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Entropy and Spontaneity

Chemistry is the science of reactions. There are some reactions that happen easily and quickly, like melting ice. Other reactions are unlikely and will not happen spontaneously, like freezing water. In this lesson we will learn about spontaneity and entropy and how they help scientists understand why some processes happen and why others do not.

What is Entropy?

Entropy is the measurement of the disorder of a system. It is a measure of how randomly the components of a system are arranged.

For example,

• Gas molecules have a high degree of disorder. Little energy is required for the gas molecules to bounce off the walls of a container and escape.
• The molecules in a solid ice lattice are also disproportionately arranged and do not have a high degree of disorder.

Essentially, energy and matter can be arranged in a high entropy state when they are spread out, and energy and matter are arranged in a low entropy state when they are compact.

Everyday Examples of Entropy

Meaning of entropy is also the number of ways in which the constituents of the system could be arranged.

Influence of Factors on Entropy

Several factors affect entropy, including the:

For Example: In 1 mole of O₂ gas, the entropy is less when compared to 1 mole of C₆H₆ due to the increased way of movement in the gas.

Spontaneous Processes

For a spontaneous process, no outside assistance is needed.

For a system, the energy changes and the entropy changes determine that spontaneity.

What are Exothermic and Endothermic Reactions

• Exothermic reactions release energy and are often spontaneous because energy disperses widely.
• Endothermic reactions absorb energy. Endothermic reactions can become spontaneous if the disorder increases.

A key insight is that reactions can release energy but that alone, does not make a reaction spontaneous. There must be a factor that increases disorder.

What is Gibbs Free energy?

G is the Gibbs Free Energy that chemists use. Gibbs Free Energy is the combination of enthalpy and entropy, and is expressed with the following formula:

Where:

• ΔG = change in Gibbs Free Energy
• ΔH = change in enthalpy
• T = the temperature measured in Kelvin
• ΔS = change in Entropy

Result: There are three key concepts that can be used to analyze spontaneity and ΔG:

Example: ice at a temperature of 298 K:

• ΔH > 0 (it is an endothermic reaction)
• ΔS > 0 (the disorder increases)
• Then ΔG = ΔH - TΔS < 0 → spontaneous

Example: freezing water at a temperature of 298 K:

• ΔH < 0 (it is an exothermic reaction)
• ΔS < 0 (the disorder decreases)
• Then ΔG = ΔH - TΔS > 0 → non-spontaneous

The Universe Entropy

Standard Molar Entropy

Each substance has a standard molar entropy (S°) recorded at 298 K and 1 atm.

Units: J mol⁻¹ K⁻¹

Trends:

• Gases > Liquids > Solids
• Complex molecules > Simple molecules

This helps in calculating the entropy changes in the reactions:

Temperature and Spontaneity

When ΔH and ΔS are of opposite signs, temperature will affect spontaneity.

• ΔH < 0, ΔS> 0 → always spontaneous
• ΔH > 0, ΔS < 0 → never spontaneous
• ΔH and ΔS same sign = spontaneity depends on T

Example:

• Endothermic with large entropy increase = spontaneous at high T
• Exothermic with entropy decrease = spontaneous at low T

Entropy and Chemical Reactions

• Dissolving of salts = usually increases entropy because the ions spread out
• Burning things = Lots of gas = high entropy
• Solid to gas = usually less entropy

Why this matters:

• Chemist help design the reactions
• Chemistry helps predict whether reactions need heat, pressure or catalyst to start

Summary

If you look around you, every reaction is guided by these principles, ice melts, gases expand, perfumes spread, fuel burns, and energy flows. This is the result of the delicate balance of entropy, enthalpy and temperature. Chemistry helps us quantify this balance in order to help us understand why nature behaves the way it does.

Key Equations