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A photo and a diagram are shown. In the photo, a paper towel is dipped into a bowl full of a red liquid sitting on a countertop. The red liquid is traveling up the lower part of the paper towel, and this section of the photo has a square drawn around it. A right-facing arrow leads from this square to the image. The image is square and has a background of two types of molecules, mixed together. The first type of molecule is composed of two bonded black spheres, one of which is single bonded to three white spheres and one of which is single bonded to two white spheres and a red sphere that is itself bonded to a white sphere. The other type of molecule is composed of six black spheres bonded together in a row and bonded to other red and white spheres. Six upward-facing arrows are drawn on top of this background. They have positive signs on their lower ends and negative signs on their heads. Four upward-facing arrows are drawn with their signs reversed.
Wine wicks up a paper towel (left) because of the strong attractions of water (and ethanol) molecules to the −OH groups on the towel’s cellulose fibers and the strong attractions of water molecules to other water (and ethanol) molecules (right). (credit photo: modification of work by Mark Blaser)

Towels soak up liquids like water because the fibers of a towel are made of molecules that are attracted to water molecules. Most cloth towels are made of cotton, and paper towels are generally made from paper pulp. Both consist of long molecules of cellulose that contain many −OH groups. Water molecules are attracted to these −OH groups and form hydrogen bonds with them, which draws the H 2 O molecules up the cellulose molecules. The water molecules are also attracted to each other, so large amounts of water are drawn up the cellulose fibers.

Capillary action can also occur when one end of a small diameter tube is immersed in a liquid, as illustrated in [link] . If the liquid molecules are strongly attracted to the tube molecules, the liquid creeps up the inside of the tube until the weight of the liquid and the adhesive forces are in balance. The smaller the diameter of the tube is, the higher the liquid climbs. It is partly by capillary action occurring in plant cells called xylem that water and dissolved nutrients are brought from the soil up through the roots and into a plant. Capillary action is the basis for thin layer chromatography, a laboratory technique commonly used to separate small quantities of mixtures. You depend on a constant supply of tears to keep your eyes lubricated and on capillary action to pump tear fluid away.

An image of two beakers and a tube is shown. The first beaker, drawn on the left and labeled “Water,” is drawn half-full of a blue liquid. Two tubes are placed vertically in the beaker and inserted into the liquid. The liquid is shown higher in the tubes than in the beaker and is labeled “Capillary attraction.” The second beaker, drawn in the middle and labeled “Mercury,” is drawn half-full of a gray liquid. Two tubes are placed vertically in the beaker and inserted into the liquid. The liquid is shown lower in the tubes than in the beaker and is labeled “Capillary repulsion.” Lines point to the vertical tubes and label them “Capillary tubes.” A separate drawing of one of the vertical tubes from the first beaker is shown on the right. A right-facing arrow leads from the liquid in the tube to a square call-out box that shows a close-up view of the liquid’s surface. The distance across the tube is labeled “2 r” in this image.
Depending upon the relative strengths of adhesive and cohesive forces, a liquid may rise (such as water) or fall (such as mercury) in a glass capillary tube. The extent of the rise (or fall) is directly proportional to the surface tension of the liquid and inversely proportional to the density of the liquid and the radius of the tube.

The height to which a liquid will rise in a capillary tube is determined by several factors as shown in the following equation:

h = 2 T cos θ r ρ g

In this equation, h is the height of the liquid inside the capillary tube relative to the surface of the liquid outside the tube, T is the surface tension of the liquid, θ is the contact angle between the liquid and the tube, r is the radius of the tube, ρ is the density of the liquid, and g is the acceleration due to gravity, 9.8 m/s 2 . When the tube is made of a material to which the liquid molecules are strongly attracted, they will spread out completely on the surface, which corresponds to a contact angle of 0°. This is the situation for water rising in a glass tube.

Capillary rise

At 25 °C, how high will water rise in a glass capillary tube with an inner diameter of 0.25 mm?

For water, T = 71.99 mN/m and ρ = 1.0 g/cm 3 .

Solution

The liquid will rise to a height h given by: h = 2 T cos θ r ρ g

The Newton is defined as a kg m/s 2 , and so the provided surface tension is equivalent to 0.07199 kg/s 2 . The provided density must be converted into units that will cancel appropriately: ρ = 1000 kg/m 3 . The diameter of the tube in meters is 0.00025 m, so the radius is 0.000125 m. For a glass tube immersed in water, the contact angle is θ = 0°, so cos θ = 1. Finally, acceleration due to gravity on the earth is g = 9.8 m/s 2 . Substituting these values into the equation, and cancelling units, we have:

h = 2 ( 0.07199 kg/s 2 ) ( 0.000125 m ) ( 1000 kg/m 3 ) ( 9.8 m/s 2 ) = 0.12 m = 12 cm

Check your learning

Water rises in a glass capillary tube to a height of 8.4 cm. What is the diameter of the capillary tube?

Answer:

diameter = 0.36 mm

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Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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Source:  OpenStax, Ut austin - principles of chemistry. OpenStax CNX. Mar 31, 2016 Download for free at http://legacy.cnx.org/content/col11830/1.13
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