AP Chemistry 9.1 Introduction to Entropy Study Notes - New Syllabus Effective fall 2024
AP Chemistry 9.1 Introduction to Entropy Study Notes- New syllabus
AP Chemistry 9.1 Introduction to Entropy Study Notes – AP Chemistry – per latest AP Chemistry Syllabus.
LEARNING OBJECTIVE
Identify the sign and relative magnitudeof the entropy change associated with chemical or physicalprocesses.
Key Concepts:
- Entropy and Dispersal of Matter
- Entropy and Dispersal of Energy
Entropy and Dispersal of Matter
Entropy is a measure of the disorder or randomness of a system. It reflects how energy and matter are distributed or dispersed within that system. A greater dispersal of matter or energy corresponds to a higher entropy. Entropy increases when matter becomes more dispersed, and particles have greater freedom of movement. This often occurs during physical and chemical changes where the arrangement of particles becomes less ordered.
Situations in which entropy increases:
Phase changes involving increased particle movement:
When a substance changes state from solid → liquid → gas, the particles become less ordered and more spread out.
Hence, entropy increases as particles gain more freedom to move and occupy a larger volume.
Example: \( \text{H}_2\text{O (s)} \rightarrow \text{H}_2\text{O (l)} \) → entropy increases.
Example: \( \text{H}_2\text{O (l)} \rightarrow \text{H}_2\text{O (g)} \) → entropy increases further.
Expansion of gases:
For a gas at constant temperature, if the volume increases, the gas molecules have more space to move randomly, leading to an increase in entropy.
Example: A gas expanding into a vacuum shows an increase in entropy because particle distribution becomes more random.
Chemical reactions involving gases:
In reactions where the number of moles of gaseous products is greater than that of gaseous reactants, the entropy usually increases.
Example: \( \text{N}_2\text{O}_4 (g) \rightarrow 2\text{NO}_2 (g) \)
The number of gas molecules increases from 1 to 2 → greater dispersal → higher entropy.
Summary Table:
| Process | Effect on Entropy | Reason |
|---|---|---|
| Solid → Liquid | Increases | Particles gain freedom to move |
| Liquid → Gas | Increases greatly | Particles become widely dispersed |
| Gas expansion (at constant temperature) | Increases | Gas occupies larger space → more randomness |
| Increase in gas moles in a reaction | Increases | More gas particles → more microstates → higher disorder |
Example :
Predict the change in entropy for the following reactions:
(a) \( \text{H}_2\text{O (l)} \rightarrow \text{H}_2\text{O (g)} \)
(b) \( \text{N}_2 (g) + 3\text{H}_2 (g) \rightarrow 2\text{NH}_3 (g) \)
▶️ Answer/Explanation
(a) Liquid water changes to gas → particles become more dispersed → entropy increases.
(b) 4 moles of gaseous reactants form 2 moles of gaseous products → fewer gas particles → entropy decreases.
Conclusion: Entropy increases when matter or energy becomes more spread out or disordered, and decreases when the system becomes more ordered.
Entropy and Dispersal of Energy
Entropy also increases when energy becomes more dispersed within a system. The spreading of energy among the particles leads to a greater number of possible energy distributions (microstates), which increases the system’s entropy.
Key Concept:
According to the Kinetic Molecular Theory (KMT), the particles of a substance are always in motion and possess kinetic energy. As temperature increases, the kinetic energy of particles becomes more widely distributed, meaning some particles move much faster while others move slower — resulting in a broader spread of energy values.
Relationship between Temperature and Entropy:
- As temperature increases, the particles gain more kinetic energy.
- The distribution of kinetic energies among particles becomes broader — energy is more evenly and widely spread.
- This greater dispersion of energy leads to an increase in entropy.
Illustration:
| Temperature | Energy Distribution | Entropy Change |
|---|---|---|
| Low Temperature | Most particles have similar kinetic energy (narrow distribution) | Lower entropy |
| High Temperature | Particles have a wider range of kinetic energies (broad distribution) | Higher entropy |
Example :
Explain how heating a gas from 300 K to 600 K affects its entropy.
▶️ Answer/Explanation
Step 1: As the gas is heated, its average kinetic energy increases.
Step 2: The energy distribution among gas particles becomes wider — some molecules move faster while others slower.
Step 3: This broader energy spread means more possible microstates (ways of arranging energy).
Final Answer: The entropy of the gas increases because energy becomes more dispersed with increasing temperature.