Hydrochloric acid, activity coefficient

For this calculation it is assumed that both the acid and the base are completely dissociated and the activity coefficients of the ions are unity in order to obtain the pH values during the course of the neutralisation of the strong acid and the strong base, or vice versa, at the laboratory temperature. For simplicity of calculation consider the titration of 100 mL of 1M hydrochloric acid with 1M sodium hydroxide solution. The pH of 1M hydrochloric acid is 0. When 50 mL of the 1M base have been added, 50 mL of unneutralised 1M acid will be present in a total volume of 150 mL. 

Thomas and Long488 also measured the rate coefficients for detritiation of [l-3H]-cycl[3,2,2]azine in acetic acid and in water and since the rates relative to detritiation of azulene were similar in each case, a Bronsted correlation must similarly hold. The activation energy for the reaction with hydronium ion (dilute aqueous hydrochloric acid, = 0.1) was determined as 16.5 with AS = —11.3 (from second-order rate coefficients (102At2) of 0.66, 1.81, 4.80, and 11.8 at 5.02, 14.98, 24.97, and 34.76 °C, respectively). This is very close to the values of 16.0 and —10.1 obtained for detritiation of azulene under the same condition499 (below) and suggests the same reaction mechanism, general acid catalysis, for each. 

If, for example, a mixture of ethanol and water is distilled, the concentration of the alcohol steadily increases until it reaches 96 per cent by mass, when the composition of the vapour equals that of the liquid, and no further enrichment occurs. This mixture is called an azeotrope, and it cannot be separated by straightforward distillation. Such a condition is shown in the y — x curves of Fig. 11.4 where it is seen that the equilibrium curve crosses the diagonal, indicating the existence of an azeotrope. A large number of azeotropic mixtures have been found, some of which are of great industrial importance, such as water-nitric acid, water-hydrochloric acid, and water-alcohols. The problem of non-ideality is discussed in Section 11.2.4 where the determination of the equilibrium data is considered. When the activity coefficient is greater than unity, giving a positive deviation from Raoult s law, the molecules of the components in the system repel each... 

The mean ionic activity coefficients of hydrobromic acid at round molalities (calculated by means of Equation 2) are summarized in Tables XI, XII, and XIII for x = 10, 30, and 50 mass percent monoglyme. Values of —logio 7 at round molalities from 0.005 to 0.1 mol-kg-1 were obtained by interpolating a least squares fit to a power series in m which was derived by means of a computer. These values at 298.15° K are compared in Figure 2 with those for hydrochloric acid in the same mixed solvent (I) and that for hydrobromic acid in water (21). The relative partial molal enthalpy (H2 — Hj>) can be calculated from the change in the activity coefficient with temperature, but we have used instead the following equations ... 

The activity coefficients of hydrobromic acid in the mixed solvents are lower, as expected, than those in water (20). Hydrobromic acid completely dissociates in the mixed solvents (e = 49.5 at 298.15° K for the 50 mass percent monoglyme) under investigation. Figure 2 clearly indicates that at a particular molality, the stoichiometric activity coefficient of hydrochloric acid is lower than that of hydrobromic acid in the same mixed solvent, and the heat capacity changes (Cp — Cp) also suggest that there are no ion-pair formations. 

It is worthwhile to discuss why the mass-action law on concentration basis (moles/litre) is plausible. It is beyond doubt that it is not always valid. The concentration 5.5 M of saturated aqueous sodium chloride indicates the solubility product 30 moles2/litre2. If an equal amount of such a solution is added to 12 M hydrochloric acid, the concentration of Na+ is 2.75 M and of Cl- (12 + 5.5)/2 = 8.75 M. Their product 24.06 M2 is distinctly below the solubility product, but nevertheless, more than 80 percent of the NaCl present crystallizes out. It would be to short-circuit this paradox to speak about the mass-action law on activity basis. The introduction of activity a as the product a =/Cof the activity coefficient/and the concentration is a tautological trick to keep the mass-action law valid, and it is more fruitful to try to explain why/varies more dramatically in some cases than in others. 

For the purpose of exact calculation of the liquid junction potential according to the last mentioned equation the activity coefficient of the hydrogen or chloride ions would have to be known. As their value is unknown it is assumed that their ratio is equal to the ratio of the mean activity coefficients of hydrochloric acid, or in other words ( +)2/( +)i — (a+)2l(a )v Then the equation (VI-28) will be written in this form ... 

Equation (47) was suggested for the first time by Bredig and Ripley [202]. In order to establish it unambiguously, it is necessary to carry out experiments at a constant ionic strength since feH and kHX are influenced by salt effects. Studies in the presence of halides at a constant ionic strength have never been done. Other approaches have been used instead. Albery and Bell [200] measured hydrolysis rates of ethyl diazoacetate in moderately concentrated perchloric acid and hydrochloric acid solutions. Rates in hydrochloric acid were faster than those in perchloric acid at the same stoichiometric concentration. In order to verify the dependence on the chloride ion concentration, it was assumed that rates of the reaction without participation of chloride (first term in eqn. (47)) are the same in perchloric acid and hydrochloric acid if the H0 values are equal. Activity coefficients were introduced in eqn. (47) as follows ... 

Activity coefficient ratios in the second term were approximated by known values of the square of the mean activity coefficient of HC1, and it was shown that the rate increase in hydrochloric acid (in comparison to perchloric acid at the same h0) depends on the first power of the chloride ion concentration. 

TABLE XLIII. MEAN ACTIVITY COEFFICIENTS OF HYDROCHLORIC ACID FROM E M.F. MEASUREMENTS AT 25°... 

Utilize these data to calculate the activity coefficients of hydrochloric acid at the several concentrations. 

Since the hydrochloric acid may be regarded as being completely ionized, ch+ and Ccr may each be taken as equal to chci, the concentration of this acid in the cell further, the product of/h+ and/cr is equal to/nci, where /hci is the mean activity coefficient of the hydrochloric acid. It follows, therefore, that the quantity aH+Ocr, which is equal to (cH ccr)/iV/cr, may be replaced by chci/hci/h" upon inserting this result in equation (9) and rearranging, it is found that... 

FIGURE 2-3 Activity coefficients calculated by the limiting Debye-Huckel equation (dotted lines) and those observed experimentally. Left, electrolytes of three charge types in water. Right, hydrochloric acid in water-dioxane mixtures with bulk dielectric constants as indicated. Adapted from Homed and Ow . )... 

Mean activity coefficients have been evaluated for hydrochloric acid by potential measurements in alcohols. The salt-effect activity coefficient (left) and its product with the transfer activity coefficient (right) are shown in Figure 4-1. The values of are lower than would be calculated from the appropriate modification of the Debye-Hiickel equation (2-21) applied in the usual way to account for interionic interactions. The low values result from significant ion pairing due to the low dielectric constant. Thus, 0.1 M hydrochloric acid in 95% ethanol is about half in the form of ion pairs rather than being completely dissociated. As shown in Figure (4-1), at low concentrations the salt-effect activity coefficients approach unity, as they must by definition, whereas at moderate concentrations they are somewhat less than unity. On... 

The values plotted in Figure 2 display the expected linear variation with molality of hydrochloric acid at constant ionic strength. The intercept measures the trace activity coefficient, yHci ", the limit of y in pure (acid-free) seawater. At 25°C, ynci " = 0.731 as compared with 0.728 in... 

Figure 2. Variation of the activity coefficient of hydrochloric acid with molality in seawater I at a constant ionic strength of 0.66...

Table IV. Trace Activity Coefficient of Hydrochloric Acid in Seawater for Cell A)...

When it is not possible to make accurate measurements of the partial vapor pressure of the solute at low concentrations, such as would be necessary to obtain pl/Nf, an alternative procedure can sometimes be adopted. Thus, if the activity at any composition of the solute is known from other measurements, such as those described below, the constant k in equation (38.2) can be evaluated by means of the vapor pressure of the solute in the same solution. The method has been utilized to determine the activities and activity coefficients of hydrochloric acid in aqueous solution. ... 

This expression provides a method for evaluating the mean ionic activity coefficient 7 in a hydrochloric acid solution of molality m from a measurement of the E.M.F., i.e., E, of the cell described above it is necessary, however, to know the value of , the standard e.m.f. For this purpose the data must be extrapolated to infinite dilution, and the reliability of the activity coefficients obtained from equation (39.58) depends upon the accuracy of this extrapolation. Two main procedures have been used for this purpose, but both are limited, to some extent, by the accuracy of b.h.f. measurements made with cells containing very dilute solutions. ... 

It will be seen in the next chapter, that by one form of the Debye-Hiickel theory the variation with the molality of the mean activity coefficient of a uni-univalent electrolyte, such as hydrochloric acid, is given by... 

Although the method described above has referred in particular to solutions of hydrochloric acid, it can be employed, in principle, to determine the activity coefficient of any suitable electrolyte. The essential requirement is a cell in which each of the two electrodes is reversible with respect to one of the ions of the electrolyte (cf. 45a) for example, if the electrolyte is then the cell can be represented formally by... 

Determine the mean ionic activity coefficients of the hydrochloric acid in the various solutions. 

Combine these data with the results obtained in Exercise 6 to determine the mean activity coefficient of the hydrochloric acid at molalities of 0.05, 0.1, 0.5 and 1.0 at 25 C. 

The e.m.p. s of the cell with transference Ag, AgCl(s) 0.1 N HCl HCl(c) AgCl(5), Ag at 25 C and the transference numbers of the hydrogen ion in the hydrochloric acid solution of concentration c mole liter , are given below [Shed-lovsky and Macinnes, J. Am. Chem. Soc., 58, 1970 (1935) Longsworth, ibid. 54, 2741 (1932)]. Utilize the data to calculate the activity coefficients of hydrochloric acid at the various concentrations. 

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