THE HYDROGEN ION CONCENTRATION OF WEAK MONOBASIC ACIDS AND THEIR SALTS1 BART PARK Michigan College of Mining and Technology, Houghton, Michigan
ACIDS ONLY
Let HA represent a monobasic acid which does not ionize completely when dissolved in water. Then in a water solution the following equilibria must be satisfied :
which may be rearranged to lH+lIA-I [HA] = K.
and [H+l[OH-] = Ko
(2)
The acid must exist in either the ionized or the molecular form and the sum of these concentrations is the total concentration of,the acid, so that [HA] [A-I = C. (3)
+
Because the solution is electrically neutral, the number of positive and negative charges must be equal, and [H+I = [A-]
+ [OH-]
Substitution of (2) in (4) gives
which is the relationship between [H+] and C. for any monobasic acid. The relative importance of the terms in equation (5) de~endsw o n the values of K , and C.,as mav be seen in ~ i h l 1. e 'rable 1 also contains calculated values for the pH of a number of weak acid solutions. The numbers in the rows opposite the individual terms are approximate values for the negative logarithms of each term, i. e., the pz values, where px = -log z. All terms with relatively large pz values may be dropped without diminishing the accuracy of the calculation. The following equations may be obtained from (5) by considering only the terms specified. Equation
Terms
(4)
Suhstitution of (1) in (3) gives Presented at the 122nd Meeting of the American Chemical Society, Atlantic City, September, 1952.
1, 3
[Hf1 = V ' z E
1, 2, 3
[H+l =
1, 3, 4
[Hf1 = d C &
I
dF
-
2
+ K,
TABLE 1 Calculated pH Values of Weak Acid Solutions PK.
I
2
s
4
3.6 3.4 3.2 15 15 1.00 1.21
4.7 5.1 4.6 15.6 16 1.50 1.57
6.1 7.0 6.0 16 17 2.00 2.02
7.5 9.0 7.5 16.5 18 2.50 2.51
C, 1 2 3 4 5
pIH+la pK.IH+la pCdLlHC1 pKdH+l pKsKu pH L 3 nH 1. 2. 3
6 =
0.1 M 9.0 11.0 9.0 17 19 3.00 3.00
6
7
8
9
10
10.5 13 10.5 17.5 20 3.50
12 15 12 18 21 4.00
13.5 17 13.5 18.5 22 4.50
15 19 15 19 23 5.00
16.5 21 16.5 19.5 24 5.50
...
...
...
...
...
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JOURNAL OF CHEMICAL EDUCATION
and
SALTS ONLY Salts of Weak Acids end Strong Bases
C,
Because
electrica1
=
+ [A-I [A-I + [OH-]
[HA1
(7)
Let BA represent the salt of a strong base and a weak [B+l [H+l = (8) monobasic acid. In a water solution equations (1) and (2) still apply. Let C; be the effective salt concentra- Substituting (1) in (7), (2) in (8), and solving as before tion, then gives C, = [B+]
(6)
[H+lS
+
+ K,[H+12 + C,[H+ll - K,[Ht]
-
K,K,
= 0
TABLE 2 Calculated n H Values of Solutions of Salts of Weak Acids and Stronm Base.
. TABLE 3 Hydmgen Ion Concentrations of Various Ammonium Salt Solutions fCaleulated from Eauation 11) Term
1 as above 2 as above 3 as above 4 as above 5 as above
9 as above 10 as above [H+I 2, 7 IH+l 3, 7 [H+l 2, 3, 7 [HCI 2, 7, 8 [H+l 2 , 3 , 7 , 8 IH+l 2, 6, 7, 8, 9, 10 OH
HIOa
CLCJlrO*
CICnHaOn
HnCOl
CnH10n
CJIIOJN,
CaHsOsNa
HClO
HCN
(9)
MAY, 1953
259
This equation differs from (5) in the third term only. However, the relative importance of the terms is different a8 may be seen in Table 2. The following equations may be obtained from (9) by considering only the terms specified: Tern 3,5
Epmtia
[H+I =
is needed. Let Cx be the effective salt concentration; then C.
=
[B+]
+ [BOH]
[A-I
+ [HA]
and
KX &-
C.
=
Equation (8) still applies. By substitution and simplification the following equation may be obtained: Table 2 contains pz and pH values, calculated from the auurouriate eauations for a number of renresenta-- . tive salts. Belts of Week Acids and Weak Basas
In addition to the equilibrium equations (1) and (21,
As a rule only terms number 2, 3, 7, and 8 are applicable. In very dilute solutions of the weakest acids terms 9 and 10 become sienificant. The following approximate equations may he obtained by consideration of the indicated terms.
-
TABLE 4 Calculated pH Values of Solutions of Weak Acids Plus Their Salts of Strong B-s
OK.
1
-
8
S
6
6
7
8
.9
10
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JOURNAL OF CHEMICAL EDUCATION Term
Epuotion
When C. is zero this simplifies to (5). When Ca is zero i t reduces to (9). The fifth term in (13) is rarely significant, but each of the others becomes important under certain conditions. Table 4 lists calculated values of px and pH. In the construction of this table the following approximate equations derived from (13) were used: Terms 3, 4
Table 3 contains px and pH values calculated for a number of representative ammonium salts. ACIDS AND SALTS TOGETHER Salts of Stmng Bases and Weak Acids
Equations (I), (2), (6), and (8) still apply. In addition, From these relationships the following equation may be derived:
Epolim
C.K. [H+] =C.
