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On the “Abnormal” Decomposition Potentials of Aqueous Solutions of Halogen Acids Yi Liang* and Jie Chen Department of Fine Chemical Engineering, Wuhan Institute of Chemical Technology, Wuhan, Hubei 430074, PRC Songsheng Qu Department of Chemistry, Wuhan University, Wuhan, Hubei 430072, PRC
According to textbooks of physical chemistry (1–3), the minimum voltage required to produce continuous electrolysis of an electrolyte is called the decomposition potential (εd) of this electrolyte. This minimum voltage can be determined by means of a setup already described (1, 3, 4 ). Ideally, εd is equal to the reversible emf (εr) for the corresponding cell (or the reversible decomposition potential of the electrolyte), but in general the predicted potential (εr) fails to agree with that observed ( εd). The case of aqueous solutions of halogen acids is just one example of this type of inharmony (1, 3, 4 ). In practice εd follows as (3–7) εd = εr + ηa + ηc + IR
εd ≥ εr r
(3)
where the inequality applies to net electrode processes (a net current flows) and the equality to reversible ones (no net current flow). Equation 3 has been accepted by almost all textbooks (1–8). For most electrolytes in aqueous solutions, decomposition potentials (1, 3, 4 ) obey eq 3. However, for aqueous solutions of halogen acids (hydrochloric, hydrobromic and hydriodic), the values of εd (Table 1) (1, 3, 4 ) disobey eq 3 but obey the relation εd < ε r
(4)
It is interesting that many textbooks (2, 3) give hydrochloric acid, whose εd is “abnormal”, as an example to explain the concept of decomposition potential. How do we explain the abnormal experimental results? Apparently, eq 4 disobeys both eq 3 and the second law of thermodynamics. From ther*Corresponding author. Present address: National Laboratory of Biomacromolecules, Institute of Biophysics, Academia Sinica, Beijing 100101, PRC. Email:
[email protected].
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2H+ + 2Cl {
(5)
and the reaction of chlorine with H2O is Cl2( p2) + H2O
H + + Cl{ + HClO
(6)
Therefore, the overall cell reaction becomes H2( p1) + 2Cl2( p2) + H2O
(2)
Here, ∆ ϕir and ∆ϕeq are the nonequilibrium reduction electrode potentials and the equilibrium ones of the anode (or cathode), respectively. The three ηa, ηc , and IR are positive or tend to zero (3– 7). Therefore, we obtain ir
H2( p1) + Cl2( p2)
(1)
due to both concentration polarization and activation overpotential. IR is the ohmic potential difference necessary to overcome the cell’s internal resistance (R), and ηa and ηc are the overpotentials of the anode and cathode, respectively, which can be calculated by the equation below (3–8). η = |∆ϕir – ∆ϕeq|
modynamic viewpoints it is anticipated that the electrical energy required to carry out a nonspontaneous reaction (e.g., the electrolysis of HCl solution) must be larger than the Gibbs free-energy increase accompanying the change, in order to overcome the irreversibility; but in the case of aqueous solutions of halogen acids, the situation is reversed. Our point is that the disproportionation reactions of halogens (Cl2[aq], Br2[aq], and I2[aq]) in aqueous solutions result in the abnormal εd of aqueous solutions of halogen acids. Consider the reversible cell Pt, H2( p 1)|HCl(a)|Cl 2( p2), Pt. In this cell the net cell reaction is
3H+ + 3Cl{ + HClO (7)
According to the thermodynamics of reversible cells, we have ∆rGm,5 = {2 Fεr
(8)
∆rGm, 6 = {R T ln K a,6
(9)
∆ rGm, 7 = {2Fεr′
(10)
Here, ∆ rG m,5, ∆rGm,6, and ∆ rG m, 7 are the standard molar Gibbs free-energy changes of reactions 5, 6, and 7, respectively, Ka,6 is the activity equilibrium constant of reaction 6, and εr′ is the apparent reversible emf of the above cell with the disproportionation reaction of chlorine. The implications of reaction 6 can be explained in simpler terms: namely, that as chlorine is partially converted to HClO and chloride ion is generated, use of the Nernst equation for just the anode reaction (2Cl{ → Cl2 + 2e{ ) reveals that the potential of this half-reaction will be more negative than if conditions of 1 mol L{1 and 1 atm are assumed. The expected concentration of hypochlorous acid in a saturated aqueous solution of chlorine is 0.030 mol L{1 and independent of the rate of electrolysis (9). From the equation ∆rGm, 7 = ∆rGm, 5 + ∆rGm, 6
(11)
we easily prove that εr′ = εr + (RT /2F ) ln K a,6
(12)
For the reversible cell composed of Br2(aq) (or I 2[aq]) and H2(g), eq 12 can be deduced by similar methods. Thus the
Journal of Chemical Education • Vol. 76 No. 3 March 1999 • JChemEd.chem.wisc.edu
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value of εr′ can be calculated from eq 12 using the experimental data of εr (1, 3, 4) and K a,6 (9). Clearly, all overpotentials would need to have been overcome, and extremely low rates of decomposition would have had to be measured to determine the value of εr . The results of the determination of the apparent reversible emf ’s of three halogen acids are given in Table 1. It can be seen from Table 1 that, provided we consider the disproportionation reaction, the values of εd of these halogen acids in aqueous solutions obey the relation εd > εr ′
(13)
Equation 13 is certainly in accord with eq 3. Thus the “abnormal” behavior of decomposition potentials of halogen acids in aqueous solutions disappears. Furthermore, the values of ( εd – εr′) calculated by this method are in agreement with literature values of (ηa + ηc) (10). Therefore, the reliability of the point above concerning the abnormal decomposition potentials of halogen acids in aqueous solutions should be considered as proved. The experimental results also mean that the electrolysis of halogen acids in aqueous solutions is a complex process and that the real composition of the solution must be considered in predicting the decomposition potential of halogen acids in aqueous solutions (1, 3, 4). For instance, whereas the decomposition potential of 1 mol L{1 hydrochloric acid is 1.31 V, the potential increases as the acid is diluted, eventually reaching a value of 1.7 V. From this it may be concluded that, although in the more concentrated solutions the products of electrolysis are hydrogen and chlorine, in dilute solutions they are hydrogen and oxygen (1, 4). The “abnormal” decomposition potential of ZnBr2 solution (1, 3) can be explained similarly. Conclusion We suggest that the disproportionation reactions of halogen acids in aqueous solutions are responsible for their “abnormal” decomposition potentials and that textbooks should preferably give sulfuric acid (H2SO4) as an example explaining the concept of εd. Evidently our explanation needs to be substantiated by precise determinations of decomposition potentials of halogen acids in aqueous solutions.
Table 1. Values of ed , er , and er 9 in Aqueous 1 M Halogen Acids ε – ε / εd – εr ′/ Electrolysis ε /V ε / V εr ′/ V d r Acid Ka , 6 / V d r V V Products HCl H 2 + Cl 2 1.31 1.37 4.2 × 10{ 4 1.27 { 0.06 0.04 HBr HI
{9
H 2 + Br 2
0.94 1.08 7.2 × 10
0.84
{ 0.14
0.10
H2 + I2
0.52 0.55 2.0 × 10{1 3 0.18
{ 0.03
0.34
N OTE: At room temperature with Pt electrodes. εd is the decomposition potential; εr is the reversible emf; K a,6 is the activity equilibrium constant of reaction 6; and εr′ is the apparent reversible emf of the cell with the disproportionation reaction of the halogen.
Acknowledgments We wish to thank Shenglu Kuang and Yuanxin Wu in Wuhan Institute of Chemical Technology for their helpful discussions of several aspects of this paper. Literature Cited 1. Maron, S. H.; Lando, J. B. Fundamentals of Physical Chemistry; Macmillan: New York, 1974; pp 599–613. 2. Adamson, A. W. A Textbook of Physical Chemistry, 3rd ed.; Academic: Orlando, 1986; pp 522–525. 3. Fu, X.; Shen, W.; Yao, T. Physical Chemistry Vol. 2, 4th ed.; Chinese Higher Education Press: Beijing, 1990; pp 658–667 (in Chinese). 4. Glasstone S. An Introduction to Electrochemistry; Van Nostrand: New York, 1942; pp 435–444. 5. Atkins, P. W. Physical Chemistry, 3rd ed.; Oxford University Press: Oxford, 1986; pp 790–803. 6. Moore, W. J. Basic Physical Chemistry; Prentice-Hall: Englewood Cliffs, NJ, 1983; pp 424–434. 7. Antropov, L. I. Theoretical Electrochemistry; Mir: Moscow, 1977; pp 322–331. 8. Moore, W. J. Physical Chemistry, 5th ed.; Longman: London, 1972; pp 553–564. 9. Cotton, F. A. Advanced Inorganic Chemistry, 5th ed.; Wiley: New York, 1988; p 564. 10. Lange’s Handbook of Chemistry, 11th ed.; Dean, J. A., Ed.; McGraw-Hill.: New York, 1973; pp 6:17–6:18.
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