University Chemistry: Thermodynamics, Entropy, and Gibbs Free Energy

Concepts of Spontaneity and Pressure Dynamics

• Spontaneous Processes: A process that can and will occur without any outside help or assistance once it has begun.
  • Thermodynamics vs. Kinetics: The term "spontaneous" does not imply a specific rate of reaction. A process can be spontaneous but extremely slow (e.g., diamond formation over millions of years) or extremely fast (e.g., a combustion explosion).
  • Directionality: In a spontaneous process, particles move wherever they can possibly go if space allows (e.g., gas escaping into a vacuum).
• Non-Spontaneous Processes: A process that requires work to be done on the system in order to obtain the desired product.
  • Example: Forcing gas particles that have dispersed back into a single bulb requires the influence of a vacuum or physical work; they will not return to their original position spontaneously.
• Enthalpy ($\Delta H$) and Spontaneity:
  • Initially, it was thought that only exothermic processes (negative $\Delta H$) were spontaneous. However, both exothermic and endothermic processes can be spontaneous.
  • Exothermic Examples:
    • Combustion of methane: $\Delta H = -890.4\,kJ\,mol^{-1}$.
    • Formation of water.
  • Endothermic Examples:
    • Water freezing (Note: The speaker clarifies that while water freezing is exothermic, certain other phase changes and solution formations like dissolving salts are endothermic yet spontaneous).
    • Ice melting ($H_2O(s) \rightarrow H_2O(l)$) is endothermic ($\Delta H > 0$) but spontaneous above $0\,^{\circ}C$.

Entropy (S): The Science of Chaos

• Definition: Entropy is the thermodynamic measurement of the disorder, randomness, or chaos within a system.
• State Function: Entropy is a state function, meaning its value depends only on the current state of the system, not the path taken to get there.
  • Calculation: $\Delta S = S_{\text{final}} - S_{\text{initial}}$
• Conditions for Increasing Entropy ($\Delta S > 0$):
  • Phase Changes: Moving from solid to liquid, or liquid to gas.
    • Solid: Highly ordered, neat, nicely packed structure; particles only vibrate in fixed locations.
    • Liquid: Particles glide past one another; less structured than solids.
    • Gas: Particles move as fast as possible, colliding with vessel walls; totally chaotic.
  • Solution Formation: Dissolving a solid solute into a liquid solvent creates a chaotic mixture where particle positions are unpredictable.
  • Temperature Increase: Increasing temperature increases kinetic energy, causing more movement and randomness.
  • Increased Particle Count: A reaction that results in more moles of product than moles of reactant usually increases entropy.
• Conditions for Decreasing Entropy ($\Delta S < 0$):
  • Processes that become more structured (e.g., gas to solid) involve a decrease in kinetic energy and entropy.

The Laws of Thermodynamics

• The Second Law of Thermodynamics: In any spontaneous process, there is always an increase in the total entropy of the universe.
  • Entropy of the Universe ($\Delta S_{\text{univ}}$): $\Delta S_{\text{univ}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}}$
  • For a process to be spontaneous, $\Delta S_{\text{univ}}$ must be greater than zero ($\Delta S_{\text{univ}} > 0$).
  • If $\Delta S_{\text{univ}} < 0$, the process is non-spontaneous.
  • If $\Delta S_{\text{univ}} = 0$, the system has reached equilibrium.
• Enthalpy's Impact on Surroundings:
  • Exothermic process: The system gives off heat to the surroundings, increasing the randomness of the surroundings ($\Delta S_{\text{surr}} > 0$).
  • Endothermic process: The system absorbs heat from the surroundings, decreasing the randomness of the surroundings ($\Delta S_{\text{surr}} < 0$).
  • Relationship: $\Delta S_{\text{surr}} = -\frac{\Delta H_{\text{sys}}}{T}$
• The Third Law of Thermodynamics: The entropy of a perfect crystalline substance at absolute zero ($0\,K$) is exactly zero.
  • Absolute Zero ($0\,K$): The temperature at which all vibrational motion stops. Nothing can vibrate; maximum order is reached. It is ethically and physically impossible to reach absolute zero based on current research.

Standard Molar Entropy and Calculations

• Standard Molar Entropy ($S^{\circ}$): The entropy of one mole of a substance at standard state ($1\,atm$ pressure and room temperature, typically $25\,^{\circ}C$ or $298\,K$).
  • Unlike enthalpy of formation ($\Delta H_f^{\circ}$), standard entropies for elements in their natural state are not zero.
• Calculating Standard Entropy Change ($\Delta S^{\circ}$):
  • Equation: $\Delta S^{\circ} = \sum n S^{\circ}(\text{products}) - \sum m S^{\circ}(\text{reactants})$
  • Where $n$ and $m$ are the stoichiometric coefficients (moles) from the balanced chemical equation.
• Example Calculation: Combustion of Methanol:
  • Balanced Equation: $2CH_3OH(l) + 3O_2(g) \rightarrow 2CO_2(g) + 4H_2O(l)$
  • Data: $S^{\circ}(CO_2) = 213.8\,J\,K^{-1}$, $S^{\circ}(H_2O(l)) = 70\,J\,K^{-1}$, $S^{\circ}(CH_3OH(l)) = 126.8\,J\,K^{-1}$, $S^{\circ}(O_2) = 205.03\,J\,K^{-1}$.
  • Calculation: $\Delta S^{\circ} = [2(213.8) + 4(70)] - [2(126.8) + 3(205.03)] = -161.1\,J\,K^{-1}$.

Gibbs Free Energy (G)

• Definition: A thermodynamic state function that combines enthalpy and entropy to determine spontaneity directly for a system without needing to calculate the surroundings.
• The Gibbs Equation: $\Delta G = \Delta H - T \Delta S$
  • Temperature ($T$) must be in Kelvin.
  • $\Delta G$ represents the "useful energy" available to do work.
• Spontaneity Criteria:
  • $\Delta G < 0$: Spontaneous process (Exergonic).
  • $\Delta G > 0$: Non-spontaneous process (Endergonic). (Note: The reverse reaction would be spontaneous).
  • $\Delta G = 0$: The process is at equilibrium.
• Standard Free Energy of Formation ($\Delta G_f^{\circ}$):
  • Calculation: $\Delta G^{\circ} = \sum n \Delta G_f^{\circ}(\text{products}) - \sum m \Delta G_f^{\circ}(\text{reactants})$

Temperature Dependence of Spontaneity

• Finding the Transition Temperature: To find the temperature at which a reaction becomes spontaneous, set $\Delta G = 0$.
  • $0 = \Delta H - T \Delta S \rightarrow T = \frac{\Delta H}{\Delta S}$
  • Example: A reaction with $\Delta H = 98.8\,kJ$ and $\Delta S = 0.1415\,kJ\,K^{-1}$ requires a temperature above $698\,K$ to be spontaneous.

Questions & Discussion

• Student Question on Visuals: A student reported they could not see the presentation. The professor suggested swiping the screen or logging out and back in.
• Dialogue on "Scouting Accounts": Two participants discussed athletic recruiting scams. They noted that certain "coaching" accounts are basically scams and that athletes are unlikely to get D1 recruitment through them unless they truly stand out.
• Spontaneity Prediction:
  • Question: How does entropy change for the reaction $2CO(g) + O_2(g) \rightarrow 2CO_2(g)$?
  • Answer: The entropy decreases (negative $\Delta S$) because the number of gas molecules decreases from 3 to 2.
• Phase Change Spontaneity (Water):
  • At $-10\,^{\circ}C$, the calculated $\Delta S_{\text{univ}}$ is negative ($\approx -0.7\,J\,K^{-1}$), meaning freezing is not spontaneous (the inverse, melting, is not spontaneous either under these specific math checks, indicating room for calculation review).
  • At $+10\,^{\circ}C$, the process of water converting from solid to liquid is spontaneous as $\Delta S_{\text{univ}} > 0$.

Exam Corrections and Study Advice

• Exam 1 Correction Policy: Students can earn half-credit back for incorrect questions.
  • Requirements:
    1. Write out the original question.
    2. Provide the correct answer using resources (textbook, website, or AI—cite all sources).
    3. Detail the mistake made (e.g., "I forgot to convert milligrams to moles").
    4. Provide a reflection on the exam/course (e.g., pace of summer course, time management).
  • AI Usage: If an AI chatbot is used, a link to the chat must be provided to show the prompt used.
• Study Tips for Summer Chemistry:
  • Do not study for hours at a single time due to the high intensity of summer courses.
  • Study in bursts of 30 minutes to 1 hour daily.
  • Attempt practice problems from lecture notes independently before checking the answers.
  • Communicate with the professor for additional practice resources if needed.