Calculating Gibbs Free Energy from Enthalpy and Entropy Changes

📚 Understanding Gibbs Free Energy

Gibbs Free Energy ($G$) is a thermodynamic potential that measures the amount of energy available in a chemical or physical system to do useful work at a constant temperature and pressure. It combines enthalpy ($H$) and entropy ($S$) to determine the spontaneity of a reaction. A negative value of $G$ indicates a spontaneous reaction, while a positive value indicates a non-spontaneous reaction.

📜 History and Background

Josiah Willard Gibbs, an American physicist and chemist, developed the concept of Gibbs Free Energy in the late 19th century. His work provided a crucial foundation for understanding chemical thermodynamics and predicting reaction outcomes. Gibbs' contributions revolutionized the field, enabling scientists to determine whether reactions would occur under specific conditions without needing to perform experiments.

⚗️ Key Principles

• 🌡️ Definition: Gibbs Free Energy ($G$) is defined by the equation: $G = H - TS$, where $H$ is enthalpy, $T$ is absolute temperature (in Kelvin), and $S$ is entropy.
• 🔥 Enthalpy ($H$): Represents the heat content of a system. A negative $\Delta H$ indicates an exothermic reaction (releases heat), and a positive $\Delta H$ indicates an endothermic reaction (absorbs heat).
• 🌪️ Entropy ($S$): Represents the disorder or randomness of a system. An increase in entropy (positive $\Delta S$) favors spontaneity.
• 🔢 Temperature ($T$): Must be in Kelvin (K). To convert from Celsius (°C) to Kelvin, use the formula: $T(K) = T(°C) + 273.15$.
• ⚖️ Spontaneity:
  • $G < 0$: The reaction is spontaneous (favorable).
  • $G > 0$: The reaction is non-spontaneous (requires energy input).
  • $G = 0$: The reaction is at equilibrium.
• ➕ Calculating Change: To calculate the change in Gibbs Free Energy ($\Delta G$), use the equation: $\Delta G = \Delta H - T\Delta S$, where $\Delta H$ is the change in enthalpy and $\Delta S$ is the change in entropy.

🧪 Real-world Examples

Let's explore some examples to illustrate how to calculate Gibbs Free Energy:

1. Example 1: Consider a reaction where $\Delta H = -100 \text{ kJ/mol}$ and $\Delta S = -200 \text{ J/(mol⋅K)}$ at $T = 300 \text{ K}$. Calculate $\Delta G$.
   • First, convert $\Delta S$ to kJ/mol⋅K: $\Delta S = -200 \text{ J/(mol⋅K)} = -0.2 \text{ kJ/(mol⋅K)}$.
   • Then, use the formula: $\Delta G = \Delta H - T\Delta S = -100 \text{ kJ/mol} - (300 \text{ K})(-0.2 \text{ kJ/(mol⋅K)})$.
   • $\Delta G = -100 \text{ kJ/mol} + 60 \text{ kJ/mol} = -40 \text{ kJ/mol}$. The reaction is spontaneous.
2. Example 2: For the reaction $N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)$, $\Delta H = -92.2 \text{ kJ/mol}$ and $\Delta S = -198.75 \text{ J/(mol⋅K)}$ at $298 \text{ K}$. Calculate $\Delta G$.
   • Convert $\Delta S$ to kJ/mol⋅K: $\Delta S = -198.75 \text{ J/(mol⋅K)} = -0.19875 \text{ kJ/(mol⋅K)}$.
   • Use the formula: $\Delta G = \Delta H - T\Delta S = -92.2 \text{ kJ/mol} - (298 \text{ K})(-0.19875 \text{ kJ/(mol⋅K)})$.
   • $\Delta G = -92.2 \text{ kJ/mol} + 59.2275 \text{ kJ/mol} = -32.9725 \text{ kJ/mol}$. The reaction is spontaneous.

📝 Practice Quiz

1. Calculate $\Delta G$ for a reaction with $\Delta H = -50 \text{ kJ/mol}$ and $\Delta S = -150 \text{ J/(mol⋅K)}$ at $T = 298 \text{ K}$.
2. Determine the spontaneity of a reaction at 25°C with $\Delta H = 30 \text{ kJ/mol}$ and $\Delta S = 50 \text{ J/(mol⋅K)}$.
3. Find $\Delta G$ if $\Delta H = -150 \text{ kJ/mol}$ and $\Delta S = -250 \text{ J/(mol⋅K)}$ at $T = 350 \text{ K}$.

💡 Tips and Tricks

• ✅ Units: Always ensure that the units for $\Delta H$ and $\Delta S$ are consistent (usually kJ/mol and kJ/(mol⋅K), respectively).
• 🌡️ Temperature: Always use Kelvin for temperature.
• ➕ Sign Conventions: Pay close attention to the signs of $\Delta H$ and $\Delta S$.
• 🤔 Problem Solving: Break down the problem into smaller steps to avoid errors.

🔑 Conclusion

Calculating Gibbs Free Energy from enthalpy and entropy changes is essential for determining the spontaneity of chemical reactions. By understanding the principles and practicing with examples, you can master this concept and apply it to various chemical and physical processes. Remember to pay attention to units, temperature, and sign conventions to ensure accurate calculations.