Entropy & Gibbs Free Energy Calculator

Calculate ΔS and ΔG to predict reaction spontaneity.

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Entropy & Gibbs Free Energy Calculator

ΔG° = ΔH° - TΔS°

Standard Thermodynamic Data

CH4(g)

O2(g)

CO2(g)

H2O(l)

Thermodynamics

This calculator determines the spontaneity of a reaction. Enthalpy (ΔH) is the heat change, Entropy (ΔS) is the change in disorder, and Gibbs Free Energy (ΔG) combines them to predict if a reaction will occur spontaneously under constant temperature and pressure. A negative ΔG indicates a spontaneous reaction.

Understanding Entropy & Gibbs Free Energy

The Drivers of Chemical Spontaneity.

What is Entropy (ΔS)?

Entropy (ΔS) is a fundamental concept in thermodynamics that represents a measure of the disorder, randomness, or chaos within a system. It is often described as the number of possible microscopic arrangements a system can have.

The Second Law of Thermodynamics states that the total entropy of an isolated system (or the universe) always tends to increase over time.

In chemical reactions, entropy generally increases when:

1. A solid turns into a liquid or gas (change of state).

2. The number of moles of gas increases in a reaction.

3. A complex molecule breaks down into smaller, simpler molecules.

Example: An ice cube has a highly ordered, crystalline structure (low entropy). As it melts into liquid water, the molecules become disordered and can move freely (high entropy). The sign of ΔS for this process is positive.

What is Gibbs Free Energy (ΔG)?

Gibbs Free Energy (ΔG) is a thermodynamic potential that can be used to calculate the maximum amount of 'free' or 'useful' work that can be extracted from a system at constant temperature and pressure.

Its most important use in chemistry is to determine the spontaneity of a chemical reaction. A spontaneous reaction is one that will proceed on its own without the continuous input of external energy.

Example:A spontaneous reaction is like a ball rolling down a hill; it happens naturally. A non-spontaneous reaction is like pushing a ball up a hill; it requires a constant input of energy to occur.

The Gibbs Free Energy Equation

Gibbs Free Energy combines the concepts of enthalpy and entropy into a single, powerful equation:

ΔG = ΔH - TΔS

Where:

ΔG: The change in Gibbs Free Energy. The sign of ΔG determines spontaneity.

ΔH: The change in Enthalpy (the heat of the reaction).

T: The absolute temperature in Kelvin (K).

ΔS: The change in Entropy (the change in disorder).

Example:This equation shows that the spontaneity of a reaction is a balance between the tendency to release heat (negative ΔH) and the tendency to increase disorder (positive ΔS).

Interpreting the Sign of ΔG

The sign of the calculated ΔG value tells us whether a reaction will be spontaneous under the given conditions:

If ΔG is negative (< 0): The reaction is spontaneous in the forward direction.

If ΔG is positive (> 0): The reaction is non-spontaneous. The reverse reaction is spontaneous.

If ΔG is zero (= 0): The system is at equilibrium, and the rates of the forward and reverse reactions are equal.

Example:The rusting of iron has a negative ΔG, so it occurs spontaneously. The conversion of rust back into iron has a positive ΔG and requires energy input (like in a blast furnace).

Real-World Application: Biology and Industry

The concept of Gibbs Free Energy is critical in many scientific fields.

Biology: Biological processes, like the folding of proteins into their correct shapes and the metabolism of food (e.g., ATP hydrolysis), are driven by a negative change in Gibbs Free Energy.

Industrial Chemistry: Chemists use ΔG to predict whether a proposed reaction for making a new chemical is feasible. If ΔG is highly positive, they know they will need to supply significant energy (e.g., high temperature or pressure) to make the reaction happen.

Example:Your body's ability to break down glucose for energy is a series of spontaneous reactions, each with a negative ΔG, that collectively release a large amount of free energy for your cells to use.

Key Summary

  • **Entropy (ΔS)** is a measure of a system's disorder or randomness.
  • **Gibbs Free Energy (ΔG)** determines the spontaneity of a chemical reaction.
  • The key equation is **ΔG = ΔH - TΔS**.
  • A **negative ΔG** indicates a spontaneous reaction. A **positive ΔG** indicates a non-spontaneous reaction.

Practice Problems

Problem: A chemical reaction has an enthalpy change (ΔH) of -120 kJ/mol and an entropy change (ΔS) of -0.05 kJ/(mol·K). Is the reaction spontaneous at 298 K (25°C)?

Use the Gibbs Free Energy equation: ΔG = ΔH - TΔS. Ensure all units are consistent.

Solution: ΔG = (-120 kJ/mol) - (298 K * -0.05 kJ/(mol·K)) = -120 - (-14.9) = -105.1 kJ/mol. Since ΔG is negative, the reaction is spontaneous at this temperature.

Problem: An endothermic reaction (positive ΔH) also results in an increase in entropy (positive ΔS). At what temperatures will this reaction be spontaneous?

Analyze the equation ΔG = ΔH - TΔS. For ΔG to be negative, the 'TΔS' term must be larger than the 'ΔH' term.

Solution: Since both ΔH and ΔS are positive, the term '-TΔS' will be negative. The reaction will become spontaneous (ΔG < 0) when the temperature (T) is high enough to make the TΔS term overcome the positive ΔH term. Therefore, this reaction is spontaneous at high temperatures.

Frequently Asked Questions

What does 'spontaneous' mean in chemistry? Does it mean the reaction is fast?

No. 'Spontaneous' only means that the reaction is thermodynamically favorable and can occur without a continuous input of external energy. It says nothing about the rate of the reaction. The rusting of iron is a spontaneous process, but it can be very slow.

Can an endothermic reaction (one that gets cold) be spontaneous?

Yes. If the increase in entropy (ΔS) is large enough, the 'TΔS' term in the Gibbs equation can be large enough to overcome a positive ΔH, making ΔG negative. A common example is an instant cold pack, where the dissolving of a salt is endothermic but highly favorable from an entropy perspective.

What is the First Law of Thermodynamics?

The First Law of Thermodynamics is the Law of Conservation of Energy, which states that energy cannot be created or destroyed, only converted from one form to another. The Second Law (involving entropy) adds a direction to this, stating that processes naturally tend toward a state of greater disorder.

Predicting Chemical Change

Gibbs Free Energy provides a master equation that combines the drive for lower energy (enthalpy) and higher disorder (entropy) to give a definitive answer on whether a chemical process will naturally occur.

It is the ultimate arbiter of chemical feasibility.