Enthalpy is only half of the story when deciding whether a chemical reaction is feasible. Many endothermic reactions, such as the dissolution of ammonium nitrate in water or the evaporation of liquid water, happen spontaneously even though they absorb heat from the surroundings. To explain this, we must introduce the concept of entropy.
🔑 Key Principle
Systems naturally tend to move from a state of low entropy (high order) to a state of high entropy (high disorder). The second law of thermodynamics states that for any spontaneous process, the total entropy of the universe must increase.
What is Entropy?
A thermodynamic property that measures the degree of disorder or randomness in a chemical system. It represents the number of ways that energy can be distributed among the particles. It is measured in units of \( \text{J K}^{-1}\text{mol}^{-1} \).
Factors Affecting Entropy
Three main factors determine the entropy of a chemical system:
1. Physical State (Solid, Liquid, or Gas)
The particles in a solid are held in highly ordered, fixed positions in a lattice. As a substance melts to a liquid and then vaporises to a gas, the particles gain kinetic energy and move more randomly, causing the entropy to increase dramatically.
2. Dissolving a Solid
When a solid ionic compound dissolves in water, the highly ordered solid lattice is broken apart, and the ions become free to move. This represents a significant increase in disorder, resulting in a positive entropy change (\( \Delta S^\theta > 0 \)).
3. Number of Gaseous Molecules
If a chemical reaction leads to an increase in the total number of moles of gas, the entropy of the system will increase (\( \Delta S^\theta > 0 \)). If the number of moles of gas decreases, the entropy of the system will decrease (\( \Delta S^\theta < 0 \)).
a) \( \text{CaCO}_3(s) \rightarrow \text{CaO}(s) + \text{CO}_2(g) \)
b) \( \text{N}_2(g) + 3\text{H}_2(g) \rightarrow 2\text{NH}_3(g) \)
Reaction a): The entropy change will be positive (\( \Delta S^\theta > 0 \)). This is because a solid reactant decomposes to form a gaseous product (\( \text{CO}_2 \)). Gases are highly disordered compared to solids, so the system disorder increases.
Reaction b): The entropy change will be negative (\( \Delta S^\theta < 0 \)). In this reaction, 4 moles of gas reactant yield only 2 moles of gas product. A decrease in the number of gaseous molecules reduces the number of ways of distributing energy, leading to an increase in order.
Calculating Standard Entropy Changes (\( \Delta S^\theta \))
Because particles are in constant motion above absolute zero, every substance has a positive entropy value (unlike enthalpy of formation, which is zero for standard elements). We calculate the standard entropy change for a reaction using the equation:
In the exam, standard entropies will always be provided in your data block in \( \text{J K}^{-1}\text{mol}^{-1} \). Do not forget to multiply each substance's entropy by its balancing coefficient in the chemical equation.
\( \text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(l) \)
Standard entropy values (\( S^\theta / \text{J K}^{-1}\text{mol}^{-1} \)):
\( S^\theta[\text{CH}_4(g)] = 186.2 \)
\( S^\theta[\text{O}_2(g)] = 205.0 \)
\( S^\theta[\text{CO}_2(g)] = 213.6 \)
\( S^\theta[\text{H}_2\text{O}(l)] = 69.9 \)
Step 1: Set up the equation. Sum the entropies of products and subtract the sum of entropies of reactants:
\( \Delta S^\theta = \left[ S^\theta(\text{CO}_2) + 2 \times S^\theta(\text{H}_2\text{O}) \right] - \left[ S^\theta(\text{CH}_4) + 2 \times S^\theta(\text{O}_2) \right] \)
Step 2: Substitute the values:
\( \Delta S^\theta = \left[ 213.6 + 2(69.9) \right] - \left[ 186.2 + 2(205.0) \right] \)
\( \Delta S^\theta = \left[ 213.6 + 139.8 \right] - \left[ 186.2 + 410.0 \right] \)
\( \Delta S^\theta = 353.4 - 596.2 \)
\( \Delta S^\theta = -242.8\text{ J K}^{-1}\text{mol}^{-1} \)
The standard entropy change for this reaction is \( -242.8\text{ J K}^{-1}\text{mol}^{-1} \). This negative sign is expected because we are converting 3 moles of gaseous reactants into only 1 mole of gas and 2 moles of liquid products.
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