Entropy (HSC SSCE Chemistry): Revision Notes

Entropy

What is standard molar entropy?

Entropy is a measure of the randomness, disorder, or chaos within a substance. The more disordered the particles in a system, the higher its entropy value. Think of entropy as a way to quantify how spread out or mixed up the energy and matter are in a substance.

The standard molar entropy (symbol: $S°$) refers to the entropy of exactly one mole of a substance when it exists in its standard state. Standard state typically means a pressure of 100 kPa, and the temperature is usually specified as 298 K (25°C), though other temperatures can be used when stated.

The crucial difference between entropy and enthalpy

There is a fundamental difference in how we measure and tabulate entropy values compared to enthalpy values. This difference is critical for calculations:

Enthalpy: We cannot measure the absolute enthalpy of a substance. We can only measure changes in enthalpy ($\Delta H$). This is why we use enthalpies of formation as a reference point - they represent the enthalpy change when a compound forms from its elements. By convention, elements in their standard states are assigned an enthalpy of formation of zero.

Entropy: Unlike enthalpy, we can measure absolute entropy values. This is a consequence of the third law of thermodynamics, which establishes an absolute zero point for entropy. This means that elements in their standard states have non-zero entropy values. For example, solid carbon has an entropy of 6 $\text{J K}^{-1}\text{mol}^{-1}$, and oxygen gas has an entropy of 205 $\text{J K}^{-1}\text{mol}^{-1}$.

Standard molar entropy values

The following table shows standard molar entropy values at 298 K for various common substances. Notice how entropy values vary significantly between different states of matter:

Substance	$S°$ ($\text{J K}^{-1}\text{mol}^{-1}$)	Substance	$S°$ ($\text{J K}^{-1}\text{mol}^{-1}$)	Substance	$S°$ ($\text{J K}^{-1}\text{mol}^{-1}$)
C(s)	6	O₂(g)	205	NO(g)	211
CO(g)	198	H₂(g)	131	NO₂(g)	240
CO₂(g)	214	H₂O(g)	189	SO₂(g)	248
CH₄(g)	186	H₂O(l)	70	SO₃(g)	257
C₃H₈(g)	270	N₂(g)	192

Key patterns in entropy values

Looking at this table reveals several important trends:

• Solids have low entropy values: Solid carbon (C) has an entropy of only 6 J K⁻¹ mol⁻¹ because its atoms are locked in a rigid crystal structure with minimal disorder.
• Gases have much higher entropy values: Gaseous substances like oxygen (O₂) have significantly higher entropy values 205 J K⁻¹ mol⁻¹ because gas particles move freely and randomly throughout their container.
• Liquids fall between solids and gases: Water as a liquid (H₂O(l)) has an entropy of 70 $\text{J K}^{-1}\text{mol}^{-1}$, while water vapour (H₂O(g)) has an entropy of 189 $\text{J K}^{-1}\text{mol}^{-1}$. The liquid state is more ordered than gas but less ordered than solid.
• Larger molecules generally have higher entropy: Compare methane (CH₄) at 186 $\text{J K}^{-1}\text{mol}^{-1}$ with propane (C₃H₈) at 270 $\text{J K}^{-1}\text{mol}^{-1}$. Larger molecules have more ways to arrange their atoms and distribute energy, creating more disorder.

Calculating standard entropy change

When a chemical reaction occurs, there is typically a change in the total entropy of the system. The standard entropy change (symbol: $\Delta S°$) for a reaction tells us how much the total entropy increases or decreases as reactants transform into products.

The formula for calculating standard entropy change is:

$\Delta S° = \text{standard entropies of products} - \text{standard entropies of reactants}$

Or written more concisely using sigma notation:

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

Where $\Sigma$ (sigma) means "sum of". This formula tells us to:

1. Add up all the entropy values for the products (weighted by their coefficients)
2. Add up all the entropy values for the reactants (weighted by their coefficients)
3. Subtract the reactant total from the product total

Investigating entropy patterns

Scientists have collected entropy data for many different substances, and analysing this data reveals consistent patterns. Some important generalisations that emerge from entropy data include:

• For any given substance, entropy increases as the substance changes from solid to liquid to gas. The increase from liquid to gas is particularly dramatic.
• While different solids have different entropy values, these differences are relatively small compared to the difference between any solid and any gas.
• When a solid or liquid dissolves in a solvent, there is usually an increase in entropy because the particles become more dispersed and disordered in solution.
• Aqueous ions generally have lower entropy values than you might expect because water molecules become ordered around the ions, reducing overall disorder.

Remember!