V O L U M E 25, NO. 10, O C T O B E R 1 9 5 3 Set
F’
=
1563
H / t , then F(v)dv = d2 M / d P = A Va F ( V ) / H
(3)
LH”
v F ( v ) dv
(5)
Hence from equations 1 and 4 one finds Thus the quantity F( V ) may be determined by means of Equation 3 if the second derivative of M can be obtained. However it is generally preferable to get the integral of F(v), instead, by means of a tangent intercept method. This will be described next. Figure 1 is intended t o represent a graph of M versus the time. At some time, t , draw a tangent to the curve. Let M’ be the intercept of this tangent on the M axis. Then the slope of the tangent line is (121 - If’)/ t . Upon setting this equal to Equation 2, and using Equation l for W,one obtains
pt
( H - a t ) F ( v ) dv
A
- AT’
=
-At
JO
M’ = A H
p
[Hit e1
Jo
V
=
H(M’ - M)/(M‘ t )
or
6 = H/t’
(7)
where 1‘ is the time intercept of the tangent line t o the M versus t curve (see Figure I), or to a k .If versus t curve, where k is any const ant. The average settling speed, i 1 2 , among particles having settling speeds lying between H / t l and H/t2 can be defined as in Equation 5, but with the limits H / t , and H/tz on the integrals. JVhen this is done one gets the follo-ing equation f o r & : Uiz ( M i - M ; ) = H ( M : / t i - M ; / t ; )
P(u)dv
(81
This simplifies to =
F ( v ) du
(6)
(4)
Thus the intercept, M’, is equal to the total mass of particles above R C, in the original, well-stirred liquid, which have settling speeds less than H / t . This is the tangent intercept which is in common use. If one is interested in average settling speeds, the other intercept of the tangent line can be used also. This will now be shown. An average speed, 6, in the interval from v = o to v = H / t , may be defined by the equation
H/t”
where t” is defined as in Figure 2. That is, t” is the time coordinate of the point of intersection of the tangent lines a t t, and t? t o the M versus t curve. LITERATURE CITED (1) Knapp, R. T., IND. ENG.CHEM., ANAL.ED.,6, 66 (1934). (2) O d h , S., “Alexander’s Colloid Chemistry,” Vol. I, p. 885, Xew Pork, Chemical Catalog, 1926.
(3) Svedberg, T., “Colloid Chemistry,” AMERICAN CHEMICAL
SOCIETY Monograph, p. 178, New York, Reinhold Publishing Corp., 1924. RECEIVED for review September 18, 1962. Accepted June ?b. 1953.
Determination of Aldonic Acids in Alkaline Media J. V. KARABINOS, A. T. BALLUN, ANDR. L. McBETH Research Laboratories, Blockson Chemical Co., Joliet, Ill.
7
THE
sequestering action of sodium gluconate for calcium in
1 highly alkaline solutions has been noted in several recent
patents ( 1 ) in connection with certain washing compositions. The authors likewise indicate the possible usefulness of other aldonic acids for this purpose. I n connection with another problem in this laboratory, it became necessary to develop a convenient method for the determination of aldonic acids in highly alkaline media. Since the sequestering action of sodium gluconate for calcium seemed applicable to the direct determination of aldonic acids, a procedure was developed for the direct titration of several aldonic acids with standardized calcium chloride solution a t a pH of 12.4, and the results are reported herein. Since some of the acids sequestered different molar ratios of calcium, the method also seems applicable to a qualitative differentiation between certain acids (Table I). REAGENTS
Calcium Chloride Solution. A 0.1 M calcium chloride solution was prepared by dissolving approximately 15 grams of calcium chloride dihydrate in distilled water. Standardization by precipitation as calcium oxalate and titration of the oxalate with permanganate indicated the calcium chloride solution to be 0.106
in 10 ml. of 37, sodium hydroxide solution. The mixture was titrated slowly with 0.106 ‘12 calcium chloride solution to a distinct turbidity. The end point was attained when the turbidity persisted and the solution became more opalescent upon standing. It was noted that the pH (12.4) was not materially altered during the titration. RESULTS
The titrations with several different aldonates are recorded in Table I.
Table I.
Titration of Aldonic Acids in Alkaline Solution
Calcium Chloride (0.106 M), Moles Calcium per Mole Aldonate MI. per hlillimole -4ldonate D-Gluconic-6-lactonea 19.4 2.06 D-Galactonic- y-lactoneb 10.1 1.07 D-Mannonic- y-lactoneb 18.9 2.00 Lactobionic-d-lactonea 14.4 1.53 Sodium gluconates 18.7 1.98 Potassium acid saccharatea 15.6 1.65 Potassium arabonatea 9.45 1.00 a
Commercial technical grade sample.
b Laboratory preparation.
M.
Sodium Hydroxide Solution. A 3y0 sodium hydroxide solution was prepared by dissolving 3 grams of sodium hydroxide pellets in 100 ml. of distilled water. PROCEDURE
Approximately 1 millimole of each aldonic lactone or salt was accuratdy weighed into a 125-ml. Erlenmeyer flask and dissolved
LITERATURE CITED
(1) Dvorkowitz, V., and Hawley, T. G., U. S. Patents 2,584,017, 2,615,846 (1952). RECEIVED for review June 17, 1953. Accepted July 22, 1953.
