Surface Area to Volume Ratio investigation.
Surface Area to Volume Ratio investigation
Introduction:
* All organisms carry out exchange between themselves and their environment.
* There is also exchange by diffusion. The rate of diffusion is affected by:
- Temperature
- Surface Area
- Steepness of the concentration gradient
- Distance over which diffusion takes part
The larger the surface area or the steeper the
concentration gradient or the thinner the membrane of diffusion barrier, the faster is the diffusion.
- Diffusion becomes less efficient as the surface area does not increase to an extent that would satisfy the increased demands of a larger volume cell.
- As the length of the sides of a cubodial cell increase then:
Surface area and volume increase exponentially, volume increases at a greater pace, surface area/volume ratio decreases exponentially.
As cell sizes increase, the surface area does not increase in proportion to the volume.
Example by means of a cube.
* All organisms need to exchange substances such as food, waste, gases and heat with their surroundings. These substances must diffuse between the organism and the surroundings. The rate at which a substance can diffuse is given by Fick's law:
Rate of Diffusion a
surface area x concentration difference
distance
The rate of exchange of substances therefore depends on the organism's surface area that is in contact with the surroundings. The requirements for materials depends on the volume of the organism, so the ability to meet the requirements depends on the surface area : volume ratio.
As organisms get bigger their volume and surface area both get bigger, but volume increases much more than surface area. A bacterium is all surface with not much inside, while a whale is all insides with not much surface. This means that as organisms become bigger it becomes more difficult for them to exchange materials with their surroundings. In fact this problem sets a limit on the maximum size for a single cell of about 100 mm. In anything larger than this materials simply cannot diffuse fast enough to support the reactions needed for life. Very large cells like birds' eggs are mostly inert food storage with a thin layer of living cytoplasm round the outside. Organisms also need to exchange heat with their surroundings, and here large animals have an advantage in having a small surface area/volume ratio: they lose less heat than small animals. Large mammals keep warm quite easily and don't need much insulation or heat generation. Small mammals and birds lose their heat very readily, so need a high metabolic rate in order to keep generating heat, as well as thick insulation. So large mammals can feed once every few days while small mammals must feed continuously. Human babies also loose heat more quickly than adults, which is why they need woolly hats. So how do organisms larger than 100 mm exists? All organisms larger than 100 mm are multicellular, which means that their bodies are composed of many small cells, rather than one big cell. Each cell in a multicellular organism is no bigger than about 30mm, and so can exchange materials quickly and independently. Humans have about 1014 cells.
Cell Differentiation
Multicellular organisms have another difference from unicellular ones: their cells are specialised, or differentiated to perform different functions. So the cells in a leaf are different from those in a root or stem, and the cells in a brain are different from those in skin or muscle. In a unicellular organism (like bacteria or yeast) all the cells are alike, and each performs all the functions of the organism.
How important is the surface area of exchange surfaces?
Unicellular organisms like amoeba have a very high surface area to volume ratio. All chemicals needed, can pass into the cells directly and all waste can pass out efficiently. Organisms which have a high surface area to volume ratio have no need for special structures like lungs or gills.
Nutrients and oxygen passing into an organism are rapidly used up. This gives a limit on the ultimate size to which a microorganism can grow. If vital chemicals did not reach all parts of a cell then death ...
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How important is the surface area of exchange surfaces?
Unicellular organisms like amoeba have a very high surface area to volume ratio. All chemicals needed, can pass into the cells directly and all waste can pass out efficiently. Organisms which have a high surface area to volume ratio have no need for special structures like lungs or gills.
Nutrients and oxygen passing into an organism are rapidly used up. This gives a limit on the ultimate size to which a microorganism can grow. If vital chemicals did not reach all parts of a cell then death would be a consequence.
A unicellular organism may satisfy all its needs by direct diffusion. However, in larger organisms cells join to adjacent ones, surface exposed for exchange of substances are reduced.
The larger an organism the lower its surface area to volume ratio. For this reason, many multicellular organisms have specially adapted exchange structures.
What is Diffusion?
Diffusion is the passive movement of molecules along a concentration gradient from a region of high concentration to a region of low concentration.
The rate of diffusion can be increased by increasing the concentration gradient, increasing the surface area across which diffusion occurs, increasing the temperature or by decreasing the distance across which molecules need to travel.
Diffusion happens without any energy input from the organism. The rate at which diffusion occurs depends on four factors:
- The difference in concentration between two areas. (The concentration gradient)
- The distance between the areas.
- The size of the molecules that are diffusing.
- Temperature
So the greater the concentration gradient and the smaller the particles, the quicker the net movement of molecules from the area of high concentration to the area of low concentration.
And diffusion happens faster when molecules need to move only microscopic distances than when they have to travel much larger distances. For example, it would take a small molecule such as oxygen at least 4 minutes to diffuse to the centre of a cell 1mm in diameter.
Some cells, such as those in the human gut and inside plant leaves, have special adaptations often reduce the distance over which diffusion occurs.
The overall rate at which a substance diffuses through a membrane also depends on the surface are in contact with the substance.
The biconcave disc shape of a red blood cell gives it a much greater surface area than if it were spherical, allowing the maximum amount of oxygen to diffuse into it.
Other Examples
An elephant has a much larger surface area than a shrew. But the elephant's volume is also much bigger. If we calculate the ratio of surface area to volume in each animal, we find that the surface area to volume ratio for the elephant is much lower than the value for the shrew. This is a general rule; the larger the animal, the smaller its surface area to volume ratio. The smaller the surface area to volume ratio, the more difficult is it for the animal to gain or loose heat. Large mammals need to compensate for this by having body features that help them to control the way they exchange heat with the environment.
Heat and water loss
Heat/water loss is affected by surface area: volume. In large organisms heat/water loss is less than in small organisms. This is because the organism has longer pathways and longer distances, probably more insulation so it is harder for the heat to escape. Conversely, in smaller organisms heat/water loss is greater than in large organisms. The organism has much shorter pathways; all its internal organs are closer to the surface and have less insulation.
In cold habitats it is an advantage to a mammal to reduce the surface area of its body to reduce the rate of heat loss.
In hot habitats it is an advantage to a mammal to increase the surface area of the body to increase the rate of heat loss.
Blood vessels near the surface of the skin help to regulate body temperature by:
* Cooling the body from the core of the body
* More heat is lost due to Radiation
* More heat is lost due to Convection
* More heat is lost due to Conduction
* More heat is lost due to sweating
* Air flow over surface can be increased
Larger organisms such as humans have evolved systems that increase the surface area available for gas exchange. This area is called the respiratory surface. The respiratory surface in the lungs is large enough to collect enough oxygen to supply all of the body's tissues and to remove carbon dioxide before it builds up toxic levels. The lungs have a very large surface area because of the thousands of tiny air sacs they contain.
These air sacs are called alveoli. The alveoli are small with very thin walls. They have a radius of 0.1mm and wall thickness of about 0.2µm. This makes the diffusion pathway between the air in the lungs and the blood very short. The lungs contain about 300 million alveoli, each wrapped in a fine mesh of capillaries.
- Gill lamellae comprise the respiratory surface in fish. The total surface area of the lamellae is enormous. The length of the diffusion path for oxygen is very short, because the layer of cells that separate the blood from the surrounding in water is very thin. Water contains only on thirtieth as much oxygen per unit volume as air and water is more difficult to push over the respiratory surface. Fish use also a countercurrent system to maximise the rate of gaseous exchange across the respirartory surface. The blood flows in the opposite direction to water, this helps to maintain a diffusion gradient right along the gill. A result of this more 02 can diffuse from the water to the blood.
- The leaves of plants have a large ratio meaning again exchange is carried out more effectively.
Very small organisms such as those consisting of a single cell have no special tissues, organs or systems for gaseous exchange. Mammals are large, multi cellular organisms and they have a complex system for gaseous exchange. Mammals needs such a system single celled organism does not.
Single celled organisms
Mammals
* Large surface area to volume (ratio) for diffusion;
* short diffusion pathway ( to all parts of organism)
* oxygen/ carbon dioxide diffuse in and out.
* Small surface area to volume
* long diffusion pathway
* waterproof/ gastight skinned internal gas exchange surface which is moist with a large surface area
The Practical
Materials and apparatus
* Agar with cresol red, (an indicator: red in alkali, yellow in acid)
* HCl (Hydrochloric Acid), scalpels, tiles, boiling tubes, bungs, timers.
Instructions:
. Place the gelatine block on a tile and use a scalpel or razor blade to cut 2 cubes of 10 mm sides (2 x 1cm cube).
2. Keep one 10 mm cube intact and cut the other in half.
3. Repeat the cutting operation as shown in the flow chart to give five blocks of the dimensions shown (on our sheet).
4. Half fill a boiling tube with dilute Hydrochloric Acid (HCl).
5. Note the time, starting with the largest block, drop all the blocks into the tube of acid and close it securely with a bung.
6. Tilt the tube to spread the cubes out along its length. Hold the tube horizontally and rotate gently to see the blocks from all sides. Do not warm the tubes in your hands.
7. Obverse and record the diffusion of the acid to the centre of each block as indicated by the disappearance of the red colour.
Our Results:
Cube
Dimensions (mm)
Surface area (mm )
Volume (mm )
Time for acid to diffuse to middle (s)
0 x 10 x 10
600
000
500
2
0 x 10 x 5
400
500
682
3
0 x 5 x 5
250
250
450
4
5 x 5 x 5
50
25
322
5
5 x 5 x 2.5
00
62.5
47
Calculations:
surface area = (length x width) x 6 sides
volume = length x width x height
ratio =
surface area
volume
Conclusion
As we can see from the results - the diffusion of acid into the centre of the cell takes longer with the increasing size of the blocks.
We could watch how the blocks got yellow after the certain times (see results). It depended on their size after what time they were not red any more. The blocks are made of agar with cresol red. It works as an indicator as it is red in alkali and yellow in acid. Placing the different sized cubes in the tube filled with Hydrochloric acid starts the reaction with the agar in the acid. Because of the different surface areas the cubes do not get yellow at the same time - the smallest block gets yellow, the fastest and the largest block, the slowest.
The surface area to volume ratio is important because it is one of the factors that determine how quickly substances can diffuse into and out of the cell. In this way, the largest block has a big volume, but a not proportional big surface area. So there is less surface for the acid to diffuse into the centre of the cube and it takes longer. The smallest block has in proportion to its small volume a big surface area. In this way, the acid has a large surface to diffuse into the centre of the small block and takes less time to get yellow.
Diffusion becomes less efficient as the surface area does not increase to an extent that would satisfy the increased demands of a larger volume block.
As the length of the sides of a cube increase then:
-Surface area and volume increase exponentially, volume increases at a greater pace, surface area/volume ratio decreases exponentially.
As block sizes increase, the surface area does not increase in proportion to the volume.
Interpretation: Each point on the graph below represents the surface area and volume for cubes that are increasing by one unit in length, starting with a cube with l = 1. The larger orange dot is the size of the cube (l = 6) at which surface area and volume have equal values (although the units are different to one is units2 and one is units3). For cubes smaller than this, surface area is greater relative to volume than it is in larger cubes (where volume is greater relative to surface area).
Sometimes a graph that shows how the relationship between two variables changes is more instructive. For example, a graph of the ratio of surface area to volume, clearly illustrates that as the size of an object increases (without changing shape), this ratio decreases.
Mathematically, that tells us that the denominator (volume) increases faster relative to the numerator (surface area) as object size increases. The star on the line (at l = 6) represents the same point mentioned above: this is the size of the cube where S and V have equal values, and so the surface area to volume ratio is equal to one.
Evaluation:
This experiment is quite reliable as you can repeat it as often as you want and you get almost the same results. As we can see the results in each group were nearly equal. But you can notice that the end result of cube 1 (10x10x10) differs the most from those of the other groups, because we could not finish the experiment in the class. For this reason, we wrote down the average time of the complete diffusion for the acid into the middle of the biggest cube (advice of our biology teacher).
Problems that could arise are for example the inexactly measurement of time for the acid's diffusion into the centre of the cube. It is difficult to watch the correct moment when this is happening. It could also be a difference in the size of the individual blocks, as we had to chop them up with a scalpel. It could have been occurred that the sizes of the blocks differed from group to group.
Additional Questions:
. What is the relationship between the diffusion of acid into the block and the size of the block?
The bigger the size of the block the longer takes the diffusion of acid into the block.
2. How much more rapidly did acid diffuse to the centre of the smallest block than to the centre of the largest block?
The acid did about 10.2 x faster diffuse to the centre of the smallest block. (1500 / 147 ~ 10.204)
3. Was the rate of diffusion the same or nearly the same for any blocks? Why?
The rate of diffusion was nearly the same for the blocks. As the rate of diffusion depends on the size of blocks and therewith surface area Because of the random nature of the motion of molecules, the rate of diffusion of molecules out of any region in a substance is proportional to the concentration of molecules in that region, and the rate of diffusion into the region is proportional to the concentration of molecules in the surrounding regions. Thus, while molecules continuously flow both into and out of all regions, the net flow is from regions of higher concentration to regions of lower concentration. Generally, the greater the difference in concentration, the faster the diffusion.
4. If the gelatine block represents a single cell organism what substances need to diffuse in and which need to diffuse out?
Oxygen (&nutrients) needs to diffuse in and carbon dioxide needs to diffuse out.
5. Single cell organisms are less than 1 mm across, the largest may be 2 mm across. Why are they no larger than this?
Unicellular organisms like amoeba have a very high surface area to volume ratio. All chemicals needed can pass into the cells directly and all waste can pass out efficiently. Organisms which have a high surface area to volume ratio have no need for special structures like lungs or gills.
Nutrients and oxygen passing into an organism are rapidly used up. This gives a limit on the ultimate size to which a microorganism can grow. If vital chemicals did not reach all parts of a cell then death would be a consequence. A unicellular organism may satisfy all its needs by direct diffusion.
6. How can the rate of diffusion be increased in a 10 mm block without changing its volume?
The rate of diffusion can be increased by enlarging the surface of the block. In this way, there would not be a straight line, but wavy borders. The larger the surface area, the larger the rate of diffusion.
The rate of diffusion can be increased by increasing the concentration gradient, increasing the surface area across which diffusion occurs, increasing the temperature or by decreasing the distance across which molecules need to travel.
Anne Kolouschek
2 MA
