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Part a of the figure shows a semi permeable membrane shown as small rectangular sections in a vertical line, separated by small gaps called as pores. Molecules are shown in all shapes on both the sides of the membranes. Some molecules are shown to diffuse through the pores. Part b of the diagram shows molecules in the form of small spheres packed on both sides of a single vertical rectangular membrane. Some molecules are shown to dissolve in this membrane and diffuse across it.
(a) A semipermeable membrane with small pores that allow only small molecules to pass through. (b) Certain molecules dissolve in this membrane and diffuse across it.

Osmosis is the transport of water through a semipermeable membrane from a region of high concentration to a region of low concentration. Osmosis is driven by the imbalance in water concentration. For example, water is more concentrated in your body than in Epsom salt. When you soak a swollen ankle in Epsom salt, the water moves out of your body into the lower-concentration region in the salt. Similarly, dialysis    is the transport of any other molecule through a semipermeable membrane due to its concentration difference. Both osmosis and dialysis are used by the kidneys to cleanse the blood.

Osmosis can create a substantial pressure. Consider what happens if osmosis continues for some time, as illustrated in [link] . Water moves by osmosis from the left into the region on the right, where it is less concentrated, causing the solution on the right to rise. This movement will continue until the pressure ρ gh size 12{ρ ital "gh"} {} created by the extra height of fluid on the right is large enough to stop further osmosis. This pressure is called a back pressure . The back pressure ρ gh size 12{ρ ital "gh"} {} that stops osmosis is also called the relative osmotic pressure    if neither solution is pure water, and it is called the osmotic pressure    if one solution is pure water. Osmotic pressure can be large, depending on the size of the concentration difference. For example, if pure water and sea water are separated by a semipermeable membrane that passes no salt, osmotic pressure will be 25.9 atm. This value means that water will diffuse through the membrane until the salt water surface rises 268 m above the pure-water surface! One example of pressure created by osmosis is turgor in plants (many wilt when too dry). Turgor describes the condition of a plant in which the fluid in a cell exerts a pressure against the cell wall. This pressure gives the plant support. Dialysis can similarly cause substantial pressures.

Part a of the figure shows a vessel having two different concentrations of sugar in water separated by a semipermeable membrane that passes water but not sugar molecules. The sugar molecules are shown as small red color spheres and water molecules as still smaller blue colored spheres. The right side of the solution shows more of sugar molecules represented as more number of red spheres. The osmosis of water molecules is shown toward right. Part b shows the second stage for figure on part a. The osmosis of water is shown toward right. The height of fluid on right is shown as h above the fluid on the left. The back pressure of water is shown toward left.
(a) Two sugar-water solutions of different concentrations, separated by a semipermeable membrane that passes water but not sugar. Osmosis will be to the right, since water is less concentrated there. (b) The fluid level rises until the back pressure ρ gh size 12{ρ ital "gh"} {} equals the relative osmotic pressure; then, the net transfer of water is zero.

Reverse osmosis and reverse dialysis    (also called filtration) are processes that occur when back pressure is sufficient to reverse the normal direction of substances through membranes. Back pressure can be created naturally as on the right side of [link] . (A piston can also create this pressure.) Reverse osmosis can be used to desalinate water by simply forcing it through a membrane that will not pass salt. Similarly, reverse dialysis can be used to filter out any substance that a given membrane will not pass.

One further example of the movement of substances through membranes deserves mention. We sometimes find that substances pass in the direction opposite to what we expect. Cypress tree roots, for example, extract pure water from salt water, although osmosis would move it in the opposite direction. This is not reverse osmosis, because there is no back pressure to cause it. What is happening is called active transport    , a process in which a living membrane expends energy to move substances across it. Many living membranes move water and other substances by active transport. The kidneys, for example, not only use osmosis and dialysis—they also employ significant active transport to move substances into and out of blood. In fact, it is estimated that at least 25% of the body’s energy is expended on active transport of substances at the cellular level. The study of active transport carries us into the realms of microbiology, biophysics, and biochemistry and it is a fascinating application of the laws of nature to living structures.

Section summary

  • Diffusion is the movement of substances due to random thermal molecular motion.
  • The average distance x rms size 12{x rSub { size 8{"rms"} } } {} a molecule travels by diffusion in a given amount of time is given by
    x rms = 2 D t , size 12{x rSub { size 8{"rms"} } = sqrt {2 ital "Dt"} } {}

    where D size 12{D} {} is the diffusion constant, representative values of which are found in [link] .

  • Osmosis is the transport of water through a semipermeable membrane from a region of high concentration to a region of low concentration.
  • Dialysis is the transport of any other molecule through a semipermeable membrane due to its concentration difference.
  • Both processes can be reversed by back pressure.
  • Active transport is a process in which a living membrane expends energy to move substances across it.

Conceptual questions

Why would you expect the rate of diffusion to increase with temperature? Can you give an example, such as the fact that you can dissolve sugar more rapidly in hot water?

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How are osmosis and dialysis similar? How do they differ?

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Problem exercises

You can smell perfume very shortly after opening the bottle. To show that it is not reaching your nose by diffusion, calculate the average distance a perfume molecule moves in one second in air, given its diffusion constant D size 12{D} {} to be 1.00 × 10 –6 m 2 /s size 12{1 "." "00" times "10" rSup { size 8{6} } `m rSup { size 8{2} } "/s"} {} .

1 . 41 × 10 3 m size 12{1 "." "41" times "10" rSup { size 8{ - 3} } " m"} {}

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What is the ratio of the average distances that oxygen will diffuse in a given time in air and water? Why is this distance less in water (equivalently, why is D size 12{D} {} less in water)?

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Oxygen reaches the veinless cornea of the eye by diffusing through its tear layer, which is 0.500-mm thick. How long does it take the average oxygen molecule to do this?

1 . 3 × 10 2 s size 12{1 "." 3 times "10" rSup { size 8{2} } " s"} {}

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(a) Find the average time required for an oxygen molecule to diffuse through a 0.200-mm-thick tear layer on the cornea. (b) How much time is required to diffuse 0 .500 cm 3 size 12{0 "." "500"`"cm" rSup { size 8{3} } } {} of oxygen to the cornea if its surface area is 1 . 00 cm 2 size 12{1 "." "00"`"cm" rSup { size 8{2} } } {} ?

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Suppose hydrogen and oxygen are diffusing through air. A small amount of each is released simultaneously. How much time passes before the hydrogen is 1.00 s ahead of the oxygen? Such differences in arrival times are used as an analytical tool in gas chromatography.

0.391 s

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Questions & Answers

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show that a particle moving under the influence of an attractive force mu/y^3 towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v^2k^2 and distance uk^2/√u-k as origin
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if u at an angle of 12 degrees their period will be same so as their velocity, that means they both move simultaneously since both both hovers at same length meaning they have the same length
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The number of protons in the nucleus of an atom
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Practice Key Terms 9

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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