CC BY
27
UDC 547.541
THE ELECTROLYTIC DISSOCIATION OF METHYL DERIVATIVES OF
SUCCINIC ACID
E.Kvaratskhelia and R.Kurtanidze
R.Agladze Institute of Inorganic Chemistry and Electrochemistry, Iv. Javakhishvili Tbilisi State University 11 Mindelyst., 0186 Tbilisi, Georgia E-mail: [email protected], [email protected]
Using the authors' suggested methods, the values of dissociation degrees of separate steps (including "partial" dissociation degrees of the second step), concentrations of various ionized and non-ionized forms, activity coefficients of hydrogen ions and mono and dianions in the dilute (0.0001-0.01M) solutions of methyl derivatives of succinic acid: methyl succinic, DL-1,2-dimethylsuccinic and meso-1,2-dimethylsuccinic acids have been calculated. Concentration intervals ofpredominance of various charged and uncharged substances in the dilute solutions of all the acids mentioned above have been identified. Simple empirical equations for fast approximate calculation of the dissociation parameters have also been suggested. Keywords: weak organic acids, dissociation constant, dissociation step, hydrogen ions concentration, equations
1. INTRODUCTION
Succinic acid and its various derivatives are widely used in the organic synthesis and polymer industry and actively involved in the biologically important Krebs cycle. Many useful properties of these acids are directly connected with interesting peculiarities of these acids' behavior in the solutions and, in particular, with regularities of their electrolytic dissociation. The paper focuses on the analysis
of regularities of the electrolytic dissociation of methylsuccinic, DL-1,2-dimethylsuccinic and meso-1,2-dimethylsuccinic acids in their dilute (0.0001-0.01M) solutions through the use of a new method of the establishment of dissociation parameters of weak multi-basic organic acids by "overlapping" equilibriums previously described by authors[1-4].
Table 1. The dissociation constants of methyl derivatives of succinic acid
Acid Ki K2 Reference
Methyl succinic 7.413x10-5 2.291x10-6 [5]
DL-1,2-Dimethylsuccinic 1.175x10-4 1.000x10-6 [6]
meso-1,2- Dimethyl 1.698x10-4 4.365x10-6 [6]
succinic
2. THE EQUATIONS
All acids analyzed in the paper are vivid values of dissociation constants of the acids examples of weak dibasic organic acids with presented in Table 1. "overlapping" equilibriums. Evidence to this are
Regularities of the dilution for both with the effect of "overlapping" equilibriums dissociation steps of weak dibasic organic acid may be expressed by the following equations:
K c(— -—) — [1-]c xi -x2 J7
K i = —j-Fi =---Fi =-Fi (1)
1 -ai i -ai c - xi
ca2(a1 + a2) a—2(1 + a2)c x (x1 + x2)
K 2 =---F2 =-1-—-F2 =---F2 (2)
—2 1 —2 xi x2
where Ki and K2 are the thermodynamic and x2 are contributions of the first and second
dissociation constants for first and second steps to the [H+] value ([H+]=x1+x2), where c
steps, a1 and a2 are the usual degrees of is the total (analytical) concentration of acid,
dissociation for these steps, a2 is the "partial" F1and F2 are the quotients of the activity
degree of dissociation for the second step, x1 coefficients:
Fi =
fH + fHA-f,
H 2 A
(3)
F =
fH + fA1 f,
HA-
(4)
According to the equations (1) and (2), the ai, successively by iterative solution of the a2, a2, x1 and x2 values may be evaluated following equations:
a1 =
K
+.
cFi \
/ \ 2
cF
+ 4
^ 2 K ^ —22 + 1
i
V
cFi
j
(5)
—2 =-
1
2
K
cF
2
+ —
+ .
2
cF
2
+ —
4 K— cF,\
(6)
' 1
a2 = — 2 2
'l K 2 ' 1 +-—
V aicF2 j
+
i
2
K2 2 1 + ——
V aicF2 j
+
4 K
a1cF2
(7)
X, —
k,
F V
i \2 Kl
V F1 y
+ 4
X2 +
Kl c
F
i y
(8)
X2 —
Kl
V F2
+ x
+
y
Kl
V F2
+ x
+
y
4 K 2 xL F
(9)
Using the above mentioned dissociation parameters, we can determine the equilibrium concentrations of hydrogen ions, mono and dianions and undissociated acid molecules;
[ H+] = c(a1 +a2) = ca1(1 + a2) = x1 + x2 (10)
[HA ] — c(aL-a2) — ca1(1 -a2) — xL -x [A ] — ca2 — caxa^ — Xl
(11) (12)
[ H2 A] — c(1 -aL) — c
aa a2
V a2 y
c Xi
(13)
In considering the equations above, we can formulate conditions for equality of concentrations of the ionized and non-ionized forms:
[ H+] — [ H 2 A]: ai —
c — 2 x, Xl
1 -a
2 a2 + 2
[HA" ] — [H2 A]: a, — 1 + 1
2 2 - a0
(14)
(15)
(16)
c — 2xL - x2 (17)
[A ] — [H2A]: a, — 1 -«2 —
a2 +1
c — x, + x2
[ A2" ] — [ HA~ ]:aL — 2a2
a2 — 0.5
(18)
(19)
(20) (21)
x, — 2 Xl
(22)
2
2
1
1
Pursuant to these conditions of the concentrations equality, the areas of dominance of mono and dianions and undissociated acid molecules may be identified.
The values of the activity coefficients can be approximated by the Debye-Huckel equation:
lg f =
z,2 a41 1 + a,B4~I (23)
where ai is the cation-anion distance of closest approach, A and B are constants depending on properties of water at a given temperature, and zi is the charge of ion. The ionic effect is
I = c(a1 + 2a2) = ca1 (1 + 2a2) = x1 + 2 x2
. The values of ai, A and B at 25°C were taken from [7]. The activity coefficient of undissociated acid is assumed to be single.
3. THE RESULTS AND DISCUSSION
Tables 2-4 presents the a1, a2, a2 and pH values for the dilute solutions (0.0001-0.01M) of analyzed methyl derivatives of succinic acid.
Table 2. The values of the dissociation parameters for the dilute solutions of methyl succinic acid at 25°C
Acid concentration, M «1 «2 «2 pH
0.0001 0.5701 0.02199 0.03857 4.231
0.0002 0.4548 0.01139 0.02504 4.035
0.0004 0.3515 0.00585 0.01665 3.851
0.0006 0.2989 0.00396 0.01323 3.747
0.0008 0.2653 0.00299 0.01129 3.676
0.001 0.2414 0.00241 0.00998 3.621
0.002 0.1783 0.00123 0.00690 3.454
0.004 0.1302 0.00063 0.00482 3.292
0.006 0.1080 0.00042 0.00393 3.199
0.008 0.0944 0.00032 0.00340 3.133
0.01 0.0850 0.00026 0.00304 3.083
The comparison of the a2and a2values shows that the values of the "partial" degree of dissociation (which more correctly characterize the completeness of dissociation at the second step) exceed appreciably those of the usual degree of dissociation (especially in case of the low K1 values and higher acid concentrations).
With the help of the equations (14)-(22), the areas of predominance of various charged and uncharged forms in the dilute solutions of analyzed methyl derivatives of
succinic acid have been determined. The calculations show that the monoanion concentration exceeds the [H2A] value when c < 0.0001M (methyl succinic acid) and c < 0.0003M (DL-1,2-dimethylsuccinic and meso-1,2-dimethylsuccinic acids). ). In all the cases
above, the inequalities: a1 >■
1 -a
2
a >
1
2 + an
and c < 2 x + x2 are carried
out.
Table 3. The values of the dissociation parameters for the dilute solutions of DL-1,2-dimethylsuccinic acid at 25°C
Acid concentration, M ai a2 a2 pH
0.0001 0.6487 0.01007 0.01552 4.185
0.0002 0.5312 0.00514 0.00968 3.975
0.0004 0.4192 0.00262 0.00625 3.779
0.0006 0.3600 0.00177 0.00490 3.671
0.0008 0.3215 0.00133 0.00415 3.596
0.001 0.2937 0.00107 0.00365 3.539
0.002 0.2193 0.00055 0.00249 3.367
0.004 0.1614 0.00028 0.00173 3.201
0.006 0.1343 0.00019 0.00140 3.106
0.008 0.1177 0.00014 0.00121 3.026
0.01 0.1062 0.00011 0.00108 2.988
Table 4. The values of the dissociation parameters for the dilute solutions of meso-1,2-dimethylsuccinic acid at 25°C
Acid concentration, M ai a2 a2 pH
0.0001 0.7101 0.04056 0.05712 4.827
0.0002 0.5947 0.02139 0.03597 3.915
0.0004 0.4783 0.01111 0.02323 3.715
0.0006 0.4146 0.00754 0.01819 3.604
0.0008 0.3723 0.00573 0.01538 3.528
0.001 0.3415 0.00462 0.01353 3.470
0.002 0.2575 0.00237 0.00921 3.295
0.004 0.1911 0.00122 0.00637 3.127
0.006 0.1595 0.00082 0.00517 3.031
0.008 0.1401 0.00063 0.00446 2.964
0.01 0.1266 0.00050 0.00399 2.912
Areas of prevailing [H+] values in comparison with the [H2A] values are as follows: c < 0.0002M (methylsuccinic acid), c < 0.0003M (DL-1,2-dimethylsuccinic acid) and c < 0.0004M (meso-1,2-dimethylsuccinic acid). In all the cases above, the inequalities:
1 -a2 1
a >-1 , a >-r and c < 2 x1 + x2
2 2 + a0
To conclude, in considering the comparative complexity of calculations made with the help of the equations (5)-(9), we also suggest simple empirical equations for prompt approximate identification of the values of usual and "partial" degrees of dissociation and pH in the dilute solutions of all analyzed derivatives of succinic acid.
are carried out.
Methylsuccinic acid
a1 = 0.018156c
(up to c = 0.002M)
-0.375
(24)
a2 = 3.177 x 10-6 c_0'96 (25)
(up to c = 0.01M)
a2 = 1.7498 x 10-4 c "0 585 (26)
(up toc = 0.002M)
pH = 1.795 - 0.606lg c (27)
(up to c = 0.01M)
DL-1,2-Dimethylsuccinic acid
a1 = lg(0.16827c -0 354) (28) (up to c = 0.001M)
a2 = 1.30317 x 10-6 c"0 972 (29)
(up to c = 0.01M)
a2 = 4.57088 x 10-5 c "0632 (30)
(up to c = 0.002M)
pH = 1.595 - 0.645lg c (31)
(up to c = 0.01M)
meso-1,2-Dimethylsuccinic acid
a = lg(0.17498c -0365)(32)
(up to c = 0.001M)
a2 = 6.85488 x 10-6 c "0 943 (33)
(up to c = 0.01M)
a2 = 1.72584 x 10-4 c "a628 (34)
(up toc = 0.002M)
pH = 1.499 - 0.655lg c (35)
(up to c = 0.01M)
REFERENCES
1. Kvaratskhelia E. and Kvaratskhelia R. The Degrees of Dissociation of Weak Multibasic Organic Acids". J. Solution Chem, 2007, vol. 36, no. 6. pp. 787792,
2. Kvaratskhelia E.and Kvaratskhelia R. The Electrolytic Dissociation of Mellitic Acid. J. Solution Chem., 2008, vol. 37, no. 9, pp. 1063-1070.
3. Kvaratskhelia E.and Kvaratskhelia R. The "Partial" Degrees of Dissociation of Weak Multibasic Organic Acids. J. Solution Chem., 2009, vol. 38, no. 3, pp. 345-349.
4. Kvaratskhelia R. and Kvaratskhelia E. On Dissociation of Weak Dibasic and Tribasic Organic Acids Participating in
Krebs Cycle. Russ. J. Electrochem., 2009, vol. 45, no. 2. pp. 221-224.
5. Dean J.A. Lange's Handbook of Chemistry; 15th Edition, McGraw-Hill: New York, St. Louis, San Francisco etc, 1999.
6. Dippy J.F.J., Hughes S.R.C., Rozanski A. The dissociation constants of some symmetrically disubstituted succinic acids. J. Chem. Soc. 1959, pp.24922498.
7. Koryta J., Dvorak J., Kavan L. Principles of Electrochemistry. 2nd Edition. L. Wiley and Sons, Chichester, New York, Brisbane, Toronto, Singapore, 1993.
ЭЛЕКТРОЛИТИЧЕСКАЯ ДИССОЦИАЦИЯ МЕТИЛПРОИЗВОДНЫХ
ЯНТАРНОЙ КИСЛОТЫ
Е.Р. Кварацхелия и Р.Р.Куртанидзе
Институт неорганической химии и электрохимии им. Р.И.Агладзе Тбилисского Государственного Университета им. Ив. Джавахишвили ул. Миндели 11, 0186 Тбилиси, Республика Грузия E-mail: elickoamail. ru, ekvarats@yahoo. com
Значения степеней диссоциации отдельных ступеней (включая «парциальные» степени диссоциации второй ступени), концентраций различных ионизированных и неионизированных форм, коэффициентов активности ионов водорода и моно- и дианионов в разбавленных (0.0001-0.01М) растворах метилпроизводных янтарной кислоты: метилянтарной, БЬ-1,2-диметилянтарной и мезо-1,2-диметилянтарной кислот были рассчитаны с помощью предложенных авторами методов. Рассчитаны концентрационные интервалы преобладания различных заряженных и незаряженных частиц в разбавленных растворах указанных кислот. Предложены также простые эмпирические уравнения для быстрого приближённого расчёта значений параметров диссоциации.
Ключевые слова: слабые органические кислоты, константа диссоциации, степень диссоциации, концентрация ионов водорода, уравнения.
Поступила в редакцию 28.10.2016.
