UK GCSE level age ~14-16, ~US grades 9-10 Biology revision notes re-edit 23/05/2023 [SEARCH]

Transport: 2. A particle model and factors affecting the rate of diffusion and Fick's Law of diffusion applied to biology

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(2A) A particle model and factors affecting the rate of diffusion

A particle model of diffusion in gases and liquids:

Reminder: All fluid particles (gases or liquids) are in constant random motion in all directions (right picture).

The picture sequence below could represent the diffusion of molecules or ions in cell fluids or blood stream or gases in the lungs. Imagine the diffusion gradient from left to right for the green particles added to the blue particles on the left (no semi-permeable shown here, just the idea of a concentration gradient adjacent to a cell membrane).

The blue particles could we water and the green particles could be a sugar, protein or carbon dioxide molecule. So, for the green particles, net migration is from left to right and will continue, in a sealed container, until all the particles are evenly distributed (as pictured).

BUT, as in living organism, if the green particles are removed or used in some process on the right, then net migration (net diffusion) would continue until there was not enough green particles to create a diffusion gradient from left to right i.e. become evenly very dilute.

 

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Be able to define diffusion as the movement of particles from an area of high concentration to an area of lower concentration.

You experience the gas diffusion experiment (or the diffusion particle picture above!) if somebody sprays perfume or deodorant into a room (green particles in the diagram above!).

Even without draughts or convection, the odour will eventually enter your nose and be detected by your sense of smell in any area of the room.

Similarly you can smell petrol or diesel fumes throughout garage due to the diffusion of fuel vapour molecules,

You should know that all liquid or dissolved particles have kinetic energy and so in constant random motion in all directions and tend to spread in all directions, BUT, on average, they will tend to migrate from a region of higher concentration to a region of lower concentration.

The two experiments described above illustrate this random spreading, but by the nature of the experiment design you will see initially the spreading on average is upwards because the coloured substance starts off at the bottom of the container where the concentration will be very high.

Note:

(i) The bigger the concentration difference between two adjacent regions, the steeper the diffusion gradient and the faster the rate of diffusion takes in terms of the net transfer of a particular molecule or ions (eg sugar or sodium ions etc.).

(ii) If the system is warmer, at a higher temperature, the particles gain kinetic energy and can on average move faster and so diffusion is faster.


(2B) Factors affecting the rate of diffusion and Fick's Law of diffusion

The diffusion situation might be exchange of gases in the lungs or movement of molecules and ions through a cell membrane. Three rate of diffusion factors are described and explained in the context of transferring substances through a membrane.

Factors affecting the rate of diffusion of particles through a membrane - you may be talking about diffusion or osmosis and active transport.

Expressed as how diffusion rate is increased - since that's usually what you want in organisms!

(i) The larger the surface area of the membrane, the greater the rate of diffusion.

This factor can also be expressed as increase in surface/volume ratio, so increasing the rate of substance transfer -  there is a bigger chance of a particle passing through a given larger area.

(ii) The steeper the concentration gradient, meaning the greater the difference between the highest concentration and the lowest concentration area on either side of membrane, the greater the rate of diffusion.

So, in a given time, more particles will diffuse from the area of highest concentration to the area of lowest concentration at a greater rate, the greater the concentration difference - more particles available to move to area of lower concentration.

If the concentration was uniform i.e. equal on both sides of the membrane, there would be no net diffusion - no net transfer (ignoring active transport which can operate against a diffusion gradient).

(iii) The shorter the distance the particles have to diffuse - e.g. the thinner the membrane.

The shorter the time needed to transfer particles, the greater the rate of diffusion - think of how thin membranes are!

FICK'S LAW relates factors (i) to (iii) and states:

Rate of diffusion (surface area x concentration difference) (diffusion distance)

(iv) Rates of transfer of substance by diffusion will increase with increase in temperature - the particles (molecules or ions) have more kinetic energy and their average speed increases - e.g. particles can move in and out of cells down diffusion gradients more rapidly.

BUT, there will be a limit e.g. in mammals, many enzyme reactions have an optimum temperature of 37oC, and malfunction if overheated!

Therefore, for a healthy organism at constant temperature, its not an important factor.

Fick's Law on the rate of diffusion of particles relating to a membrane

Fick's Law expresses the three diffusion factors (i) to (iii) described above in a 'proportional' mathematical formula for a thin membrane context:

In this context Fick's Law can be stated as:

Rate of diffusion (surface area x concentration difference) (thickness of membrane)

Diffusion rate (factor (i) x factor (ii)) factor (iii)

Rate {(surface area) x (concentration difference - gradient)} (thickness of membrane - diffusion gradient distance)

In terms of the simple graph diagram above where d = ∆x = membrane thickness:

Diffusion rate (membrane area x ∆c) ∆x

(i) A bigger surface area of membrane - bigger net rate of diffusion.

If you can double or triple the surface area in an organ, you can double or triple the rate of diffusion = rate of transfer of substances.

This assumes a constant diffusion gradient due to constant concentrations, same thickness of membrane (and constant temperature).

In terms of particles, you can argue there is a bigger chance of a particle passing through a given larger area.

(ii) A bigger concentration difference - bigger net rate of diffusion

For a given membrane of fixed surface area and thickness, the bigger the difference in concentration between the two sides of the membrane, the steeper the diffusion gradient, the faster the particle diffusion rate.

Suppose in terms of concentrations on either side of a membrane

(a) the concentrations were 0.05 mol/dm3 and 0.10 mol/dm3

(b) the concentrations were 0.025 mol/dm3 and 0.15 mol/dm3

concentration differences:

(a) 0.10 - 0.05 = 0.05;  (b) 0.15 - 0.025 = 0.125

For a given membrane (constant surface area and thickness) the ratio of the rates of diffusion will be 0.125/0.05 = 2.5

In other words the rate of diffusion in situation (b) is 2.5 times faster than situation (a).

This argument assumes the same thickness of membrane and the same surface area (and constant temperature).

(iii) A thinner membrane - bigger net rate of diffusion

Less distance for particles to travel, so less time needed for transfer.

If you can halve the thickness of a membrane you can double the rate of diffusion through it because you are halving the distance and time needed to diffuse through the membrane and for the same concentrations you are doubling the diffusion gradient.

This assumes a constant surface area and a constant the diffusion gradient.

 

Some examples of Fick's Law calculations

Ex. 1. Suppose an exchange surface has an area 20 m2 and a membrane thickness of 0.005 m.

If the concentrations of a substance are 0.20 mol/dm3 and 0.05 mol/dm3 on either side of the membrane, calculate a relative rate of diffusion.

Relative diffusion rate surface are x concentration difference thickness of membrane

Diffusion rate (membrane area x ∆c) ∆x

Relative diffusion rate = 20 x (0.20 - 0.05) / 0.005 = 600

 

Ex. 2. Lets change the values to decrease the rate of diffusion across a membrane.

Suppose an exchange surface has an area 15 m2 and a membrane thickness of 0.010 m.

If the concentrations of a substance are 0.15 mol/dm3 and 0.05 mol/dm3 on either side of the membrane, calculate a relative rate of diffusion.

Relative diffusion rate surface are x concentration difference thickness of membrane

Diffusion rate (membrane area x ∆c) ∆x

Relative diffusion rate = 15 x (0.15 - 0.05) / 0.01 = 150


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