RATE OF REACTION OF BROMINE WITH AQUEOUS FOBMIO ACID. 2715 CCCLXX1.-The Bate of Reaction of Bromine with Aqueous Formic Acid. By DALZIEL ~ W E L L Y N HAMMICK W- KENNETH HUTCHISON, FORMIC acid in aqueous solution is oxidised by each of the halogens to carbon dioxide and halogen acid the reactions in the cases of bromine and iodine proceeding a t rates that make velocity measure-ments possible. An account is now given of a study of the kinetics of the oxidation by bromine. Somewhat similar reactions have been studied by Bugarsky (2. physikul. Chem. 1901 38 561; 1904 48 63) who recognised clearly the disturbing effects due to the products of the reaction to which effects further reference will be made. That the reaction goes to completion in accordance with the equation HC0,H + Br = 2HBr + CO was established in the following manner.A strong solution of bromine in water was contained in an apparatus as described by Richards (ibid. 1902, 41 544) which delivered bromine solution of constant strength. The amount of bromine in one measure (about 15 c.c.) was estimated iodometrically. A mixture of exactly 20 C.C. of a solution of formic acid of known strength 4 measures of bromine water and 20 C.C. of approx. N-hydrobromic acid was kept in a thermostat a t 25" for 3 days. By estimating the residual bromine it was found that 2.23 g.-mols. of formic acid react with 2-24 g.-mols. of bromine. Materials and Nethod.-The bromine prepared from pure potassium bromide contained 99.6% Br and no detectable iodine. The anhydrous formic acid contained 99.7% HC0,H.A Jena glass flask of about 450 C.C. capacity with a narrow neck and ground glass stopper was used as the reaction vessel placed in a thermostat a t 25-00' -J- 0.04". The initial volume of reaction mixture was always 400 C.C. Preliminary experiments established the following points (1) Under the conditions of working light has no appreciable effect on the rate of reaction. (2) The rate of reaction is greatly diminished by the presence of hydrogen- or bromine-ion. Experiments were therefore made to determine the rate of dis-appearance of bromine in solutions containing excess of both formic acid and hydrobromic acid. Quantities of 25 C.C. of the reaction mixture were withdrawn at measured times and discharged into potassium iodide solution.The iodine liberated was then titrated with standard thiosulphate. In all these experiments the titration of the initial quantity of bromine was carried out under similar and FREDERICK ROWLBNDSON S N ~ . 4x* 2716 HAMMICK HUTCHISON AND SNEU THE RATE OF conditions of acidity. But no attempt was made to neutralise the excess of acid in the titrations since the form of the monomolecular velocity coefficient ensures that any proportional error in the titration will be eliminated. Table I shows that the rate of disappearance of bromine follows the monomolecular law k = 2*303/t . log @/(a - z)) where a is the initial titre equivalent to 25 C.C. of reaction mixture and (a - z) is the titre a t time t (mins.). A zero time correction was introduced owing to the time of mixing being rather long compared with the time of reaction.This correction obtained by plotting values of log @/(a - z)} against t and extrapolating back to zero was never very large being generally of the order of - 0-1 min. All the values of k have been computed after the addition or subtraction of the necessary correction thus obtained. TABLE I. CHB~ C H ~ E and initial concentration of bromine = 0.1665 0.278 and 0-0108 g.-mol. per litre respectively. t ............... 0.00 1.82 3.30 4.32 5.68 7.30 11.80 Br titre (c.c.) 27.12 18.69 13-32 10-81 8-18 5-82 2.40 k ............ - 0.205 0.215 0.213 0.212 0.211 0.206 Mean 0-210 Zero time = -0-05 min. Table I1 summarises the results of similar experiments carried out in order t o determine the influence of the concentration of the formic acid on the rate of reaction.The value of the monomolecular velocity coefficient kobs. is the measure of the rate of the reaction, and the consfancy of the quotient kObs./cHCO,H is satisfactory proof that the rate is proportional to the concentration of formic acid. The reaction between bromine and formic acid is therefore of the second order. It remained to investigate the influence of the hydrogen and bromine ions on the rate of reaction. TABLE 11. CHCO~H ............ 0.1409 0.1409 0.2113 0.2818 0.4227 kob. ............... 0.092 0.096 0.146 0.102 0.284 ~ O ~ . / C H C C J ~ H ...... 0.653 0.681 0-693 0.683 0.673 Jakowkin (2. physihl. Chem. 1896,20,19) and others have shown, as a result of partition experiments that bromine in a solution containing excess of bromine ions is present largely as the tribromide ion.The equilibrium constant has been calculated to about 0-063 assuming complete dissociation of the electrolytes involved. The corresponding constant for the CHB~ = 0.1820 g.-mol. per litre. . . . . R = [Br’][Br,]/[Br,’] * (1 REACTION OF BROMIXE WITH AQUEOUS FORMIC ACID. 2717 combination of bromine molecules with chlorine ions is of the order of 0.8. Now in order to study the reaction at different concentrations of hydrogen ion it is necessary to add varying quantities of some strong acid and for this purpose hydrochloric acid appeared most suitable. But sufficient hydrobromic acid must be present not only to maintain the bromine-ion concentration constant but also to outweigh the much slighter influence of the chlorine ion in removing bromine molecules from the solution and so render the disturbing effect of the chlorine ion negligible.Table I11 summarises the results of experiments carried out on these lines. The normality of the hydrobromic acid was 0.1213 throughout and that of the hydrochloric acid never exceeded 0,2540 so that the disturbing effect of the chlorine ion would never be serious. Under " a " are given the activity coefficients of hydro-chloric acid (Lewis and Randall " Thermodynamics," 1923 p. 336) for the total acid concentration; for since coefficients for hydro-bromic acid were not available it was assumed that they would not be very different from those for hydrochloric acid. TABLE 111.CHCO~H = 0.282 g.-mol. per litre. Cmr = 0.1213N. CHCi ( N ) . C(HBr,HCI) ( N ) . a. kOb6. Q x c(HBr.HQ) x ICObr. 0.0oO 0.1213 0.807 0.353 0.0346 0-0252 0.1467 0-798 0.298 0.0349 0.0402 0.1637 0.793 0.269 0.0349 0.0807 0.2020 0.782 0.216 0.0341 0.1794 0.2907 0.769 0.157 0.035 1 0-2540 0.3753 0.763 0.125 0.0346 The constancy of the figures in the last column shows that the rate of reaction is inversely proportional to the active or effective concentration of the hydrogen ion. This is readily explained on the assumption that the ions of formic acid react and not the undissociated molecules. Formic acid is a comparatively weak acid obeying the dilution law so that in the presence of excess of hydrogen ion the concentration of formyl ion is inversely propor-tional to the concentration of the hydrogen ion.It was anticipated that the influence of the bromine ion on the rate of reaction might be accounted for by the removal of bromine molecules as tribromide ions provided that these do not take pad in the reaction. If the expression (eq. 1) for the equilibrium between free bromine molecules bromine ions and tribromide ions is combined with equation 2 which represents the total concen-tration of bromine in the solution (= {Br,}) in terms of the concen-tration of free bromine molecules (= [Br,]) and of tribromide ion 2718 -CK CHISO ON AND SNELL THE RATE OF a relation (eq. 3) is obtained between total bromine free bromine, and bromine-ion concentrations. . . Assuming now that the reaction is due to the free bromine molecules, it is found that the reaction velocity should be proportional to their concentration at any instant and that the monomolecular velocity coefficient should be related to the bromine-ion concentration by the equation k ~ b .= K2/(l + l/Kl[Br‘]) . . . . (4) Two methods are available for testing these conclusions. The h t of these the results of which are in Table IV consists in keeping the hydrogen-ion concentration constant by the introduction of a sufficient quantity of hydrobromic acid which also supplies the minimum excess of bromine ion necessary to give the mono-molecular velocity coefficient and then varying the bromine-ion concentration by the addition of potassium bromide. TABLE IV. C H C ~ H = 0.278 g.-mol. per litre. 0-OOO 0-1010 0.050 0-151 0.101 0.202 0-140 0.251 0-202 0.303 0.303 0.404 CgBr ( N ) .C(HBrtKBr)(N). The value of the constant R (eqs. 1 and 4) was obtained by plotting the reciprocal of the monomolecular velocity coefficient against the corresponding bromine-ion concentration and for this it was assumed that all the electrolytes were completely diisociated. A good straight line was obtained (compare eq. 4) and from the point where this cuts the Br’ axis the value of K can be deduced. The constancy of the numbers in the last column shows that for the value of 0.110 for K the figures agree well with the theory, although this is a value considerably higher than that (0.065) found by Jakowkin (loc. cit.). It was realised that a possible reason for the discrepancy may be the assumption made that the electrolytes are completely dis-sociated; whereas the activity of the bromine ion varies quite considerably over the range of concentration used.Accordingly, in the second method of studying the effect of the bromine ion a correction has been made for the activity. Here the concentration of the hydrobromic acid was vaned and the corresponding mono-molecular coefficients were determined. The simple relation tha REACTION OF B R O ~ E WITH AQUEOUS F O ~ C ACID. 2719 was shown to exist between the effective concentration of the hydrogen ion and the velocity of the reaction (Table III) was then employed to eliminate the influence of the changing hydrogen-ion concentration. Table V contains the results of the experiments carried out in order to test this method of attack.The second column gives the activity coefficients for hydrochloric acid (loc. cit.) which as before, were assumed to be not very different from those for hydrobromic acid. The pairs of values of kob. given in the fourth column are TABLE V. C H ~ H = 0.278 g.-mol. per Iitre. K = 0.070. 8 = b b a . Q x CHBr (1 + 1/Q x kOba.CHBr). CHBr ( N ) . a. a x e€tBr(N). kod. a x koba~mr. 0.0555 0.848 0.0471 ;::$} 1.014 0.0478 0.1110 0.820 0-091 1 ~ ~ ~ ~ ) 0.398 0-0362 0.1665 0.793 0.1320 ~ ~ ; ~ } O - Z I l 0.0280 0.2220 0-780 0.1730 :::%36)0-140 0.0242 0.2775 0.771 0.2140 :::;:} 0-094 0.0201 8 . 0*0800 0.0833 0-0808 0.0836 0.0816 the results of pairs of experiments under identical conditions. In the first of each pair the initial concentration of bromine was about 0.010 g.-mol.per litre whilst in the second it was about 0.005 g.-mol. per litre. The mean of each pair (fifth column) was used in the subsequent calculations. The activity of the hydrobromic acid is given in the third column. The product of this activity and the corresponding monomolecular velocity coefficient giva (sixth column) the corrected values of kOb. The reciprocals of these corrected values were plotted against the activities of the hydro-bromic acid or effective concentrations of the bromine ion and the value of 0.070 for Kl was deduced from the resulting straight line.* The constancy of the numbers in the seventh column shows that for this value of K the results of the experiments are in good agreement with the theory.It is necessary from the point of view of this treatment that the activity of the tribromide ion should be considered equal to its concentration. This assumption is justified by the fact that the concentration of the tribromide ion is always low. And further the two experiments of each pair agreed well * If the value of R is calculated from the results in Table V (as it was in the case of the results in Table IV) without introducing the activities of the ions the resulting figure is 0.105. This is in good agreement with the value 0-110 obtained from Table IV 2720 RATE OF REACTION OF BBOXINE WTTH AQUEOUS FORMIC ACID with each other in every case although the initial concentration of bromine and therefore of tribromide ion was halved in the second of the two.For the purpose of accurate comparison with Jakowkin’s results ( b c . cit.) it was necessary to recalculate using activity coefficients the value of K from his figures. He gives no results for cases where the concentration of bromine was less than 0.04 g.-mol. per litre and the value of the constant tends to increase with increasing dilution of the bromine. For this reason only those figures were considered which refer to the most dilute bromine solutions and to concentrations of potassium bromide of the same order as those of hydrobromic acid used in the present investigation. The activity coefficients for potassium bromide were taken as identical with those for potassium chloride (Lewis and Randall, op. cit.). The mean value of K, in terms of the effective concen-tration or activity of bromine ion was then calculated to be 0.048 as compared with 0.070 the value deduced from the results in Table V.It follows that like those in Table IVY the results in Table V agree in giving a figure for K considerably higher than that generally accepted for pure aqueous solutions. Summary and Discussion. The reaction between bromine and formic acid has been studied in dilute aqueous solution using the Ostwald isolation method. It is shown that formic acid is completely oxidised to carbon dioxide. The reaction is of the second order but the rate is retarded by the hydrobromic acid produced. From a study of the separate effects of the hydrogen and bromine ions it is deduced that the reaction takes place between the formyl ions and free bromine molecules i.e. those molecules of bromine which are not combined with bromine ions to give the complex ions Br3’. It is necessary to give to the constant for the equilibrium between bromine mole-cules bromine ions and tribromide ions a value considerably higher than that due to Jakowkin. Jakowkin’s experiments however, were performed with concentrations of bromine considerably higher than those used in the present investigation and his constants show it regular increase with increasing dilution of bromine. THE BALLIOL AND TRINITY LABORATORIES, OXFORD. [Received August 28th 1925.