Entropy (OCR A-Level Chemistry A): Revision Notes

Entropy

What is entropy?

Entropy is a fundamental concept in thermodynamics that helps us understand why certain processes happen spontaneously in nature. The symbol for entropy is $S$.

Entropy is a measure of how dispersed energy is within a chemical system, and it also represents the degree of disorder in that system. The key idea is that energy naturally tends to spread out rather than stay concentrated in one place.

The relationship between entropy and disorder:

• The greater the entropy value, the more dispersed the energy
• The greater the entropy value, the greater the disorder in the system
• Higher entropy means particles are arranged more randomly

Units of entropy: Entropy is measured in joules per kelvin per mole: $\text{J K}^{-1}\text{mol}^{-1}$

The higher the entropy value, the more energy is spread out per kelvin per mole of substance.

Entropy and states of matter

In general, there is a clear trend in entropy values across the three states of matter:

• Solids have the smallest entropies
• Liquids have greater entropies than solids
• Gases have the greatest entropies

This trend exists because:

• In solids, particles are held in fixed positions with limited movement - low disorder
• In liquids, particles can move past each other - moderate disorder
• In gases, particles are completely free to move randomly - high disorder

Predicting entropy changes

Understanding how entropy changes in chemical and physical processes is crucial for predicting whether reactions will occur spontaneously.

Entropy at absolute zero: At $0\text{ K}$ (absolute zero), there would be no thermal energy available and all substances would have an entropy value of zero. This is the only situation where entropy equals zero.

Above $0\text{ K}$, energy becomes dispersed among the particles, and all substances have positive entropy values.

Systems and disorder: Systems that are more disordered have higher entropy values. When analyzing changes:

Predicting entropy changes from equations: You can predict whether entropy increases or decreases in a physical or chemical change by comparing the physical states and the number of gas molecules on either side of an equation.

Changes of state

Entropy increases significantly during phase transitions that create more random arrangements of particles:

$\text{solid} \rightarrow \text{liquid} \rightarrow \text{gas}$

When any substance changes state from solid to liquid to gas, its entropy increases because:

• Melting and boiling increase the randomness of particles
• Energy becomes more spread out
• The entropy change $\Delta S$ is positive

Change in the number of gaseous molecules

Reactions that change the number of gas molecules present have significant effects on entropy because gases have very high entropy compared to solids and liquids.

Reactions producing gases: When reactions produce gas molecules, entropy increases. For example, calcium carbonate reacting with hydrochloric acid:

$\text{CaCO}_3\text{(s)} + 2\text{HCl(aq)} \rightarrow \text{CaCl}_2\text{(aq)} + \text{CO}_2\text{(g)} + \text{H}_2\text{O(l)}$

• Production of carbon dioxide gas increases the disorder of particles
• Energy spreads out more
• $\Delta S$ is positive

Reactions consuming gases: You can predict the sign of entropy change for reactions where reactants and products have different numbers of gas molecules.

Standard entropies

To perform calculations involving entropy changes, we use tabulated standard entropy values.

Definition: Every substance has a standard entropy $S°$, which is the entropy of one mole of a substance under standard conditions.

Standard conditions are:

• Pressure: $100\text{ kPa}$
• Temperature: $298\text{ K}$ ($25°\text{C}$)

Standard entropy values can be found in data books and are essential for calculating entropy changes in reactions.

Example standard entropy values:

Some standard entropy values for common substances are shown in the tables below:

Substance	$S°$ / $\text{J K}^{-1}\text{mol}^{-1}$
$\text{NO(g)}$	$+211$
$\text{O}_2\text{(g)}$	$+205$
$\text{NO}_2\text{(g)}$	$+240$

Substance	$S°$ / $\text{J K}^{-1}\text{mol}^{-1}$
$\text{SO}_2\text{(g)}$	$+248$
$\text{O}_2\text{(g)}$	$+205$
$\text{SO}_3\text{(l)}$	$+96$
$\text{H}_2\text{S(g)}$	$+206$
$\text{H}_2\text{O(l)}$	$+70$
$\text{CO}_2\text{(g)}$	$+214$

Calculating entropy changes

Standard entropies allow us to calculate the entropy change for a reaction, $\Delta S°$, using a formula similar to that used for enthalpy changes.

Formula: $\Delta S° = \Sigma S°\text{(products)} - \Sigma S°\text{(reactants)}$

where $\Sigma$ means "sum of"

This is analogous to Hess's law calculations - we sum all the standard entropies of products and subtract the sum of all standard entropies of reactants.