Surface Tension Measurement by Traube Stalagmometric Method

Surface tension measurement by Traube stalagmometric method

Surface tension can be measured by several methods, e.g. Whilhelmy plate, spinning drop, pendant drop, sessile drop, bubble pressure etc. methods. One of them is the stalagmometric method. These are all based on the differences between the forces affecting the molecules in the bulk phase and that of on the surface. It causes several differences in the behaviour and shape of liquid drops or bubbles as well as in the force with which an object can be removed from the liquid. Traube’s stalagmometer is an instrument for measuring surface tension by determining the exact number for drops in a given quantity of a liquid. When using the Traube stalagmometer to measure surface tension, a fixed volume of liquid is delivered as freely falling drops from the end of a tube and the number of drops formed is counted. So, the stalagmometer is a special pipette, with very carefully shaped end. The pipette is mounted vertically on a stand, and is filled with liquid. When we leave an exact amount of liquid to drop out from the pipette, the number of drops will depend on the surface tension of the liquid. High surface tension – few drops. Low surface tension – more drops. (Because it is the surface tension that holds together water molecules into a drop, the higher the surface tension, the more molecules it can hold together.) This method is the most accurate, if we use it as a relative method. It means we have to count the drop number of a liquid with known surface tension, than the drop number of the unknown sample of the same volume, and use the ratio of the drop numbers in calculation of the surface tension.

End of stalagmometer. It is shaped as a small plate.

The plate holds the liquid around its perimeter (as if hanging down from the glass plate, kept in place by the surface tension). The surface tension as a force around the perimeter: 2 r π γ

The weight of a drop: Vx ρ g, where Vx is the volume of a drop, ρ is its density.

The size of the drop depends on the surface tension, because it is held together by the surface tension. The whole volume in the pipette (V) is the product of the volume of an individual drop and the drop number: V1n1 = V2n2= V where n is the number of drops, Vx is the volume of a drop.

If we let drip out from the pipette two liquids with different surface tensions (and probably different density), the equations for the two liquids will be 2rπγ1 =V1ρ1g 2rπγ2 =V2ρ2g

Dividing the two equations with each other (neither of them can be zero):  V  1  1 1  2 V22 V1 1 1   2  the equations refer to the individual drop volumes. V2 2

V V1  the volume of one drop can be calculated dividing the whole volume by the n1 number of drops, for each of the liquids. V V2  n 2

V1 = V/n1 and V2 = V/n2 , the ratio of drop-volumes can be substituted by ratio of drop numbers, because the whole volume of the stalagmometer is the same for both of the liquids.

V n  n      1  1    2  1 1 2 V 2 2 n1 2

n water 1 1   water   n1 water

We have to know one fo the surface tensions (that of the water for example), and have to count the drop numbers of the same volume in case of the known and unknown liquid, as well as measure the densities. In this case we can calculate the surface tension of the unknown liquid.

Difficulties:

1. Surface tension determines the drop size. If however the surface of the orifice is not clean (we touched with bare hand greasing it inadvertently), it changes the wettability. Care should be taken that the stalagmometer is thoroughly clean and dry before operations are begun! So, do not touch the platelet of the stalagmometer!

2. Equations are valid only for equal volumes. On the other hand, equal volumes are hard to achieve, because the liquid outflow is quantized, we can change it only drop by drop. That’s why the tube of the stalagmometer is graduated. The scale on the stalagmometer is calibrated to find the number of scale divisions corresponding to one drop of liquid. This must be done for each liquid in turn before the main observations are commenced. So, before measurements, we have to calibrate the tube, determining how much of the divisions equal to one drop of the corresponding liquid. In this way we can count fraction drops as well. Having calibrated the scale, fractions of a drop can now be estimated, if necessary, with an accuracy of 0.05 of a drop. The meniscus has to be adjusted only near to the sign running around the tube, and calculate the fraction drop which equals to the volume corresponding the difference between the round-mark and the actual mark. This fraction has to be added (or subtracted) to the counted drop numbers, on the upper and lower positions as well.

Example: Let’s suppose that during the preliminary counting we gained the following result: one drop of water equals to 6 divisions on the tube’s upper end, and the same is valid for the lower end too. If during the measurement we can place the meniscus of the water at e.g. the 9th mark above the round-mark, it means 9/6 (that is, 1.5) plus drops added to the volume of the pipette. At the end of the drop-counting, the last drop drops out at the 3rd mark above the lower round-mark. It means, the volume is 0.5 drops less than it would have been had we achieved exactly the round-mark with the last drop. So the counted drop number has to be increased by 0.5 drops (because on the lower and we dropped 0.5 drops smaller amount), and has to be decreased by 1.5 drops (because on the upper end we started the counting a bit earlier, by 1.5 drops) The same fraction numbers have to be established for any measured liquids, of course.

3. Surface tension dependence on temperature: (°C) (N/·m) -5 0,0764 0 0,0756 10 0,0742 20 0,0727 30 0,0712 40 0,0696 60 0,0662 80 0,0626 100 0,0589

4. The liquid is allowed to flow from the stalagmometer at a rate not greater than 15 drops per min. The rate of flow may be adjusted by attaching a piece of rubber tubing with a screw clip to the top of the stalagmometer. 5. In the experiments, we determine the surface tension of water solutions of different household detergents. For the calculations we need the densities of the liquids. Instead of the densities in the equation, we use the relative density with respect to water. Relative density, or specific gravity, is the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material. Specific gravity usually means relative density with respect to water. The term "relative density" is often preferred in modern scientific usage. Density is often determined with the aid of a pycnometer. A pycnometer is a small volumetric flask, its volume can be adjusted accurately because of the extreme small diameter of its orifice. One has to measure only the exact mass of the exact volume, and the specific gravity can be calculated easily. This device enables a liquid's density to be measured accurately by reference to an appropriate working fluid, such as water, using an analytical balance (relative density). Pycnometers have to be termostatted, because density of liquids is strongly dependent on the temperature. If one has to measure the relative density of a liquid with respect to an other liquid, then only the two masses have to be measured, because the volume is the same in both cases. The ratio of the masses gives the relative densities. Pycnometer filled with a blue liquid. The capillary along the stopper enables us to adjust volume accurately. We have to fill the flask thoroughly (overfill, actually) and carefully put in the stopper. The excess liquid can flow out through the capillary, and an exact meniscus can be adjusted with the aid of small paper fidibuses. (If we use the same pycnometer for each of the measurements, then using fidibuses is not necessary, we only have to adjust the meniscus exactly to the upper end of the capillary. That is, we have to assure that none of the fluid is sucked out when we wipe down the device.) The pycnometer has to be wiped dry, meanwhile not warmed up by our hands.

m1 m   V  1 because V is the same in both cases. rel m 2 m2 V

6. Surface tension depends on the materials solved in the liquid, so every device used must be extremely clean!