James 0. Osburn and II C. Choi
Float Method for the
State University of lowa Iowa City
Analysis of Solutions
The need often arises in chemical research to measure the concentration of solutions with a high degree of precision. If a sensitivity in the order of 1 X grams/ml is required, ordinary methods are not suitable. Chemical or colorimetric methods will work when the total concentration is of this order of magnitude, but not a t higher concentrations. Physical methods such as specific gravity or refractive index are not sensitive enough. An interferometer, often suitable for the application, is expensive, and the magnetically controlled float method (1) is complicated and rather expensive. In this article we will describe a simple method of making precise and reproducible concentration measurements. This method, the thermal equilibrium float method, is not new, but deserves wider notice because of its simplicity and ease of operation. The only items of expense are a differential thermometer and a wellregulated water bath, and these are within the reach of every department. In the thermal equilibrium float method, a float is sus~endedwithin the liouid whose concentration is to be measured. The temperature is adjusted until the float neither rises nor sinks. For a given float, a correlation can be made between this temperature and the concentration. This method was first described by Richard and Shipley (6) in 1912. Lewis and McDonald (5) used this method for measuring the concentration of deuterium in water. They measured the density of water by findiug the temperature a t which a 10-cc float would neither rise nor sink in the sample, and ohtained an accuracy in density of one part per million. Giffilan (9) used the same principle to measure the isotopic composition of sea water. He held the temperature constant a t the ice-point and changed the buoyancy of the float by varying the hydrostatic pressure. The measurements were made in test tubes connected to a pump and manometer system. Hutchison and Johnston (4) applied the method to the accurate determination of the density of lithium fluoride by mixing two liquids of different density until the solid lithium fluoride would neither rise nor sink in the liquid mixture. Tollert (7) used the method to study the radial concentration gradient in laminar flow.
of the method, it may be assumed that the density of the solid is independent of temperature. Then the concentration change corresponding to a small change in temperature depends on the change of density with concentration, Ap/AC, and the change in density with temperature, Ap/At: ACJAl = ( A p / A l ) / ( A p / A C )
A small value for AC/At is obtained if Ap/At is small and Ap/AC large. Fortunately, this is the case for many systems. Instead of measuring the individual factors in equation (I), however, it is more convenient to calibrate the float directly. A calibration curve is prepared by making up solutions of known concentrations, and measuring the equilibrium float temperature for each solution. Description and Operation of the Apparatus
Key to the method is the float. This must be small so that temperature uniformity is achieved rapidly. Our floats are hollow spheres of soft glass, made by drawing a glass tube into a capillary, then blowing spheres in a tiny flame. This requires some practice, and it is usually necessary to make several floats before obtaining one of the desired density. A photograph of some floats, about 3 mm in diameter, is shown in Figure 1. The remainder of the apparatus consists of a water bath with temperature regulated to 0.005'C, a Beckmann thermometer with O.Ol°C graduations, and a test tube to contain the sample. The sample of unknown solution is placed in a 20 ml test tube along with the calibrated float. The Beckmann thermometer is placed in the water bath. Experiment showed that the temperature in the test tube is not noticeably different from that in the water bath for the rates of heating and cooling used. The amount of solution taken is about 10 ml, so that the liquid level in the test tube does not touch the stopper when the
Theory and Method of Calibration
Consider a solid object suspended in a liquid, a t such a temperature tl that the densities of solid and liquid are equal. Another solution of different concentration would cause the solid to be suspended a t another temperature tz, a t which the density of the solution is again equal to that of the solid. To estimate the sensitivity 578
/
Journal of Chemical Education
(1)
Figure 1.
Photograph of Roatr
tube is shaken to remove air bubbles from the float. To make a measurement, the temperature of the bath is increased slowly until the float starts to come down from the top of the liquid. At this instant the temperature control system of the bath is activated. By this time, the float has reached the bottom of the test tube. The temperature of the bath is now lowered until the float begins to move upward, a t which point the temperature is changed by very small intervals until the float stays in one position. Since the movement of the float is slow, it is usually possible to find the final temperature a t which the float stays stationary in the liquid before the float reaches the top of the liquid. Instead of viewing the float directly, it is more convenient to view the float by means of its shadow projected on a scale attached to the outside wall of the test tube. The surface of the float must be clean and free from air bubbles, which would result in an erroneous temperature reading. Air bubbles are dislodged by shaking and swirling the liquid in the test tube. Results
To give an indication of the extreme sensitivity of the method, typical results for tap water and for distilled water are shown in Table 1, using the same float for both cases. This table shows typical observations of temperature and float motion made during the progress of a determination. Table 1.
Observed Float Motion for Tap Water and Distilled Water with Same Float
Time
Temperature
Imin)
resdine
Direction of float motion
Figure 2. Equilibrium R o d temperature for different concentrdons in the system, n-butyl alcohol and distilled water.
Comparison with Magnetic Float Method
The magnetic float apparatus is similar, but is a constant temperature device. The float contains a piece of iron, which is attracted by an electromagnet to keep the float suspended. The current through the electromagnet is correlated with density. This method was compared with the thermal equilibrium float method for KC1 solutions. The calibration curve prepared for the thermal equilibrium float by Goel (3) is shown in Figure 3. A temperature difference of O.Ol°C corresponds to a concentration difference of 0.00047, KCl. In comparison, voltage and temperature fluctuations limited the accuracy of the magnetically controlled float to about 0.003% KC1. A concentration difference of less than 0.00670 KC1 could not be detected by refractive index measurements.
Tap W d e v
5.80 5.53 5.72 5.57 5.68 5.63 5.55
Down UP Down UP Down Down Stationery
Distilled Woter
4.35 4.15 4.25 4.29 4.30 4.295
Down UP UP UP Down Stationary
As shown in Table 1, the float motion is so sensitive that a change of a temperature of O.Ol°C will cause a noticeable change of the float velocity. This high sensitivity means that small density or concentration differences can be detected. To show how this method can be used for measurement of concentration, a series of solutions were made by adding weighed amounts of n-hutyl alcohol to distilled water. The float equilibrium was measured for each solution. The corresponding temperature for float equilibrium is plotted against the weight percentage of n-butyl alcohol in Figure 2. Using a thermometer with a precision of 0.0l0C, this method makes it possible to estimate the amount of n-butyl alcohol present in water within 0.001% with good reproducibility.
0
l
078
I
/
0 18
KC,
l
l
l
OBO WT
1
082
l
l
084
1
l
086
%
Equilibrium R o d temperature for different concentrations in the ry$tem, KC1 ond water. Figure 3.
The thermal equilibrium float method cannot be used when the temperature must be constant, as in the reaction rate measurements described by Cartan and hacker (I). Volume 38, Number 1 1, November 196 1
/
579
Conclusion
Literature Cited
The thermal equilibrium float method is a simple, reliable, and sensitive method for determining the concentration of solutions. It compares favorably with the magnetic float method in accuracy. A minimum of inexpensive equipment is needed to determine the temperature a t which a float remains stationary in a solution. Since the float motion is extremely sensitive, small changes in concentration may be detected with a high degree of precision.
(1) CARTAN, F.,
580 / Journol of Chemkol Educofion
AND
ANACKER, E. W., J. CHEM.EDUC.,37, 36
(19Iin. \----,-
(2) GIFFILAN, JR., E. S., J. Am. Chem. Soc., 56,406 (1934). (3) GOEL,J., unpublished data. (4) H u ~ c n x s o C. ~ , A., AND JOHNSTON, H. L., J. Am. Chem. Sac., 62, 3165 (1940). R. T.,J. Chem. Phys., 1 , (5) LEWIS,G. N., AND MCDONALD, 341 (1933). J. W., J. Am. Chem. Soc., 34, (6) Rxcnhm, T. W., AND SHIPLEY, 599 (1912). (7) TOLLERT, H., Chem. Eng. Teehnik, 26, 270 (1951).
