C. Metabolic Processes · Metabolic ProcessesEnergy in Living Systems: Metabolism and the Laws of Thermodynamics
C3.3 C2.1 C1.1 A1.12 A1.13About 70 minutes
Learning goals- I can define metabolism, catabolism and anabolism and give an example of each.
- I can state the first and second laws of thermodynamics and apply them to cells and ecosystems.
- I can explain entropy and why living things need a constant input of energy.
- I can use ΔG = ΔH − TΔS to decide whether a reaction is exergonic or endergonic.
- I can read and draw free-energy diagrams, including activation energy.
Words to know
metabolism
All the chemical reactions in a cell or organism: catabolism plus anabolism.
catabolism
Metabolic pathways that break large molecules into smaller ones and release energy (e.g. cellular respiration).
anabolism
Metabolic pathways that build large molecules from smaller ones and require energy (e.g. protein synthesis, photosynthesis).
kinetic energy
Energy of motion, including heat (the random motion of particles).
potential energy
Stored energy; in biology, mostly chemical energy stored in the arrangement of atoms in bonds.
first law of thermodynamics
Energy cannot be created or destroyed, only transferred or transformed.
second law of thermodynamics
In every energy transfer some energy becomes unusable heat, and the total entropy of the universe increases.
entropy (S)
A measure of disorder, or of how spread out energy and matter are.
free energy (G)
Gibbs free energy: the energy in a system that is available to do useful work.
exergonic
A reaction that releases free energy (ΔG < 0); it can happen spontaneously.
endergonic
A reaction that requires an input of free energy (ΔG > 0).
activation energy (Ea)
The energy needed to start a reaction, by straining or breaking bonds in the reactants.
Why do you need to eat every day?
You ate breakfast this morning. By supper you will be hungry again, even if you spent the day sitting still. Your body isn't using up matter (most of the atoms you eat leave as CO₂ and water), so what is it using up?
The answer is usable energy. Every cell in your body runs thousands of chemical reactions every second, and each one turns some useful energy into heat that escapes into the room. That is why a crowded classroom in February gets warm, and why you need a steady supply of food. This lesson gives you the physics behind that idea: the laws of thermodynamics. They are the rules for every process in this unit, from glycolysis to the Calvin cycle.
Remember from earlier grades
In Grade 9 you learned that plants capture light energy by photosynthesis and that all cells release energy from glucose by cellular respiration: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + energy (ATP and heat). In the Biochemistry unit you studied enzymes and the four types of biochemical reactions, including redox reactions. This unit asks how those energy changes happen, step by step, and why they obey the laws of physics.
Metabolism: two directions
Metabolism is the sum of all the chemical reactions in a cell. Biologists group the reactions into metabolic pathways: chains of steps, each one catalysed by its own enzyme, where the product of one step is the reactant of the next.
- Catabolic pathways break big molecules into smaller ones and release energy. Cellular respiration is the main example: glucose is broken down to CO₂ and water.
- Anabolic pathways build big molecules from small ones and use energy. Examples: making proteins from amino acids, making glycogen from glucose, and photosynthesis (making glucose from CO₂ and water).
The two directions are linked. Cells capture energy from catabolism in a molecule called ATP, and spend that ATP to drive anabolism. You will study ATP in detail in the next lesson.
Forms of energy in a cell
Energy is the capacity to do work, that is, to move matter against a force. Cells do three main kinds of work: chemical work (building molecules), transport work (pumping ions across membranes) and mechanical work (contracting muscles, beating cilia).
Energy comes in two basic forms:
- Kinetic energy is energy of motion. Heat (thermal energy) is the random motion of atoms and molecules. Light is also a form of kinetic (radiant) energy.
- Potential energy is stored energy. In biology the most important form is chemical energy, stored in the arrangement of atoms in molecules. A glucose molecule has a lot of chemical potential energy compared with the CO₂ and H₂O it can be broken into.
A key idea: breaking a chemical bond always requires energy, and forming a bond always releases energy. When we say "energy is stored in glucose", we really mean that the bonds formed in the products (CO₂ and H₂O) are much stronger and more stable than the bonds broken in the reactants, so the overall reaction releases energy.
The first law: energy is conserved
The first law of thermodynamics: energy cannot be created or destroyed. It can only be transferred from one place to another or transformed from one form to another.
- A maple leaf does not make energy. It transforms light energy into chemical energy in sugar.
- Your muscles do not make energy either. They transform the chemical energy of glucose into mechanical energy (movement) and heat.
So the total energy before a process equals the total energy after it. The catch is in what form the energy ends up.
The second law: every transfer costs something
The second law of thermodynamics: every energy transfer or transformation increases the entropy (disorder) of the universe. In practice, in every energy conversion some energy is lost as heat that is too spread out to do useful work.
Entropy (S) measures how spread out, or disordered, energy and matter are. A sugar cube has low entropy; the same sugar dissolved and spread through your tea has higher entropy. One glucose molecule has lower entropy than the 12 small molecules (6CO₂ + 6H₂O) it is broken into.
This has big consequences for living things:
- No conversion is 100% efficient. When your cells turn glucose energy into ATP, a large share escapes as heat. (In birds and mammals this heat keeps the body warm, a happy side effect.)
- Energy flows; it does not cycle. In a food chain, most of the energy at each trophic level is lost as heat and is not passed on. A common rule of thumb is that only about 10% reaches the next level. That is why food chains rarely have more than four or five links. Matter (carbon, oxygen) cycles, but energy enters as sunlight and leaves as heat.
- Life needs a constant energy input. Cells are highly ordered (low entropy). Does life break the second law? No. A cell is an open system: it takes in energy and matter and releases heat and simpler waste molecules. The cell stays orderly only by increasing the entropy of its surroundings even more. Total entropy (cell + surroundings) always goes up.
Free energy: will a reaction go?
Chemists combine energy and entropy into one quantity: Gibbs free energy (G), the energy available to do useful work. For any reaction, the change in free energy is
ΔG = ΔH − TΔS
- ΔH is the change in enthalpy (total heat content; negative if heat is released).
- T is the temperature in kelvins (K = °C + 273.15).
- ΔS is the change in entropy (positive if the products are more disordered).
The sign of ΔG tells you the direction:
- ΔG < 0: exergonic. The products have less free energy than the reactants. Energy is released, and the reaction is spontaneous (it can happen without an energy input).
- ΔG > 0: endergonic. The products have more free energy. The reaction needs an input of energy and is not spontaneous.
- ΔG = 0: equilibrium. No net change happens. A cell at equilibrium can do no work. A cell at equilibrium is a dead cell!
For glucose: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O, ΔG = −2870 kJ/mol (standard conditions). The reverse reaction, photosynthesis, has ΔG = +2870 kJ/mol and needs sunlight to drive it.
"Spontaneous" does not mean "fast". Sugar in a bowl reacts with oxygen spontaneously (ΔG < 0), but so slowly that you will never notice. Before any reaction can proceed, molecules must get over an energy hill, the activation energy (Ea). Enzymes (from the Biochemistry unit) lower Ea so reactions happen quickly at body temperature. They do not change ΔG.
Worked exampleLet's use ΔG = ΔH − TΔS
A reaction in a cell has ΔH = −20.0 kJ/mol and ΔS = +0.0400 kJ/(mol·K). The cell is at body temperature, 37 °C. Calculate ΔG and decide whether the reaction is exergonic or endergonic.
- Convert temperature to kelvins: T = 37 + 273.15 = 310.15 K (use 310 K).
- Calculate TΔS: 310 K × 0.0400 kJ/(mol·K) = 12.4 kJ/mol.
- Substitute: ΔG = ΔH − TΔS = −20.0 − 12.4 = −32.4 kJ/mol.
- ΔG is negative, so the reaction releases free energy. Both terms help: heat is released (ΔH < 0) and disorder increases (ΔS > 0).
ΔG ≈ −32.4 kJ/mol, so the reaction is exergonic (spontaneous). Watch the units: ΔS is often given in J/(mol·K), so divide by 1000 before combining it with ΔH in kJ.
Worked exampleLet's apply the second law to a food chain
In a boreal forest food chain, grasses and shrubs store 20 000 kJ of energy per square metre per year. Snowshoe hares eat the plants, and lynx eat the hares. Using the 10% rule of thumb, estimate the energy available to the lynx, and explain where the rest goes.
- Producers → hares: 10% of 20 000 kJ = 2000 kJ.
- Hares → lynx: 10% of 2000 kJ = 200 kJ.
- Where did the other 19 800 kJ go? Most was released as heat by cellular respiration at each level (second law). Some was in parts that were not eaten or digested (roots, bones, fur) and went to decomposers, who also release it as heat.
- None of it was destroyed (first law): it was converted to heat, which cannot be used to make ATP.
About 200 kJ/m² per year reaches the lynx. Energy is conserved but is degraded to heat at each step, so it flows one way through the ecosystem.
Just for funYour body at rest gives off roughly as much heat as a 100 W incandescent light bulb. So if you've ever been told you "light up a room", thermodynamics agrees, at least in the infrared.
Hands-on activityEntropy and energy in your kitchen
You need: two clear glasses, cold and hot tap water, food colouring, an ice cube, a kitchen thermometer if you have one, a notebook.
Safety note: use hot tap water only, not boiling water.
- Spreading out (entropy). Fill one glass with cold water and one with hot tap water. Let them sit still for a minute. Gently add one drop of food colouring to each. Watch for 3 minutes. Sketch what you see at 0, 1 and 3 minutes.
- Heat flows one way. Put an ice cube in a glass of room-temperature water. Measure the water temperature at the start and after 10 minutes (or just feel the glass).
- Your body as an open system. Sit quietly for 5 minutes in a small room with the door closed, then step out and back in. Does the room feel warmer? Where did the energy come from?
Questions:
- In step 1, the dye spreads on its own. Is entropy increasing or decreasing? Why is it faster in hot water?
- In step 2, could the water ever spontaneously get warmer while the ice gets colder? Which law says no?
- Would the colouring ever gather itself back into one drop? What would it take to "un-mix" it?
What to look for: the dye spreads faster in hot water because the molecules have more kinetic energy; entropy increases as the dye disperses. Heat always flows from the warmer water to the ice, never the reverse, as the second law predicts. Un-mixing would need an input of energy and work (for example, a filtering or distillation process), just as a cell needs energy to keep molecules concentrated in the right places. Your body's heat comes from cellular respiration: the chemical energy of food is transformed and much of it is released as heat.
Your turn
1Define metabolism, and explain how catabolism and anabolism differ.
Metabolism is all the chemical reactions in a cell. Catabolism breaks large molecules into smaller ones and releases energy; anabolism builds large molecules from smaller ones and requires energy.
2State the first law of thermodynamics and give a biological example.
Energy cannot be created or destroyed, only transferred or transformed. Example: a chloroplast transforms light energy into chemical energy in glucose (or muscles transform chemical energy into mechanical energy and heat).
3State the second law of thermodynamics in terms of entropy.
Every energy transfer or transformation increases the total entropy (disorder) of the universe; some energy always becomes unusable heat.
4A reaction has ΔG = +14 kJ/mol. Is it exergonic or endergonic? Is it spontaneous?
Endergonic (ΔG > 0). It is not spontaneous; it needs an energy input (in a cell, usually by coupling it to ATP hydrolysis).
5Calculate ΔG for a reaction at 25 °C with ΔH = −50.0 kJ/mol and ΔS = −0.100 kJ/(mol·K).
T = 298 K. TΔS = 298 × (−0.100) = −29.8 kJ/mol. ΔG = −50.0 − (−29.8) = −20.2 kJ/mol: exergonic, even though entropy decreases, because enough heat is released.
6Why does energy flow through an ecosystem but matter cycles?
Atoms are reused again and again (carbon goes from CO₂ to sugar and back). Energy, however, is converted to heat at every transfer (second law), and heat cannot be used by organisms to make ATP, so new energy must keep arriving as sunlight.
7Does an enzyme change ΔG of a reaction? Explain.
No. An enzyme lowers the activation energy, so the reaction reaches equilibrium faster, but the free energies of the reactants and products, and so ΔG, stay the same.
More practice: warm-up
A measure of disorder, or how spread out energy and matter are.
2Is cellular respiration catabolic or anabolic?
Catabolic: it breaks glucose down to CO₂ and H₂O and releases energy.
3Give the sign of ΔG for an exergonic reaction.
4Convert 37 °C to kelvins.
37 + 273.15 = 310.15 K (about 310 K).
5Name two kinds of work a cell does.
Any two: chemical work (building molecules), transport work (pumping substances across membranes), mechanical work (movement, muscle contraction).
More practice: on your own
1Explain why a living cell does not violate the second law of thermodynamics, even though it is highly ordered.
A cell is an open system. It takes in energy (food or light) and releases heat and simple molecules (CO₂, H₂O) to its surroundings. The increase in the surroundings' entropy is larger than the decrease inside the cell, so total entropy still increases.
2A reaction has ΔH = +10.0 kJ/mol and ΔS = +0.0500 kJ/(mol·K). Find ΔG at 37 °C, and explain what drives it.
T = 310 K; TΔS = 310 × 0.0500 = 15.5 kJ/mol. ΔG = 10.0 − 15.5 = −5.5 kJ/mol, so it is exergonic. It absorbs heat (ΔH > 0) but is driven by the large increase in entropy.
3The same reaction as in the previous question is cooled to 0 °C. Is it still spontaneous? Show your work.
T = 273 K; TΔS = 273 × 0.0500 = 13.65 kJ/mol. ΔG = 10.0 − 13.65 = −3.65 kJ/mol (about −3.7). Still spontaneous, but less so: at lower temperature the entropy term matters less.
4A reaction is spontaneous (ΔG < 0) but no product forms after a day at room temperature. Explain.
Its activation energy is high, so very few molecules have enough energy to react. ΔG tells you whether a reaction can happen, not how fast. An enzyme or a spark (for burning) could supply the needed push.
5A deer eats 50 000 kJ of plant material. Only about 10% ends up stored in its body tissue. Account for the other energy.
About 45 000 kJ is not stored: some is in material that is not digested and leaves as feces (to decomposers); most of the rest is used in cellular respiration to power the deer's activities and is ultimately released as heat. None is destroyed (first law).
Challenge
1Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ has ΔG = +2870 kJ/mol. Use the second law to explain why it can still happen in a leaf.
On its own the reaction is endergonic and non-spontaneous. In a leaf it is coupled to the absorption of light: sunlight energy drives electrons uphill. When you include the Sun's energy (which comes from a hugely exergonic, entropy-increasing process in the Sun) and the heat the leaf gives off, the total entropy of the universe still increases, so the second law is satisfied.
2For a reaction with ΔH = −40.0 kJ/mol and ΔS = −0.200 kJ/(mol·K), find the temperature (in °C) at which ΔG = 0. Above or below that temperature is it spontaneous?
Set 0 = ΔH − TΔS, so T = ΔH/ΔS = (−40.0)/(−0.200) = 200 K, which is −73 °C. Below 200 K, TΔS is small, so ΔG < 0 (spontaneous). Above 200 K (including body temperature), −TΔS = +T(0.200) is larger than 40.0, so ΔG > 0: not spontaneous.
3A student says, "In a food chain, energy is lost, so the first law of thermodynamics doesn't apply to ecosystems." Correct the student's reasoning.
Energy is not lost in the sense of destroyed. The first law still holds: at each trophic level the chemical energy is converted, mostly into heat, which leaves the ecosystem. What is "lost" is usable (free) energy. That is the second law: every conversion increases entropy and degrades some energy to heat. The total energy (stored + heat) stays the same.
Quiz
1. Which statement is the first law of thermodynamics?
2. Protein synthesis from amino acids is best described as:
3. A reaction at 310 K has ΔH = −30 kJ/mol and ΔS = +0.010 kJ/(mol·K). ΔG is about:
4. Why can a living cell stay highly ordered without breaking the second law?
5. What does an enzyme do to a reaction's free-energy diagram?
6. Why do food chains rarely have more than four or five trophic levels?
Big idea: This lesson lays the foundation for the whole unit (C3.3): energy is conserved (first law), but every conversion turns some into unusable heat and increases entropy (second law). ΔG tells whether a reaction releases or needs free energy.
How to help: Ask your teen to explain, in their own words, why they need to eat every day even though their atoms mostly leave as CO₂ and water. Check the ΔG calculations: the most common slip is mixing kJ and J (ΔS is often given in J/(mol·K)) or forgetting to convert °C to kelvins. The kitchen activity uses hot tap water only.
Common difficulties:
- Thinking energy is "used up" or "destroyed". It is converted, mostly into heat.
- Thinking that "spontaneous" means "fast". ΔG says nothing about rate.
- Believing enzymes change ΔG. They only lower activation energy.
- Saying bonds "store" energy that is released when they break. Breaking bonds always needs energy; energy is released when stronger bonds form in the products.