2 Determination of the Surface Pressure by Bubble Pressure Method
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Name of student:………………………………… 2 DETERMINATION OF THE SURFACE PRESSURE BY BUBBLE PRESSURE METHOD Task: Determine the surface tension of one liguid The surface tension of liquids The molecules of liquids attract each other by cohesive forces resulting into small distances between the molecules (on the order of 0.1 nm). Hence the compressibility of liquids is lower than that of gas, while the density is much higher. On the other hand, these cohesive forces are not strong enough to result into the fixed position of molecules that can be seen in solid matter. Liquids do not keep a fixed shape, but adapt the shape of a container. Attractive cohesive forces are short range forces which are based on the electronic interactions. They affect only molecules in their close vicinity (zone of molecular interaction). In the bulk of the liquid, each molecule is attracted equally in all directions by the neighboring molecules, thus resulting in a total force of zero (Fig. 1). However, the molecules at the surface do not have other like molecules on all sides of them and they are pulled inwards the liquid core by non-zero total force (Fig. 1). Consequently, they cohere more strongly to those directly associated with them on the surface and form a surface "film". Nevertheless, these surface molecules are in the energetically unfavorable state, which makes liquid to minimize the surface area. The geometrical requirement of smallest surface area at the fixed volume is satisfied by the sphere. It is the reason why the free drops of water form spherical droplets. Figure 1 Cohesive forces in a case of the molecule at the liquid surface and in the bulk Surface area increase (S) is balanced out by the increase of energy (E) where: E S [1] The coefficient defines the surface tension in the units of J m2 = N m-1. Each liquid is characterized by its own surface tension, which decreases with an increasing temperature (see Table 2). The molecules of the liquid interact with the walls of the container through adhesive forces. The surface bends up (concave meniscus) when the adhesive intermolecular forces are stronger than the cohesive forces inside the liquid (e.g. water in a glass 1 container shown on Figure 2), while it bends down (convex meniscus) when the adhesive forces are weaker (e.g. mercury in a glass container). Capillary action is the result of interplay between the surface tension and adhesive forces. Water inside the capillary arises above the water level in the container (capillary elevation). Capillary pressure (pk), that draws water into capillary is determined by the radius of capillary (r) and the surface tension of water () as follows from: 2 p [Pa] [2] k r Capillary pressure and capillary elevation is higher for narrower capillary. The method of surface pressure determination by pushing the bubbles through the capillary The capillary of radius (r) is immersed in the liquid of density () and surface tension (), such that the bottom of capillary is at the depth of (h) bellow the water level. We would need to apply pressure equivalent to the capillary pressure (pk) to bring the liquid level in the capillary to the same level as that in the container. The hydrostatic pressure (ph) ph h g [3] where: g - is a gravitational acceleration [g = 9.81 m s-2] h - is depth [m] The pressure equal or greater than p pk ph [4] would push the air all the way through the capillary and will create a bubble at its end. The combination of equations [2] and [3] with the equation [4] yields 2 p h g [5] r It is the equation that establishes the method of surface tension determination via pushing the bubbles through the capillary. Figure 3 describes the standard apparatus employed in such a measurement. A M C1 Figure 3 The apparatus for the determination of surface tension via hv K pushing the bubbles through the capillary h C2 2 The investigated liquid is contained in a beaker, with the capillary immersed in it. Water contained in a funnel A will create the desired pressure upon the opening of the knob C1. This pressure is measured by the manometer M, which consists of a U-shape glass tube filled with water. The water levels in the both arms of manometer are equivalent at the beginning of the experiment. However, pressure (p) will create a difference in water levels (hW), after opening the knob C1. This pressure is determined by: p hW W g [6] where W - is a density of water The combination of the equation [6] and [5] determines the surface tension () as r h h g [7] 2 W W where the water density is in kg m-3 from the Table 2 and the density of the investigated liquid is marked on a beaker of stock solution. The capillary radius (r) can be determined from the control measurement in which we measure the known surface tension of water. It is shown in Table 2 as a function of temperature. The radius (r) is than expressed from equation [7] using the known parameters (, W and ) and measured water levels (h) and hW. Equiment: Apparatus displayed in Figure 3, capillary, 2 beakers, liquids with unknown surface tension, ethanol for cleaning the capillary Experimental procedure: 1 Flush the capillary K with distilled water and ethanol, and dry it using the water aspirator. Mount the capillary on the apparatus arm. 2 Fill the smaller beaker with the liquid of unknown surface tension (water) and immerse the capillary into it. 3 Measure of the depth of capillary in water in beaker - h and write measured value to the Table 1 4 Fill the funnel A with water, while the knobs C1 and C2 stay closed. 5 Slowly open the knob C1, thus create an additional pressure in the apparatus. Watch the bubbles that are being pushed through the capillary. The pressure (p) decreases as the water level in funnel A decreases, which results into the slow reduction in a rate of bubbling. Close the knob C1 right at the moment when the bubble formation stops. Read out the water levels and hW on U-tube of manometer. 6 Open the knob C2 to release water form apparatus into the larger beaker. 7 Repeat the measurement (sections 4 and 5) 10 times and write the measured values into a Table 1. Calculate the average value of hW av. 8 Wash the beaker and capillary. 9 Repeat the measurement using an liquid with unknovn surface pressure. 10 Measure the room temperature t. 11 Determine water surface tension at measured this temperature using the Table 2. 12 Calculate radius of capillary (r) from maesurements of water according Equation [7]. 13 Calculate the surface tension of the investigated liquids using the equation [7]. 3 Table 1 The difference of water levels hW on manometer and the depth of capillary immersion h measurement Water Liguid 1 hW [m] h [m] hW [m] h [m] 1 2 3 4 5 6 7 8 9 10 hW av= m hWav= m water= liquid= -1 -1 N m N m r= m Table 2 Water surface tension and density as function of the temperature -1 -3 t [C] [N m ] H2O [g cm ] 15 0.07349 0.99996 16 0.07334 0.99994 17 0.07319 0.99990 18 0.07305 0.99985 19 0.07290 0.99978 20 0.07275 0.99820 21 0.07259 0.99799 22 0.07244 0.99777 23 0.07228 0.99754 24 0.07213 0.99730 25 0.07197 0.99705 Calculations: Conclusion: 4 5 .