Gibbs Free Energy

Gibbs Free Energy ($G$) is a measure of the energy available in a system to do work at a constant temperature and pressure. It serves as the ultimate decider for whether a chemical process can occur naturally without external intervention.

The Gibbs Equation relates the change in free energy ($\Delta G$) to the change in enthalpy ($\Delta H$), the absolute temperature ($T$), and the change in entropy ($\Delta S$): $\Delta G = \Delta H - T\Delta S$

Standard Conditions: When measured at $298$ K and $100$ kPa, the value is denoted as $\Delta G^\ominus$. This allows for a consistent comparison between different chemical reactions.

Units and Conversion: Enthalpy and Free Energy are typically measured in kJ mol$^{-1}$, while Entropy is measured in J K$^{-1}$ mol$^{-1}$. It is critical to divide the entropy value by $1000$ to ensure unit consistency within the Gibbs equation.

The Gibbs Equation Method: This is the primary method used when the enthalpy change and entropy change of a reaction are known. You must ensure $T$ is in Kelvin and $\Delta S$ is converted to kJ K$^{-1}$ mol$^{-1}$.

Summation of Free Energies: Similar to Hess's Law for enthalpy, the standard free energy change of a reaction can be calculated using the standard free energies of formation ($\Delta G_f^\ominus$) of the products and reactants: $\Delta G_{reaction}^\ominus = \sum \Delta G_f^\ominus(products) - \sum \Delta G_f^\ominus(reactants)$

Determining the Threshold Temperature: To find the exact temperature at which a reaction becomes feasible, set $\Delta G = 0$ and rearrange the equation to solve for $T$: $T = \frac{\Delta H}{\Delta S}$

Feasibility vs. Rate: A negative $\Delta G$ indicates a reaction is thermodynamically possible (feasible), but it does not guarantee the reaction will occur at a measurable speed. A reaction might be feasible but have a very high activation energy, making it kinetically stable (e.g., the conversion of diamond to graphite).

Feasible vs. Spontaneous: While often used interchangeably, 'feasible' usually refers to the energetic favorability, whereas 'spontaneous' implies the reaction occurs without continuous external input.

The 1000 Rule: Always check the units for entropy. Exams frequently provide $\Delta S$ in J K$^{-1}$ mol$^{-1}$ and $\Delta H$ in kJ mol$^{-1}$. Forgetting to divide $\Delta S$ by $1000$ is the most common cause of lost marks.

Kelvin Conversion: Ensure all temperatures are in Kelvin ($K = ^\circ C + 273$). Using Celsius will result in incorrect values for the $T\Delta S$ term.

Graph Interpretation: In a plot of $\Delta G$ vs $T$, the $y$-intercept is $\Delta H$ and the gradient is $-\Delta S$. If the line slopes upwards, the entropy change is negative; if it slopes downwards, the entropy change is positive.

State Symbols: Pay close attention to state symbols in equations, as a change from solid to gas significantly increases entropy, which can flip the feasibility of a reaction.

Misinterpreting $\Delta G = 0$: Students often think the reaction stops at $\Delta G = 0$. In reality, this point represents chemical equilibrium, where the forward and backward reactions occur at the same rate.

Assuming Negative $\Delta H$ means Feasible: While exothermic reactions are often feasible, an endothermic reaction can be feasible if the entropy increase is large enough to overcome the positive enthalpy change at high temperatures.

Ignoring Stoichiometry: When using the summation method ($\sum \Delta G_f^\ominus$), remember to multiply the $\Delta G_f^\ominus$ values by the coefficients in the balanced chemical equation.