E. Animals: Structure and Function · Animals: Structure and FunctionExchange Surfaces: Why Animals Need Respiratory, Digestive and Circulatory Systems
E3.1 E3.2 E3.3 E2.1 A1.12 A1.13About 65 minutes
Learning goals- I can explain how a diffusion gradient, surface area and distance control the rate of diffusion.
- I can calculate surface-area-to-volume ratios and explain why large animals need specialized exchange surfaces.
- I can describe the features shared by good exchange surfaces such as alveoli, villi and capillaries.
- I can explain how the respiratory, digestive and circulatory systems work together to supply cellular respiration.
Words to know
diffusion
The net movement of particles from a region of higher concentration to a region of lower concentration, caused by their random motion. It needs no energy from the cell.
diffusion gradient
The difference in concentration of a substance between two places (over a given distance). A steeper gradient (bigger difference) gives faster diffusion. Also called a concentration gradient.
surface-area-to-volume ratio (SA:V)
Surface area divided by volume. It gets smaller as an object gets bigger.
exchange surface
A surface where substances move between an organism and its surroundings, or between blood and cells, such as alveoli, villi and capillaries.
cellular respiration
The reactions in cells (mostly in mitochondria) that release energy from glucose: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + energy (ATP).
ATP
Adenosine triphosphate, the molecule cells use to carry and spend energy.
anatomy / physiology
Anatomy is the structure of the body and its parts. Physiology is how those parts work.
A problem of size
An amoeba in a pond has an easy life when it comes to oxygen. It is one tiny cell, so oxygen simply diffuses in through its membrane and reaches every part of it in a fraction of a second.
You are made of tens of trillions of cells. A muscle cell deep in your thigh is many centimetres from the nearest air and the nearest food. Diffusion alone would take far too long to get oxygen there. So animals like us need systems: a respiratory system to take in oxygen, a digestive system to take in nutrients, and a circulatory system to carry both to every cell and carry wastes away.
This unit is about the anatomy (structure) and physiology (function) of those three systems, how they connect, what goes wrong with them, and how technology helps us study and treat them.
Remember from Grades 9 and 10
In Grade 9 you learned that cells release energy by cellular respiration. In Grade 10 (Tissues, Organs, and Systems) you followed food through the digestive organs, air through the respiratory tract to the alveoli, and blood through the four chambers of the heart. You saw that villi and alveoli have huge surface areas and thin walls. In Grade 11 we go deeper: the chemistry of digestion, the physics of breathing and gas transport, the heart's electrical system and blood pressure, and the disorders and technologies of these systems.
Diffusion and the diffusion gradient
Diffusion is the net movement of particles from where they are more concentrated to where they are less concentrated. Particles move randomly all the time; because more of them start on the crowded side, more of them end up crossing to the less crowded side than the other way. Diffusion does not use energy from the cell.
The difference in concentration between two places is called the diffusion gradient (or concentration gradient). The rate of diffusion across a surface depends on three main things:
- The gradient. A bigger concentration difference means faster diffusion.
- Surface area. More surface means more particles can cross at once.
- Distance (thickness of the barrier). A thinner barrier means faster diffusion. Diffusion time grows with the square of the distance: twice as far takes about four times as long.
Scientists combine these ideas as: rate of diffusion ∝ (surface area × concentration difference) ÷ thickness. This relationship is called Fick's law.
The surface-area-to-volume problem
As an object grows, its volume grows faster than its surface area. For a cube with side length s:
- surface area = 6s²
- volume = s³
- SA:V = 6s² ÷ s³ = **6 ÷ s**
So when the side doubles, SA:V is cut in half. A cell's needs (oxygen, food) depend on its volume, but its supply comes in through its surface. Big organisms have far too little surface, compared with their volume, to supply themselves by diffusion through their skin. That is why cells stay small, and why large animals have folded, branched exchange surfaces inside the body plus a transport system (blood) to carry materials.
Worked exampleExample 1: Calculating SA:V
A cube-shaped model "cell" has sides of 3.0 cm. (a) Find its surface area, volume and SA:V. (b) If the side were 0.30 cm instead, what would SA:V be? (c) Which model would exchange materials better, and why?
- (a) SA = 6s² = 6 × (3.0 cm)² = 6 × 9.0 = 54 cm².
- V = s³ = (3.0 cm)³ = 27 cm³.
- SA:V = 54 ÷ 27 = 2.0 : 1 (that is, 2.0 cm² of surface for every cm³ of volume). Check with the shortcut: 6 ÷ 3.0 = 2.0. ✓
- (b) SA:V = 6 ÷ 0.30 = 20 : 1.
- (c) The 0.30 cm model has 10 times as much surface per unit of volume, so materials can enter and reach its centre much faster. Small size favours exchange by diffusion.
(a) 54 cm², 27 cm³, SA:V 2.0 : 1. (b) 20 : 1. (c) The smaller cube, because it has more surface for each unit of volume and a shorter distance to its centre.
What makes a good exchange surface?
Every exchange surface in your body follows the same design rules, all straight from Fick's law:
- Large surface area: alveoli (hundreds of millions of tiny sacs), villi and microvilli in the small intestine, and a capillary network that reaches almost every cell.
- Thin: alveolus and capillary walls are a single layer of flat cells.
- Moist: gases must dissolve before they can diffuse across a membrane.
- A steep gradient kept steep: breathing keeps bringing fresh air to the alveoli, and blood keeps flowing past, carrying oxygen away so the oxygen level in the blood beside the alveoli stays lower than in the air.
The three systems are a team. The respiratory system brings oxygen in; the digestive system breaks food into small molecules and absorbs them; the circulatory system carries both to cells, where cellular respiration happens:
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + energy (ATP)
The circulatory system then carries the carbon dioxide back to the lungs to be breathed out.
| Exchange surface | What is exchanged | Surface area feature | Thin? | How the gradient is kept steep |
|---|
| Alveoli (lungs) | O₂ in, CO₂ out | hundreds of millions of tiny sacs | 1 cell thick | breathing renews air; blood flow carries O₂ away |
| Villi (small intestine) | digested nutrients in | folds, villi and microvilli | 1 cell thick lining | blood and lymph flow carry nutrients away |
| Capillaries (tissues) | O₂ and nutrients out, CO₂ and wastes in | a huge branching network | 1 cell thick | cells keep using O₂; blood keeps flowing |
| Gills (fish) | O₂ in, CO₂ out | many thin filaments | very thin | water flows one way, opposite to the blood |
Worked exampleExample 2: Using Fick's law to explain
Explain, using the three factors that affect diffusion, why each change below slows gas exchange in the lungs. (a) Fluid builds up and thickens the alveolar walls. (b) Some alveolar walls break down and many small sacs become a few large ones. (c) A person is at high altitude, where the air has less oxygen per litre.
- Recall: rate ∝ (surface area × concentration difference) ÷ thickness.
- (a) The barrier is thicker, so the distance increases and the rate falls.
- (b) A few large sacs have less total surface area than many small ones (the SA:V idea again), so the rate falls.
- (c) Less oxygen in the air gives a smaller concentration difference (a shallower diffusion gradient) between the alveoli and the blood, so the rate falls.
(a) thicker barrier; (b) less surface area; (c) smaller gradient. You will meet (a) and (b) again as real disorders (pneumonia and emphysema) in the respiratory disorders lesson.
Hands-on activityHow far can diffusion reach? (gelatin cubes)
Grown-up needed for the hot water and the knife.
You need: one packet of unflavoured gelatin (or a box of light-coloured jelly powder), hot water, a small flat container, a sharp knife, a ruler, a cup, dark food colouring, a spoon and a timer.
- With a grown-up, make the gelatin about twice as firm as the package says (use half the water). Pour it about 3 cm deep into the container and chill it until firm (a few hours).
- Cut three cubes: 1 cm, 2 cm and 3 cm on each side. Measure carefully.
- Calculate SA, V and SA:V for each cube before you start. Predict which will be fully coloured first.
- Fill a cup with water and add about 20 drops of food colouring. Put all three cubes in. Start the timer.
- After 20 minutes, lift the cubes out with a spoon, blot them, and cut each in half. Measure how far the colour moved in from the surface (in mm), and the size of the uncoloured core.
- Calculate what percentage of each cube's volume is coloured. (Hint: if the colour moved in d cm, the uncoloured core is a cube of side s − 2d.)
What to look for: the colour moves in about the same distance in every cube (diffusion depends on distance, not cube size), so the small cube is coloured through a much larger percentage of its volume. That is the SA:V problem a large animal solves with lungs, intestines and blood.
Just for funA shrew is one of the smallest mammals, and like many small mammals it has a very high resting heart rate and must eat often. Its body loses heat fast through all that surface area. Being small: great for diffusion, terrible for skipping lunch.
Your turn
1Define diffusion gradient.
The difference in concentration of a substance between two places (over a given distance). Substances diffuse down the gradient, from high to low concentration.
2List the three factors in Fick's law and say how each affects the rate of diffusion.
Surface area (more area, faster), concentration difference (bigger gradient, faster), thickness/distance (thicker, slower).
3A cube has a side of 5 cm. Find its SA:V.
SA = 6 × 25 = 150 cm²; V = 125 cm³; SA:V = 150 ÷ 125 = 1.2 : 1 (shortcut: 6 ÷ 5 = 1.2).
4Why can't a large animal rely on diffusion through its skin alone to get oxygen?
Its SA:V is too small: there is not enough surface for its large volume, and most cells are too far from the surface for diffusion to reach them in time.
5Give the four features of a good exchange surface.
Large surface area, thin, moist, and a steep gradient that is maintained (by breathing and blood flow).
6Write the word equation and the balanced chemical equation for cellular respiration.
glucose + oxygen → carbon dioxide + water + energy; C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + energy (ATP).
7Which system delivers glucose to a muscle cell, and which system first took that glucose into the body?
The circulatory system delivers it; the digestive system absorbed it (in the small intestine).
More practice: warm-up
1Does diffusion need energy from the cell?
No. It is driven by the random motion of particles down a concentration gradient.
2What is anatomy? What is physiology?
Anatomy is structure; physiology is function (how parts work).
3How thick are the walls of alveoli and capillaries?
One cell thick (a single layer of flat cells).
4As a cube gets bigger, does SA:V increase or decrease?
It decreases (SA:V = 6 ÷ side).
5Name the exchange surface in the small intestine.
The villi (and the microvilli on their cells).
More practice: on your own
1Cube A has side 1.5 cm and cube B has side 4.5 cm. Find each SA:V and how many times larger A's ratio is.
A: 6 ÷ 1.5 = 4.0 : 1. B: 6 ÷ 4.5 ≈ 1.3 : 1. A's ratio is 3 times B's, because B's side is 3 times as long.
2Why must gas exchange surfaces be moist?
Gases must dissolve in water before they can diffuse across cell membranes.
3Explain how continuous blood flow past the alveoli helps keep gas exchange fast.
Blood carries newly absorbed oxygen away, so the blood arriving at the alveoli always has less oxygen than the air. This keeps the diffusion gradient steep.
4If oxygen takes time t to diffuse 10 µm, about how long would it take to diffuse 30 µm?
Time grows with distance squared: (30 ÷ 10)² = 9, so about **9t**.
5A flatworm is flat and thin and has no circulatory system. Use SA:V to explain how it survives.
Being flat gives it a very high SA:V and keeps every cell close to the surface (short diffusion distance), so diffusion through its body surface supplies enough oxygen.
Challenge
1In the gelatin activity, colour moved 0.40 cm into each cube. What percentage of the 2.0 cm cube's volume was coloured?
Uncoloured core side = 2.0 − 2(0.40) = 1.2 cm, so core V = 1.2³ = 1.728 cm³. Total V = 8.0 cm³. Coloured = 8.0 − 1.728 = 6.272 cm³. Percentage = 6.272 ÷ 8.0 × 100 ≈ 78%.
2Explain why a large, active animal such as a moose needs both a large internal exchange surface and a pump-driven circulatory system, while a sponge needs neither.
A moose has a tiny SA:V and high oxygen demand, so it needs a huge internal surface (lungs) to take in enough oxygen, and bulk flow (blood pumped by a heart) to carry it the long distances to cells, because diffusion is far too slow over centimetres. A sponge has a low metabolic rate and water flows through its body past every cell, so each cell is close to the water and diffusion is enough.
3Some people state that rate of diffusion depends "only on the concentration of oxygen in the air." Use Fick's law to give a complete correction, with one body example for each factor.
Rate ∝ (surface area × concentration difference) ÷ thickness. It depends on the difference in concentration (e.g., blood flow keeps blood O₂ low beside the alveoli), on surface area (e.g., hundreds of millions of alveoli, villi), and on thickness (e.g., one-cell-thick alveolus and capillary walls). Air concentration matters only through the gradient it creates.
Quiz
1. Which change would increase the rate of diffusion across a membrane?
2. A cube with 2 cm sides has an SA:V of 3 : 1. What is the SA:V of a cube with 6 cm sides?
4. Which feature is not shared by good exchange surfaces?
5. In cellular respiration, which molecule is a product?
6. Which system carries oxygen from the lungs to a muscle cell?
Big idea: this opening lesson connects all three systems in the unit (E3.1 respiratory, E3.2 digestive, E3.3 circulatory) to one physical idea: diffusion is fast over short distances and big areas, and slow otherwise. It introduces the curriculum term diffusion gradient (E2.1) and practises calculations with units and sensible precision (A1.12, A1.13).
How to help: Do the gelatin activity together; it makes SA:V visible. Ask your teen to explain, in their own words, why a whale or a moose can't "breathe through its skin" but a flatworm can.
Common difficulties:
- Thinking bigger objects have bigger SA:V. They have more surface in total, but less per unit of volume.
- Confusing breathing with cellular respiration. Breathing moves air; cellular respiration is a chemical reaction in cells.
- Forgetting units: SA in cm², V in cm³, SA:V is per cm (often written as a ratio such as 3 : 1).
Safety: the activity uses hot water and a knife, so a grown-up should do those steps.