12.7 Molecular transport phenomena: diffusion, osmosis, and related  (Page 3/12)

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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 $\rho \text{gh}$ 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 $\rho \text{gh}$ 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.

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 ${x}_{\text{rms}}$ a molecule travels by diffusion in a given amount of time is given by
${x}_{\text{rms}}=\sqrt{2D\text{t}},$

where $D$ 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?

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

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 $D$ to be $1.00×{\text{10}}^{–6}\phantom{\rule{0.25em}{0ex}}{\text{m}}^{2}\text{/s}$ .

$1\text{.}\text{41}×{\text{10}}^{-3}\phantom{\rule{0.25em}{0ex}}\text{m}$

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 $D$ less in water)?

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?

$1\text{.}3×{\text{10}}^{2}\phantom{\rule{0.25em}{0ex}}\text{s}$

(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 $0\text{.500}\phantom{\rule{0.25em}{0ex}}{\text{cm}}^{3}$ of oxygen to the cornea if its surface area is $1\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}{\text{cm}}^{2}$ ?

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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