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A program for calculation and graphic representation of conditional constants — II. Solubility products
Compu~er.sClrem. Vol. 20. No. 3. pp. 3X553X7. 1996 Copyright
Pergamon
0097~8485(95)ooo80-1
Printed
c;
in Great
1996 Elsevier Britain.
All
0097-8485/96
SOFTWARE
Science Ltd
rights
reserved $I 5.00 + 0.00
NOTE
A PROGRAM FOR CALCULATION AND GRAPHIC REPRESENTATION OF CONDITIONAL CONSTANTS-II. SOLUBILITY PRODUCTS M. P. GARCIA Departamento
ARMADA
de Ingenieria Quimica Industrial, Universidad C. Jose Gutierrez Abascal 2, 28006 Madrid, (Received 25 April 1995: in revised form
Politenica Spain
17 Augusr
de Madrid.
1995)
Abstract-A BASIC program (PKSCOND) is described. Given the stability constants values of metal and ligand, solubility product, concentration of metal and stoichiometry it calculates and draws the conditional solubility product diagram versus pH. This program can be linked with the CONSCOND program by means of three supplementary BASIC lines.
The PKSCOND program uses the same base of calculation used by the graphical methods; it displays the graphical representation of conditional constant values versus pH, reducing the long calculation time to a few seconds.
INTRODUCTION
The purpose of this work is to continue with the simplification of numerical calculations of conditional constants. In this case, analytical systems with a solid species are treated. Frequently, the analytical chemist searches for the optimum conditions to carry out a precipitation or maintain a substance in solution and, taking into account that the solubility product is a particular type of equilibrium constant, the concept of conditional constant can be successfully applied to its treatment (Kolthoff & Elving, 1959). In a previous work (Garcia Armada, 1995) the simplification of side-reaction coefficients, or alpha coefficients (Schwarzenbach, 1957) calculations due to Ringbom (1963) (tabulation of alpha values for some reactions), and graphic calculations by logarithmic diagrams (Vicente-Perez, 1981; Burriel et al., 1989) were cited. Several applications that use the stability constants (Meihoun et a/., 1988), and commercial codes (American Institute of Chemical Engineers, 1993) were also taken into account and compared with the purpose of these works. A new BASIC program, PKSCOND, has been developed to perform all the specific mathematical calculations which allow the prediction of precipitation reactions in aqueous medium. The PKSCOND program, like the CONSCOND program (Garcia Armada, 1995) consists of a single BASIC file (87 lines) and, furthermore, can be merged with the CONSCOND program to obtain one single BASIC file, with 116 lines, suitable to calculate both constant types: complex formation constants and solubility products.
PRINCIPLES
AND ALGORITHMS
For a M,,A, precipitate, the conditional solubility product expression is defined by the equation: K’S = Ks c(‘“c(” M A,
(1)
where KS is the classical solubility product and a,,.,and CQ are the side-reaction coefficients for metal and anion, respectively. The calculation and graphic treatment of rcoefficients, if only interfering side-reactions with H+ and OH- are considered, are the same as those used in the CONSCOND program. The graphical representation of every log x versus pH value consists of one curve composed of as many straight lines as predominant species exist and whose slope is the coordination number of the corresponding predominant species. The conditional solubility product values are obtained by adding the metal and anion alpha logarithms (logarithmic form of equation (1) to the thermodynamic constant: log K$ = log Ks + (m log tlhl + n log x~).
(2)
The PKSCOND program performs the log LXcalculation for the metal and anion, for each pH value, and stores them in two matrices, C(pH) and D(pH). The K& versus pH values, calculated by means of a loop from expression (2). are stored in a new matrix X(pH). 385
Software Note
386
Taking into account that log Ks is always ~0, the ratio between the scales of the Ki axis and the a-axis will be: if: then:
14.4
log a log K;
=I
=o = log KS
= log KS + I
.
1olrK’ 5
I
-
=-log = I
Ks+ I
= -log =o
KS
= -log
Ks- I
= -I.
program for the Mg-oxinate is shown as an example. Data supplied by the user to the program are (in the order established above):
. / OX-; (4 HIOX+ / HOX 9.9
. -1.0
5.0 Mg’+ / MgOH+; (b) II 4 (cl according to (a) and (b); (4 pKs = 15.4; (4 [Mg*+] = 10-i M; and (0 l:2.
.
-
. . . . .
-16.4 0
.
.
a
7
.
C 14
PH displayed for log K& of Mg-oxinate (the handled data are reported in the text).
Fig.
1. Screen
In order to ascertain the pH range in which the precipitation is quantitative or is inhibited, the following criteria have been applied: l
if the initial concentration of reactants (stoichiometric quantities of metal and anion are considered) is decreased 1000 times, so:
Quantitatiw
(3) l
Inhibitedif the concentration in its initial value, so:
of reactants remains
K; 2 [Ml”” [A]“‘.
(4)
RESULTS The PKSCOND program starts by displaying a series of questions on the screen, which prompt the user to supply:
Table I. Comparison of Mg-oxinate K, values obtained by three ditkent methods
(4 stability constants of the proton-anion (b) (cl (4 (4 07
complexes; transformation pH values of hydroxo complexes; coordination number of proton and hydroxo compounds; P&; concentration (in M) of reactant to precipitate; and stoichiometry of studied precipitate.
The upper horizontal line shows the pH range in which the precipitation is inhibited (designated as I) and the lower one shows the quantitative range (designated as C), following the criteria outlined above. From this screen, it is possible to obtain numeric values of log Ki for any pH value by means of the BASIC order: PRINT X(pH) (writing the pH value inside parentheses). Moreover, it is possible to obtain a printout of the screen. In Table I the obtained Kk values for the Mgoxinate are compared with those calculated by both numerical and graphical methods. The results are completely concordant. With the purpose of obtaining both calculation options (complex formation and solubility constants) in a single BASIC file, a way to combine CONSCOND and PKSCOND programs to obtain a single shorter one has been designed. Those lines which were equal in both programs have been unified, the data input questions have been generalized in order to avoid duplication and only
It then performs the calculations and displays on screen the graphic representation of log Kk versus pH. In Fig. I the final screen from running the
PH 0
8 9 IO II I2 13 14
log K: (program)
log K; (numerical)
log K; (graphical)
14.4 IO 4 6.4 2.4 - I.6 -5.6 -7.6 -9.6 -I I.6 - 13.6 - 15.4 - 15.4 - 14.8 ~ 13.8 - 12.8
14.4 10.4 6.4 2.4 - 1.6 -5.0 - 1.6 - 9.6 -I I.6 - 13.5 - 14.9 - 15.2 - 14.9 - 14.1 - 13.1
14.4 10.4 6.4 2.4 -- 1.6 - 5.6 -1.6 -9.6 - Il.6 - 13.5 - 14.9 - 15.3 -14.X -13.8 - 12.8
Software Note three supplementary lines should be inserted. unified program structure is as follows:
The
llines 1 to 56 are generalized data input; lline 57, Input to select the log K’ or pKi
calculation; l lines 58 to 61 are the screen setting up: w line 62 is an IF statement to guide the program flow; *lines 64 to 90 are the CONSCOND lines for calculation and graphic representation of conditional formation constant; llines up to I16 are the PKSCOND lines for calculation and graphic representation of conditional solubility product. The whole program consists of a single file with I I6 lines and will offer the option to calculate the conditional formation constant of a complex or the conditional solubility product of a precipitate.
387
Program acailabi/irJ-This program is available in list or diskette form from the author upon request.
REFERENCES American Institute of Chemical Engineers (I 993) 1994 CEP Sqfiuue Direc/ory Supplement to Chern. Engng Prog. New York. Burriel F., Lucena F.. Arribas S. & Hernandez J. (1989) Quimicu Analiricu Cuafitutiru. Paraninfo. Madrid. Spain. Garcia Armada M. P. (1995) Computers Chem. 19, 137. Kolthoff I. M. & Elving P. J. (1959) Trearise on Anu!,rica/ Chemisrr~~, Part 1. Vol. I. Interscience, New York. Melhoun M., Have1 J. & Hogfeldt E. (1988) Compuration o/ Solution Equilibria. Ellis Horwood, New York. Rmgbom A. (I 963) Compkyation in Antrlyrkul Clremisrr~. Interscience. New York. Schwarzenbach G. (1957) Complexometric Titrarions. Interscience, New York. V.icen te_p’erez S. (198I) Quimicrr de las Disoluciones: Diagrumay y Ch_dos Gr$ico.v. Alhambra, Madrid, Spain.
Pergamon
0097~8485(95)ooo80-1
Printed
c;
in Great
1996 Elsevier Britain.
All
0097-8485/96
SOFTWARE
Science Ltd
rights
reserved $I 5.00 + 0.00
NOTE
A PROGRAM FOR CALCULATION AND GRAPHIC REPRESENTATION OF CONDITIONAL CONSTANTS-II. SOLUBILITY PRODUCTS M. P. GARCIA Departamento
ARMADA
de Ingenieria Quimica Industrial, Universidad C. Jose Gutierrez Abascal 2, 28006 Madrid, (Received 25 April 1995: in revised form
Politenica Spain
17 Augusr
de Madrid.
1995)
Abstract-A BASIC program (PKSCOND) is described. Given the stability constants values of metal and ligand, solubility product, concentration of metal and stoichiometry it calculates and draws the conditional solubility product diagram versus pH. This program can be linked with the CONSCOND program by means of three supplementary BASIC lines.
The PKSCOND program uses the same base of calculation used by the graphical methods; it displays the graphical representation of conditional constant values versus pH, reducing the long calculation time to a few seconds.
INTRODUCTION
The purpose of this work is to continue with the simplification of numerical calculations of conditional constants. In this case, analytical systems with a solid species are treated. Frequently, the analytical chemist searches for the optimum conditions to carry out a precipitation or maintain a substance in solution and, taking into account that the solubility product is a particular type of equilibrium constant, the concept of conditional constant can be successfully applied to its treatment (Kolthoff & Elving, 1959). In a previous work (Garcia Armada, 1995) the simplification of side-reaction coefficients, or alpha coefficients (Schwarzenbach, 1957) calculations due to Ringbom (1963) (tabulation of alpha values for some reactions), and graphic calculations by logarithmic diagrams (Vicente-Perez, 1981; Burriel et al., 1989) were cited. Several applications that use the stability constants (Meihoun et a/., 1988), and commercial codes (American Institute of Chemical Engineers, 1993) were also taken into account and compared with the purpose of these works. A new BASIC program, PKSCOND, has been developed to perform all the specific mathematical calculations which allow the prediction of precipitation reactions in aqueous medium. The PKSCOND program, like the CONSCOND program (Garcia Armada, 1995) consists of a single BASIC file (87 lines) and, furthermore, can be merged with the CONSCOND program to obtain one single BASIC file, with 116 lines, suitable to calculate both constant types: complex formation constants and solubility products.
PRINCIPLES
AND ALGORITHMS
For a M,,A, precipitate, the conditional solubility product expression is defined by the equation: K’S = Ks c(‘“c(” M A,
(1)
where KS is the classical solubility product and a,,.,and CQ are the side-reaction coefficients for metal and anion, respectively. The calculation and graphic treatment of rcoefficients, if only interfering side-reactions with H+ and OH- are considered, are the same as those used in the CONSCOND program. The graphical representation of every log x versus pH value consists of one curve composed of as many straight lines as predominant species exist and whose slope is the coordination number of the corresponding predominant species. The conditional solubility product values are obtained by adding the metal and anion alpha logarithms (logarithmic form of equation (1) to the thermodynamic constant: log K$ = log Ks + (m log tlhl + n log x~).
(2)
The PKSCOND program performs the log LXcalculation for the metal and anion, for each pH value, and stores them in two matrices, C(pH) and D(pH). The K& versus pH values, calculated by means of a loop from expression (2). are stored in a new matrix X(pH). 385
Software Note
386
Taking into account that log Ks is always ~0, the ratio between the scales of the Ki axis and the a-axis will be: if: then:
14.4
log a log K;
=I
=o = log KS
= log KS + I
.
1olrK’ 5
I
-
=-log = I
Ks+ I
= -log =o
KS
= -log
Ks- I
= -I.
program for the Mg-oxinate is shown as an example. Data supplied by the user to the program are (in the order established above):
. / OX-; (4 HIOX+ / HOX 9.9
. -1.0
5.0 Mg’+ / MgOH+; (b) II 4 (cl according to (a) and (b); (4 pKs = 15.4; (4 [Mg*+] = 10-i M; and (0 l:2.
.
-
. . . . .
-16.4 0
.
.
a
7
.
C 14
PH displayed for log K& of Mg-oxinate (the handled data are reported in the text).
Fig.
1. Screen
In order to ascertain the pH range in which the precipitation is quantitative or is inhibited, the following criteria have been applied: l
if the initial concentration of reactants (stoichiometric quantities of metal and anion are considered) is decreased 1000 times, so:
Quantitatiw
(3) l
Inhibitedif the concentration in its initial value, so:
of reactants remains
K; 2 [Ml”” [A]“‘.
(4)
RESULTS The PKSCOND program starts by displaying a series of questions on the screen, which prompt the user to supply:
Table I. Comparison of Mg-oxinate K, values obtained by three ditkent methods
(4 stability constants of the proton-anion (b) (cl (4 (4 07
complexes; transformation pH values of hydroxo complexes; coordination number of proton and hydroxo compounds; P&; concentration (in M) of reactant to precipitate; and stoichiometry of studied precipitate.
The upper horizontal line shows the pH range in which the precipitation is inhibited (designated as I) and the lower one shows the quantitative range (designated as C), following the criteria outlined above. From this screen, it is possible to obtain numeric values of log Ki for any pH value by means of the BASIC order: PRINT X(pH) (writing the pH value inside parentheses). Moreover, it is possible to obtain a printout of the screen. In Table I the obtained Kk values for the Mgoxinate are compared with those calculated by both numerical and graphical methods. The results are completely concordant. With the purpose of obtaining both calculation options (complex formation and solubility constants) in a single BASIC file, a way to combine CONSCOND and PKSCOND programs to obtain a single shorter one has been designed. Those lines which were equal in both programs have been unified, the data input questions have been generalized in order to avoid duplication and only
It then performs the calculations and displays on screen the graphic representation of log Kk versus pH. In Fig. I the final screen from running the
PH 0
8 9 IO II I2 13 14
log K: (program)
log K; (numerical)
log K; (graphical)
14.4 IO 4 6.4 2.4 - I.6 -5.6 -7.6 -9.6 -I I.6 - 13.6 - 15.4 - 15.4 - 14.8 ~ 13.8 - 12.8
14.4 10.4 6.4 2.4 - 1.6 -5.0 - 1.6 - 9.6 -I I.6 - 13.5 - 14.9 - 15.2 - 14.9 - 14.1 - 13.1
14.4 10.4 6.4 2.4 -- 1.6 - 5.6 -1.6 -9.6 - Il.6 - 13.5 - 14.9 - 15.3 -14.X -13.8 - 12.8
Software Note three supplementary lines should be inserted. unified program structure is as follows:
The
llines 1 to 56 are generalized data input; lline 57, Input to select the log K’ or pKi
calculation; l lines 58 to 61 are the screen setting up: w line 62 is an IF statement to guide the program flow; *lines 64 to 90 are the CONSCOND lines for calculation and graphic representation of conditional formation constant; llines up to I16 are the PKSCOND lines for calculation and graphic representation of conditional solubility product. The whole program consists of a single file with I I6 lines and will offer the option to calculate the conditional formation constant of a complex or the conditional solubility product of a precipitate.
387
Program acailabi/irJ-This program is available in list or diskette form from the author upon request.
REFERENCES American Institute of Chemical Engineers (I 993) 1994 CEP Sqfiuue Direc/ory Supplement to Chern. Engng Prog. New York. Burriel F., Lucena F.. Arribas S. & Hernandez J. (1989) Quimicu Analiricu Cuafitutiru. Paraninfo. Madrid. Spain. Garcia Armada M. P. (1995) Computers Chem. 19, 137. Kolthoff I. M. & Elving P. J. (1959) Trearise on Anu!,rica/ Chemisrr~~, Part 1. Vol. I. Interscience, New York. Melhoun M., Have1 J. & Hogfeldt E. (1988) Compuration o/ Solution Equilibria. Ellis Horwood, New York. Rmgbom A. (I 963) Compkyation in Antrlyrkul Clremisrr~. Interscience. New York. Schwarzenbach G. (1957) Complexometric Titrarions. Interscience, New York. V.icen te_p’erez S. (198I) Quimicrr de las Disoluciones: Diagrumay y Ch_dos Gr$ico.v. Alhambra, Madrid, Spain.