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  • Define diffusion, osmosis, dialysis, and active transport.
  • Calculate diffusion rates.


There is something fishy about the ice cube from your freezer—how did it pick up those food odors? How does soaking a sprained ankle in Epsom salt reduce swelling? The answer to these questions are related to atomic and molecular transport phenomena—another mode of fluid motion. Atoms and molecules are in constant motion at any temperature. In fluids they move about randomly even in the absence of macroscopic flow. This motion is called a random walk and is illustrated in [link] . Diffusion is the movement of substances due to random thermal molecular motion. Fluids, like fish fumes or odors entering ice cubes, can even diffuse through solids.

Diffusion is a slow process over macroscopic distances. The densities of common materials are great enough that molecules cannot travel very far before having a collision that can scatter them in any direction, including straight backward. It can be shown that the average distance x rms size 12{x rSub { size 8{"rms"} } } {} that a molecule travels is proportional to the square root of time:

x rms = 2 Dt , size 12{x rSub { size 8{"rms"} } = sqrt {2 ital "Dt"} } {}

where x rms stands for the root-mean-square distance and is the statistical average for the process. The quantity D size 12{D} {} is the diffusion constant for the particular molecule in a specific medium. [link] lists representative values of D size 12{D} {} for various substances, in units of m 2 /s size 12{m rSup { size 8{2} } "/s"} {} .

The figure shows the path of a random walk. The random thermal motion of a molecule is shown to begin at a start point and then the particles move about zigzag in all directions and end up at the finish point. The distance between the start and finish point is shown as x. Continuous arrows show various directions of motion.
The random thermal motion of a molecule in a fluid in time t size 12{t} {} . This type of motion is called a random walk.
Diffusion constants for various molecules At 20°C and 1 atm
Diffusing molecule Medium D (m 2 /s)
Hydrogen ( H 2 ) Air 6.4 × 10 –5
Oxygen ( O 2 ) Air 1.8 × 10 –5
Oxygen ( O 2 ) Water 1.0 × 10 –9
Glucose ( C 6 H 12 O 6 ) Water 6.7 × 10 –10
Hemoglobin Water 6.9 × 10 –11
DNA Water 1.3 × 10 –12

Note that D size 12{D} {} gets progressively smaller for more massive molecules. This decrease is because the average molecular speed at a given temperature is inversely proportional to molecular mass. Thus the more massive molecules diffuse more slowly. Another interesting point is that D size 12{D} {} for oxygen in air is much greater than D size 12{D} {} for oxygen in water. In water, an oxygen molecule makes many more collisions in its random walk and is slowed considerably. In water, an oxygen molecule moves only about 40 μ m in 1 s. (Each molecule actually collides about 10 10 size 12{"10" rSup { size 8{"10"} } } {} times per second!). Finally, note that diffusion constants increase with temperature, because average molecular speed increases with temperature. This is because the average kinetic energy of molecules, 1 2 mv 2 size 12{ { { size 8{1} } over { size 8{2} } } ital "mv" rSup { size 8{2} } } {} , is proportional to absolute temperature.

Calculating diffusion: how long does glucose diffusion take?

Calculate the average time it takes a glucose molecule to move 1.0 cm in water.


We can use x rms = 2 D t size 12{x rSub { size 8{"rms"} } = sqrt {2 ital "Dt"} } {} , the expression for the average distance moved in time t size 12{t} {} , and solve it for t size 12{t} {} . All other quantities are known.


Solving for t size 12{t} {} and substituting known values yields

t = x rms 2 2 D = ( 0.010 m ) 2 2 ( 6 . 7 × 10 10 m 2 /s ) = 7 . 5 × 10 4 s = 21 h .


This is a remarkably long time for glucose to move a mere centimeter! For this reason, we stir sugar into water rather than waiting for it to diffuse.

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Questions & Answers

how can we find absolute uncertainty
ayesha Reply
it what?
in physics
the basic formula is uncertainty in momentum multiplied buy uncertainty In position is greater than or equal to 4×pi/2. same formula for energy and time
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Ojeh Reply
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Joy Reply
Is there a formula for time of free fall given that the body has initial velocity? In other words, formula for time that takes a downward-shot projectile to hit the ground. Thanks!
Cyclone Reply
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watt is the unit of power
watt can also be expressed as Nm/s
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SI unit of mass is Kg(kilogram).
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Formula for for the falling body with initial velocity is:v^2=v(initial)^2+2*g*h
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2 forces whose resultant is 100N, are at right angle to each other .if one of them makes an angle of 30 degree with the resultant determine it's magnitude
Victor Reply
50 N... (50 *1.732)N
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Is earth is an inertial frame?
Sahim Reply
The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system
Most welcome
Hey.. I've a question.
Sahim Reply
Is earth inertia frame?
only the center
What is an abucus?
what would be the correct interrogation "what is time?" or "how much has your watch ticked?"
prakash Reply
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a load of 20N on a wire of cross sectional area 8×10^-7m produces an extension of 10.4m. calculate the young modules of the material of the wire is of length 5m
Ebenezer Reply
Young's modulus = stress/strain strain = extension/length (x/l) stress = force/area (F/A) stress/strain is F l/A x
so solve it
two bodies x and y start from rest and move with uniform acceleration of a and 4a respectively. if the bodies cover the same distance in terms of tx and ty what is the ratio of tx to ty
Oluwatola Reply
what is cesium atoms?
prakash Reply
The atoms which form the element Cesium are known as Cesium atoms.
A material that combines with and removes trace gases from vacuum tubes.
what is difference between entropy and heat capacity
Heat capacity can be defined as the amount of thermal energy required to warm the sample by 1°C. entropy is the disorder of the system. heat capacity is high when the disorder is high.
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What is realm
Vinodhini Reply
The quantum realm, also called the quantum scale, is a term of art inphysics referring to scales where quantum mechanical effects become important when studied as an isolated system. Typically, this means distances of 100 nanometers (10−9meters) or less or at very low temperature.
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Vinodhini Reply
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revolutionary Reply
Practice Key Terms 9

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