Gibbs Free Energy Topical Review- Key Concepts

What Gibbs Free Energy Actually Is

Gibbs free energy (G) tells you whether a process will happen on its own. That's it. No philosophy, no ambiguity—just a yes-or-no answer to spontaneity.

Scientists named it after Josiah Willard Gibbs, who figured this out in the 1870s. You might see it written as ΔG (change in Gibbs free energy). The delta means we're measuring the difference between starting and ending states.

Here's the core idea: systems naturally move toward lower energy and higher disorder. Gibbs free energy combines both factors into one number you can actually calculate.

The Equation

The standard equation looks like this:

ΔG = ΔH - TΔS

Where:

• ΔG = change in Gibbs free energy (in joules or kilojoules)
• ΔH = change in enthalpy (heat content)
• T = temperature in Kelvin
• ΔS = change in entropy (disorder)

That's the version you'll use most often. There's also the thermodynamic relationship:

ΔG = ΔG° + RT ln(Q)

Where ΔG° is standard state free energy, R is the gas constant, and Q is the reaction quotient. Use this when conditions aren't at standard state.

What the Sign Means

This is the part that matters most.

ΔG < 0 (negative) → The process is spontaneous. It will happen without external input.

ΔG > 0 (positive) → The process is non-spontaneous. It won't happen on its own. You need to add energy.

ΔG = 0 → The system is at equilibrium. Nothing net is changing.

Students mess this up constantly. Remember: negative ΔG means "yes, this happens." Positive means "no, this doesn't happen by itself."

The Enthalpy-Entropy Relationship

Gibbs free energy is really just enthalpy and entropy fighting each other, with temperature as the referee.

Exothermic reactions (negative ΔH) favor spontaneity. They release heat.

Endothermic reactions (positive ΔH) oppose spontaneity. They absorb heat.

Increased entropy (positive ΔS) favors spontaneity. More disorder is natural.

Decreased entropy (negative ΔS) opposes spontaneity. Systems don't naturally become more ordered.

Four Possible Scenarios

This table shows why temperature matters so much. A reaction that won't happen at room temperature might become spontaneous if you heat it up enough—or vice versa.

Standard Gibbs Free Energy

ΔG° refers to conditions at 25°C (298 K), 1 atm pressure, and 1 M concentration. It's the baseline reference point.

For standard free energy of formation (ΔG°f), pure elements in their standard states have a value of zero. Everything else you can look up in tables.

The relationship between standard free energy and the equilibrium constant:

ΔG° = -RT ln(K)

Solve for K and you get:

K = e^(-ΔG°/RT)

When ΔG° is negative, K > 1. Products dominate at equilibrium. When ΔG° is positive, K < 1. Reactants dominate.

Getting Started: How to Calculate ΔG

Here's the step-by-step process:

Method 1: From ΔH and ΔS

1. Look up or calculate ΔH (enthalpy change)
2. Look up or calculate ΔS (entropy change)
3. Convert temperature to Kelvin if needed (K = °C + 273)
4. Plug into ΔG = ΔH - TΔS
5. Check the sign

Example: A reaction has ΔH = -50 kJ/mol and ΔS = +100 J/(mol·K). Calculate ΔG at 298 K.

First, make units match. Convert ΔS: 100 J = 0.1 kJ

ΔG = -50 kJ - (298 K × 0.1 kJ/K)

ΔG = -50 kJ - 29.8 kJ

ΔG = -79.8 kJ/mol

Negative. Spontaneous.

Method 2: From Standard Free Energies of Formation

ΔG° = Σ(n × ΔG°f products) - Σ(n × ΔG°f reactants)

Example: For the reaction 2H₂ + O₂ → 2H₂O

ΔG° = [2(-237 kJ)] - [2(0) + 0]

ΔG° = -474 kJ

Highly negative. This reaction wants to happen badly—which matches reality. Hydrogen and oxygen don't stay mixed for long.

Method 3: From Cell Potential (Electrochemistry)

For redox reactions:

ΔG = -nFE°

Where n is moles of electrons transferred, F is Faraday's constant (96,485 C/mol), and E° is standard cell potential.

This connects electrochemistry to thermodynamics. A positive E° gives negative ΔG, meaning a spontaneous electrochemical reaction.

Real Applications

Chemical Equilibrium

At equilibrium, ΔG = 0. This gives you the relationship:

0 = ΔH - TΔS

T = ΔH/ΔS

This temperature is where the reaction switches from spontaneous to non-spontaneous (or vice versa). It's your "transition temperature."

Phase Transitions

Melting, boiling, sublimation—all phase changes occur at the temperature where ΔG = 0 for that transition. At the melting point, solid and liquid coexist in equilibrium.

Biochemistry

Living systems don't violate thermodynamics. ATP hydrolysis has ΔG ≈ -30 kJ/mol under cellular conditions. That's negative, so it's spontaneous. Cells couple this reaction with non-spontaneous processes to drive them forward.

Drug Design

Gibbs free energy determines binding affinity. ΔG for drug-receptor binding tells you how strongly a drug will attach. More negative = tighter binding. This is why ΔG calculations show up in computational drug discovery.

Common Mistakes to Avoid

• Forgetting to convert units. kJ and J don't mix. Temperature must be in Kelvin.
• Confusing ΔG with ΔG°. Standard conditions vs. actual conditions—totally different numbers.
• Ignoring temperature. A positive ΔG at room temperature might become negative if you heat the system.
• Assuming "spontaneous" means "fast." Thermodynamics tells you IF a reaction happens. Kinetics tells you HOW FAST. They are separate.
• Using the wrong ΔS sign. Check your units (J/K vs kJ/K) before plugging in.

Key Equations Summary

The Bottom Line

Gibbs free energy is a thermodynamic state function that predicts spontaneity. The equation is simple—ΔG = ΔH - TΔS—but applying it correctly requires attention to units, conditions, and what the sign actually means.

Negative ΔG means spontaneous. Positive means not spontaneous. Zero means equilibrium. Everything else is just working through the math.