Cellular Energy — AP Biology Study Guide

For: AP Biology candidates sitting AP Biology.

Covers: Gibbs free energy change (ΔG), endergonic vs exergonic reactions, activation energy, ATP hydrolysis thermodynamics, coupled reaction energetics, and enzyme role in cellular energy transformations.

You should already know: Basic cell structure and organelle function, the first and second laws of thermodynamics, chemical bond properties and energy storage.

A note on the practice questions: All worked questions in the "Practice Questions" section below are original problems written by us in the AP Biology style for educational use. They are not reproductions of past College Board / Cambridge / IB papers and may differ in wording, numerical values, or context. Use them to practise the technique; cross-check with official mark schemes for grading conventions.

1. What Is Cellular Energy?

Cellular energy describes the capacity of living cells to do work, via controlled transformations of stored chemical energy into usable forms to power growth, active transport, reproduction, homeostasis, and synthesis of biological molecules. As the opening topic of AP Biology Unit 3: Cellular Energetics, it makes up 4-6% of the total AP exam weight, and appears in both multiple-choice (MCQ) and free-response (FRQ) sections, often as a conceptual foundation for longer questions on respiration and photosynthesis.

Notation for cellular energy follows standard thermodynamics: we use $\Delta G$ to denote the change in Gibbs free energy, the amount of usable energy available to do work under the constant temperature and pressure found in cells. The field is sometimes called bioenergetics, but cellular energy specifically focuses on energy transformations within living systems, rather than generalized thermodynamic systems. Unlike uncontrolled energy release (like combustion of sugar in open air), cells manage energy to stay far from equilibrium — a requirement for life, since equilibrium means no net work can be done.

2. Gibbs Free Energy and Reaction Spontaneity

Gibbs free energy is the core metric for predicting whether a reaction can proceed spontaneously in a cell. The fundamental formula relating free energy change to enthalpy (total bond energy) and entropy (disorder of the system) is: $$\Delta G=\Delta H-T\Delta S$$ Where:

• $\Delta G$ = change in Gibbs free energy (usable energy)
• $\Delta H$ = change in enthalpy (total energy stored in chemical bonds)
• $T$ = absolute temperature in Kelvin
• $\Delta S$ = change in entropy (disorder of the system)

The sign of $\Delta G$ tells us everything we need to know about reaction spontaneity:

• $\Delta G<0$: Reaction is exergonic (releases free energy) and spontaneous, meaning it can proceed without a net input of energy.
• $\Delta G>0$: Reaction is endergonic (requires input of free energy) and non-spontaneous, meaning it cannot proceed on its own in cells.
• $\Delta G=0$: Reaction is at equilibrium, no net work can be done.

It is critical to note that spontaneity does not equal speed: a spontaneous reaction can take thousands of years to proceed on its own if it has a high activation energy.

Worked Example

Problem: A researcher measures reaction parameters for the breakdown of a 10-carbon fatty acid in a mammalian cell at 25°C. The reaction has $\Delta H=-850$ kJ/mol and $\Delta S=2.1$ kJ/(mol·K). Calculate $\Delta G$ and determine if the reaction is spontaneous.

Solution:

1. Convert temperature from Celsius to the required absolute Kelvin scale: $T=25+273=298$ K.
2. Write the Gibbs free energy formula: $\Delta G=\Delta H-T\Delta S$.
3. Substitute the given values, keeping the negative sign for $\Delta H$: $\Delta G=(-850\text{ kJ/mol})-(298\text{ K}\ast 2.1\text{ kJ/(molcdotpK)})=-850-625.8=-1475.8$ kJ/mol.
4. Evaluate the sign of $\Delta G$: $-1475.8<0$, so the reaction releases free energy.
5. Conclusion: The reaction is exergonic and spontaneous under these conditions.

Exam tip: AP Biology questions almost always give temperature in Celsius to match real biological contexts; always convert to Kelvin before plugging into the $\Delta G$ formula, even if the question does not remind you.

3. ATP Hydrolysis and Coupled Cellular Reactions

Adenosine triphosphate (ATP) is the cell's primary energy currency. Its structure consists of an adenine base, ribose sugar, and three linked phosphate groups, with high-energy phosphoanhydride bonds between adjacent phosphate groups. The negative charges on the phosphate groups repel each other, so hydrolysis of one phosphoanhydride bond (breaking ATP into ADP and inorganic phosphate, $P_i$) releases a large amount of free energy: $$\text{ATP}+{\text{H}}_2\text{O}\to \text{ADP}+P_i\Delta G\approx -30.5\text{ kJ/mol}$$

Cells rely on coupled reactions to power non-spontaneous endergonic processes: they pair an endergonic reaction (positive $\Delta G$) with the highly exergonic hydrolysis of ATP, such that the total $\Delta G$ of the combined coupled reaction is negative, making the entire process spontaneous. Free energy change is additive for coupled reactions: the total $\Delta G$ is the sum of the $\Delta G$ values of each individual reaction in the pair.

Worked Example

Problem: The synthesis of the dipeptide alanine-glycine from two free amino acids has a $\Delta G$ of +18 kJ/mol. Is this reaction spontaneous on its own? If a cell couples this reaction to hydrolysis of one ATP molecule ($\Delta G=-30.5$ kJ/mol), what is the total $\Delta G$ of the coupled reaction, and is it spontaneous?

Solution:

1. Evaluate the uncoupled reaction: $\Delta G=+18$ kJ/mol, which is greater than 0, so the reaction is not spontaneous on its own.
2. Recall that total $\Delta G$ for coupled reactions is the sum of individual $\Delta G$ values, with signs preserved: $\Delta G_{total}=\Delta G_{synthesis}+\Delta G_{ATPhydrolysis}$.
3. Substitute values: $\Delta G_{total}=(+18\text{ kJ/mol})+(-30.5\text{ kJ/mol})=-12.5$ kJ/mol.
4. A negative total $\Delta G$ means the coupled reaction is spontaneous, so it can proceed in the cell.

Exam tip: Never drop the sign of $\Delta G$ when adding coupled reaction values; endergonic reactions are always positive, exergonic are always negative, and mixing up signs is the most common error on these questions.

4. Activation Energy and Enzyme Function

All reactions, even spontaneous exergonic ones, require an initial input of energy to break existing reactant bonds and reach the unstable transition state before products can form. This initial energy input is called activation energy ($E_A$), defined as the energy difference between the reactants and the highest-energy transition state of the reaction.

Enzymes are biological catalysts that speed up reaction rates by lowering the activation energy of a reaction. Enzymes do this by binding the reactant(s) at their active site and stabilizing the transition state, reducing the energy required to reach it. A critical conceptual point for the AP exam: enzymes never change the $\Delta G$ of a reaction. They only lower $E_A$, so they do not make a non-spontaneous reaction spontaneous — they just make spontaneous reactions proceed fast enough to support life.

Worked Example

Problem: A student draws a reaction coordinate for an exergonic reaction catalyzed by an enzyme, but makes two errors: they draw the product endpoint lower than the uncatalyzed reaction, and draw the peak (transition state) higher than the uncatalyzed reaction. Identify the errors and correct them.

Solution:

1. First error: The product endpoint for the catalyzed reaction cannot be lower than the uncatalyzed reaction. $\Delta G$ is the difference between reactant and product free energy, which enzymes do not change, so the endpoints for both must be at the same free energy level.
2. Second error: The transition state peak for the catalyzed reaction cannot be higher than the uncatalyzed reaction. Enzymes lower activation energy, so the transition state peak must be lower than the uncatalyzed peak.
3. Corrected profile: Same reactant and product endpoints (same $\Delta G$ for both reactions) with a lower peak for the enzyme-catalyzed reaction (lower $E_A$).

Exam tip: Any AP question asking if an enzyme changes $\Delta G$ will always have "no" as the correct answer; only activation energy is altered by enzymes.

5. Common Pitfalls (and how to avoid them)

• Wrong move: Stating that enzymes change the $\Delta G$ of a reaction to make it spontaneous. Why: Students confuse the effect of enzymes on reaction rate with their effect on reaction thermodynamics, mixing up activation energy and free energy change. Correct move: Always remember enzymes only lower activation energy; $\Delta G$ is determined by the difference in free energy between reactants and products, which enzymes do not alter.
• Wrong move: Using Celsius temperature directly in the $\Delta G=\Delta H-T\Delta S$ calculation. Why: Most problems give temperature in Celsius to match biological contexts, and students forget the formula requires absolute temperature. Correct move: Always add 273 to Celsius temperature before plugging into the Gibbs free energy formula, even if the question doesn't remind you.
• Wrong move: Calling exergonic reactions "fast" because they are spontaneous. Why: The definition of spontaneity from $\Delta G$ is confused with reaction rate, which is a separate property. Correct move: When asked to describe spontaneity, only reference $\Delta G$ sign; explicitly note that spontaneity does not tell you anything about reaction speed.
• Wrong move: Misattributing ATP's high energy to the adenine base or ribose sugar. Why: Students recognize adenine from nucleotide structure and incorrectly assume it stores the energy. Correct move: Always associate ATP's energy storage with the phosphoanhydride bonds between the three phosphate groups.
• Wrong move: Calculating coupled reaction $\Delta G$ as the difference of $\Delta G$ values instead of the sum. Why: Students confuse coupled reaction calculations with other energy problems that require subtraction. Correct move: Always add the $\Delta G$ of each reaction in the coupled system, keeping the original sign of each value.
• Wrong move: Stating that healthy, living cells exist at equilibrium. Why: Students associate equilibrium with stability and forget what $\Delta G=0$ means for work. Correct move: Remember that healthy cells are always far from equilibrium; $\Delta G=0$ means no net work can be done, which equals cell death.

6. Practice Questions (AP Biology Style)

Question 1 (Multiple Choice)

A cell couples two reactions: Reaction 1 (breakdown of glucose) has $\Delta G=-2800$ kJ/mol. Reaction 2 (synthesis of 10 ATP molecules from ADP and $P_i$) requires energy input, with a total $\Delta G$ of +280 kJ/mol for all 10 reactions. What is the net $\Delta G$ of the coupled system, and is the overall reaction spontaneous? A) Net $\Delta G=-3080$ kJ/mol, spontaneous B) Net $\Delta G=-2520$ kJ/mol, spontaneous C) Net $\Delta G=+2520$ kJ/mol, non-spontaneous D) Net $\Delta G=+3080$ kJ/mol, non-spontaneous

Worked Solution: For coupled reactions, total $\Delta G$ is the sum of the individual $\Delta G$ values, with signs preserved. Reaction 1 is exergonic ($\Delta G=-2800$ kJ/mol) and Reaction 2 is endergonic ($\Delta G=+280$ kJ/mol). Adding these gives $\Delta G_{net}=-2800+280=-2520$ kJ/mol. A negative net $\Delta G$ means the overall reaction is spontaneous. The correct answer is B.

Question 2 (Free Response)

The conversion of lactate to pyruvate in human muscle cells during exercise has the following properties at 37°C (normal body temperature): $\Delta H=+12$ kJ/mol, $\Delta S=0.08$ kJ/(mol·K). (a) Calculate $\Delta G$ for this reaction, show all your work. (2 points) (b) Identify whether the reaction is endergonic or exergonic, and state if it is spontaneous under these conditions. (2 points) (c) Lactate dehydrogenase is the enzyme that catalyzes this reaction. Explain the effect of the enzyme on $\Delta G$ and activation energy, and justify your answer. (3 points)

Worked Solution: (a) First convert temperature to Kelvin: $T=37+273=310$ K. Substitute into the Gibbs free energy formula: $$\Delta G=\Delta H-T\Delta S=(+12)-(310\ast 0.08)=12-24.8=-12.8\text{ kJ/mol}$$ (b) $\Delta G$ is negative ($-12.8<0$), so the reaction is exergonic. All reactions with negative $\Delta G$ are spontaneous under the tested conditions, so this reaction is spontaneous. (c) Lactate dehydrogenase has no effect on the $\Delta G$ of the reaction, and lowers the activation energy of the reaction. $\Delta G$ depends only on the difference in free energy between the reactant (lactate) and product (pyruvate), which is not altered by the enzyme. The enzyme stabilizes the reaction's transition state, reducing the energy input required to reach the transition state, which lowers activation energy and speeds up the reaction.

Question 3 (Application / Real-World Style)

2,4-dinitrophenol (DNP) is an uncoupler that makes the inner mitochondrial membrane leaky to protons, disrupting the coupling of proton flow down the gradient to ATP synthesis. Normally, the formation of 30 ATP from ADP and $P_i$ has a total $\Delta G$ of +915 kJ/mol, and the oxidation of glucose has a $\Delta G$ of -2800 kJ/mol. Predict the net $\Delta G$ of glucose oxidation when DNP is present, and explain why DNP causes cell damage at high doses.

Worked Solution: When DNP uncouples glucose oxidation from ATP synthesis, the energy released from glucose oxidation is not used to power the endergonic synthesis of ATP. The net $\Delta G$ of glucose oxidation alone is -2800 kJ/mol, all of which is released as heat instead of being captured as usable ATP. Without coupled ATP synthesis, the cell cannot produce enough ATP to power essential endergonic processes like active transport and macromolecule synthesis. The excess heat released also raises body temperature, causing further damage to proteins and cell structures.

7. Quick Reference Cheatsheet

8. What's Next

This chapter lays the thermodynamic foundation for all other topics in Unit 3: Cellular Energetics. Next you will apply the rules of cellular energy, coupled reactions, and enzyme function to study enzyme regulation and cellular respiration, where cells break down glucose to produce ATP. Without understanding $\Delta G$, coupled reactions, and how enzymes alter activation energy, you will not be able to explain how the electron transport chain generates ATP or how chemiosmosis works. This topic also feeds directly into photosynthesis, the other major energy transformation in living cells, and connects to later topics like cell division and cell signaling, both of which require ATP to power essential processes. All energy transformations across the entire AP Biology course follow the rules laid out here.

Enzyme Structure and Regulation Cellular Respiration Photosynthesis Cell Signaling