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Thermodynamics in
Biochemistry

Master the energy language of life: \(\Delta G\), \(\Delta H\), \(\Delta S\), and how cells couple reactions to drive unfavorable processes forward.

Biochemistry

Why Does Energy Matter in Biology?

Every biological process: muscle contraction, DNA replication, protein folding: requires energy transformations. Thermodynamics tells us which reactions happen spontaneously and which ones cells must push uphill by coupling them to favorable reactions.

The Three Thermodynamic Variables

\(\Delta H\) : Enthalpy
Heat absorbed or released. Negative \(\Delta H\) = exothermic (heat out). Positive = endothermic (heat in).
\(\Delta S\) : Entropy
Disorder of the system. Positive \(\Delta S\) = more disorder. Nature favors increasing entropy.
\(\Delta G\) : Free Energy
The master predictor. Combines enthalpy and entropy to tell you if a reaction is spontaneous.

Enthalpy \(\Delta H\): Heat Flow

Exothermic Reactants Heat out Products ΔH < 0 Endothermic Products Heat in Reactants ΔH > 0

Entropy \(\Delta S\): The Drive Toward Disorder

Ordered (Low S) e.g. Crystal lattice ΔS > 0 Disordered (High S) e.g. Gas molecules

The Gibbs Free Energy Equation

ΔG = ΔH − TΔS
\(\Delta G < 0\)
Exergonic: spontaneous, releases free energy. Reaction proceeds forward.
\(\Delta G > 0\)
Endergonic: non-spontaneous, requires energy input. Must be coupled.
\(\Delta G = 0\)
Equilibrium: no net change. Forward and reverse rates are equal.

Energy Diagram: Exergonic vs Endergonic

Free Energy (G) Reaction Progress R P ΔG < 0 Exergonic R P ΔG > 0 Endergonic

Exergonic vs Endergonic: Key Distinction

Exergonic Endergonic
\(\Delta G\) Negative (< 0) Positive (> 0)
Spontaneity Spontaneous Non-spontaneous
Energy Released Required
Biological example ATP hydrolysis Protein synthesis
Product stability More stable Less stable

\(\Delta G^\circ\) vs \(\Delta G\): Standard vs Actual

\(\Delta G^\circ\) Standard
Measured at standard conditions: 25 °C, 1 atm, 1 M concentrations. A fixed reference value.
\(\Delta G\) Actual
Depends on real concentrations inside the cell. Can differ dramatically from \(\Delta G^\circ\).

ATP and Reaction Coupling

A → B ΔG = +13.8 kJ/mol ATP → ADP + Pᵢ ΔG = −30.5 kJ/mol + Coupled A + ATP → B + ADP + Pᵢ ΔG = −16.7 kJ/mol ✓

How to Predict Spontaneity

1
Identify \(\Delta H\). Is the reaction exothermic (−) or endothermic (+)?
2
Identify \(\Delta S\). Does disorder increase (+) or decrease (−)?
3
Apply \(\Delta G = \Delta H - T\Delta S\). Plug values in. Remember \(T\) is in Kelvin.
4
Check the sign. Negative = spontaneous. Positive = requires energy input or coupling.
5
Consider temperature. If signs of \(\Delta H\) and \(-T\Delta S\) compete, temperature determines which wins.

The Four Sign Combinations

\(\Delta H\) \(\Delta S\) \(\Delta G\) Spontaneity
− + Always − Always spontaneous
+ − Always + Never spontaneous
− − Depends Spontaneous at low T
+ + Depends Spontaneous at high T

Example 1: Is Ice Melting Spontaneous?

At 37 °C (body temperature), given: \(\Delta H = +6.01 \text{ kJ/mol}\), \(\Delta S = +22.0 \text{ J/(mol·K)}\).

1
Convert units: \(\Delta S = 0.0220 \text{ kJ/(mol·K)}\). Convert \(T\): \(37 + 273 = 310 \text{ K}\).
2
Calculate \(T\Delta S\): \(310 \times 0.0220 = 6.82 \text{ kJ/mol}\).
3
Apply the equation: \(\Delta G = 6.01 - 6.82 = -0.81 \text{ kJ/mol}\).

Example 2: Glucose Oxidation in Cells

The complete oxidation of glucose: \(\text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O}\)

\(\Delta H\)
\(-2803 \text{ kJ/mol}\) — highly exothermic
\(\Delta S\)
\(+259 \text{ J/(mol·K)}\) — more gas molecules produced
\(\Delta G^\circ\)
\(-2880 \text{ kJ/mol}\) — overwhelmingly spontaneous

Example 3: Coupling in Glutamine Synthesis

Glutamate + NH\(_3\) → Glutamine has \(\Delta G^\circ = +14.2 \text{ kJ/mol}\) — not spontaneous alone.

1
Unfavorable reaction: Glu + NH\(_3\) → Gln, \(\Delta G^\circ = +14.2\)
2
Coupled to ATP: ATP → ADP + P\(_i\), \(\Delta G^\circ = -30.5\)
3
Net reaction: Glu + NH\(_3\) + ATP → Gln + ADP + P\(_i\), \(\Delta G^\circ = -16.3 \text{ kJ/mol}\)

Common Mistakes to Avoid

✕ Spontaneous = Fast
\(\Delta G\) tells you direction, not speed. Kinetics (activation energy, enzymes) controls rate.
✕ Forgetting Units
\(\Delta H\) is often in kJ/mol but \(\Delta S\) in J/(mol·K). Always convert before plugging in.
✕ Ignoring Temperature
Using °C instead of Kelvin in \(\Delta G = \Delta H - T\Delta S\) gives completely wrong answers.
✕ Enzymes Change \(\Delta G\)
Enzymes lower activation energy (\(E_a\)), not \(\Delta G\). They speed up reactions but don't change equilibrium.

Question 1 of 5

A reaction has \(\Delta H = -80 \text{ kJ/mol}\) and \(\Delta S = +150 \text{ J/(mol·K)}\). This reaction is:

Question 2 of 5

Calculate \(\Delta G\) for a reaction at \(25 \,^\circ\text{C}\) with \(\Delta H = -20 \text{ kJ/mol}\) and \(\Delta S = -100 \text{ J/(mol·K)}\).

Question 3 of 5

Why can cells run endergonic reactions like protein synthesis?

Question 4 of 5

A reaction has \(\Delta H = +100 \text{ kJ/mol}\) and \(\Delta S = +250 \text{ J/(mol·K)}\). Above what temperature does it become spontaneous?

Question 5 of 5

Which statement about \(\Delta G^\circ\) and \(\Delta G\) is correct?