of afurther acceleration as the alkali subsequently diminishes. We areunable to explain these facts.The Temperature Effect.Experiments were made with sodium persulphate and with per-sulphuric acid a t 70° and 90° for comparison with those at 80°already described. The mean values of the unimolecular coefficientsare given in the following table. In the case of persulphuric acid,it must be remembered that this coefficient is largely dependent oA SIMPLE METHOD OF PREPARING TETRANITROMETHANE. 2099the initial concentration ( A ) , for it has been shown to be the sumof two terms, k,+ k A , whereas in the case of the salt it is a simpleconstant, k,. It appears, however, that the constants at 90° are allabout tenfold those at 70°.TABLE VIII.The Temperature Effect.UniriiolecularSalt. A. coefficients. Temperature.0.125 0*0016 70"0.126 0.0055 80 Na,S,08H2W* 0'124 0'0111 70H28208 0'124 0.0302 80Na2S2OsNa29,0s 0'130 OqOl6l 90H2S208 0'118 0'1035 90UNIVERSLTY OF NELBOURNE