Calorimetry & Entropy
Measure heat, predict chaos, and determine spontaneity. Master the mechanics of calorimeters, the definition of the Second Law, and the crucial exceptions in predicting $\Delta S$.
Module Focus
The First Law of Thermodynamics tells us that energy is conserved, but it completely fails to explain why a process occurs in a particular direction (e.g., why heat always flows from hot to cold). To predict Spontaneity, we must introduce the concepts of Entropy and the Second Law of Thermodynamics. Before diving into chaos, we will first master how to physically measure heat using Calorimetry.
1. Calorimetry (Measurement of Heat)
Calorimetry is the experimental technique of measuring heat changes accompanying a chemical reaction or physical process. It relies on the principle that Heat Lost = Heat Gained.
A heavily constructed steel vessel used specifically for measuring the heat of combustion of organic compounds.
- The volume is rigidly fixed ($\Delta V = 0$).
- Therefore, work done $w = -P\Delta V = 0$.
- The heat measured ($q_v$) is exactly equal to the Change in Internal Energy ($\Delta U$).
An insulated container open to the atmosphere. Used for measuring heat of neutralization, solution, or simple aqueous reactions.
- The pressure is constant atmospheric pressure ($\Delta P = 0$).
- The system can do expansion/compression work.
- The heat measured ($q_p$) is exactly equal to the Change in Enthalpy ($\Delta H$).
The Heat Equation
To calculate the heat ($q$) absorbed or released by the calorimeter fluid (usually water), we use:
- $m$: Mass of the substance.
- $c$ (or $s$): Specific heat capacity (heat required to raise 1 gram by $1^\circ \text{C}$). It is an Intensive property.
- $C$: Heat capacity of the entire calorimeter system. It is an Extensive property.
2. Entropy ($S$)
Entropy is a thermodynamic state function that measures the degree of randomness, disorder, or chaos in a system. The greater the disorder, the higher the entropy.
Mathematical Definition
For a reversible process at a constant temperature, the change in entropy ($\Delta S$) is defined as the heat absorbed isothermally and reversibly divided by the absolute temperature.
Units: Joules per Kelvin per mole ($\text{J K}^{-1} \text{mol}^{-1}$).
Entropy generally increases ($\Delta S > 0$) when randomness increases. Memorize these standard rules and their exceptions:
- Phase Changes: Entropy increases as you go from Solid $\rightarrow$ Liquid $\rightarrow$ Gas.
(Example: Melting of ice $\implies \Delta S > 0$). - Change in Gaseous Moles ($\Delta n_g$): If $\Delta n_g > 0$, entropy increases.
(Example: $PCl_5(g) \rightarrow PCl_3(g) + Cl_2(g) \implies 1 \text{ mole to } 2 \text{ moles} \implies \Delta S > 0$). - Heating: Increasing temperature increases kinetic energy and randomness. ($\Delta S > 0$).
- Expansion: A gas expanding into a larger volume increases randomness. ($\Delta S > 0$).
Highly Tested Exceptions & Traps:
Even though the liquid egg turns "solid" (coagulates), the heat breaks the hydrogen bonds in the proteins, causing them to uncoil and denature from a highly ordered structure to a random structure.
Result: $\mathbf{\Delta S > 0}$ (Increases).
A relaxed rubber band has coiled, randomly arranged polymer chains. When you stretch it, the chains are forced to align linearly, increasing order.
Result: $\mathbf{\Delta S < 0}$ (Decreases).
When a highly chaotic gas binds to a solid surface, its freedom of movement is restricted.
Result: $\mathbf{\Delta S < 0}$ (Decreases).
3. Standard Entropy of Phase Transitions
Phase transitions (melting, boiling) occur at a constant temperature and pressure. They are considered to be at equilibrium, making them reversible processes.
| Entropy of Fusion ($\Delta S_{\text{fusion}}$) | Entropy of Vaporization ($\Delta S_{\text{vap}}$) | Entropy of Sublimation ($\Delta S_{\text{sub}}$) |
|---|---|---|
| $\frac{\Delta H_{\text{fusion}}}{T_m}$ | $\frac{\Delta H_{\text{vap}}}{T_b}$ | $\frac{\Delta H_{\text{sub}}}{T_{\text{sub}}}$ |
| Solid to Liquid at Melting Point ($T_m$) | Liquid to Gas at Boiling Point ($T_b$) | Solid directly to Gas at Sublimation Temp |
4. The Second Law of Thermodynamics
The Second Law provides the ultimate criterion for predicting the spontaneity of a process. It dictates the fundamental direction of time and energy flow in the universe.
"For any spontaneous process, the total entropy of the universe must increase."
- If $\mathbf{\Delta S_{\text{universe}} > 0}$: The process is Spontaneous (irreversible).
- If $\mathbf{\Delta S_{\text{universe}} = 0}$: The process is at Equilibrium (reversible).
- If $\mathbf{\Delta S_{\text{universe}} < 0}$: The process is Non-spontaneous (it will be spontaneous in the reverse direction).
The entropy of the system can decrease ($\Delta S_{\text{system}} < 0$) during a spontaneous process! For example, water freezing into ice below $0^\circ \text{C}$ is spontaneous, yet the system's entropy decreases. How? Because it releases heat to the surroundings ($-\Delta H$), causing an massive increase in the entropy of the surroundings ($\Delta S_{\text{surroundings}} > 0$). The total sum ($\Delta S_{\text{universe}}$) remains positive.
NEET Grand Test: Entropy & Calorimetry
15 High-Order Thinking Questions testing $\Delta S$ signs, phase transitions, and spontaneity criteria.
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