In organic chemistry, understanding a reaction's favorability and direction relies on three key concepts: Gibbs Free Energy (ΔG), Enthalpy (ΔH), and Entropy (ΔS). These are interrelated and tell us a story about the energy landscape of the reaction.
Imagine ΔG as the net usable energy in a reaction. A negative ΔG indicates a spontaneous reaction, meaning it can proceed without external input and tends to reach a state of equilibrium with more products. Conversely, a positive ΔG suggests a non-spontaneous reaction that wouldn't occur on its own. A negative ΔG signifies an exoergonic reaction, while a positive
ΔH represents the heat exchange between the reaction and its surroundings. A negative ΔH signifies an exothermic reaction, which releases heat as the reaction progresses. An endothermic reaction, with a positive ΔH, absorbs heat from the surroundings.
We can estimate ΔH for a reaction using bond enthalpies, which are the average energy required to break a specific type of bond. For example, consider the combustion of methane:
CH₄ (g) + 2O₂ (g) → CO₂ (g) + 2H₂O (g)
Here, we look up the bond enthalpies (available in reference tables) for each bond broken (C-H, O=O) and formed (C=O, O-H).
ΔH ≈ Σ (Bond enthalpies of broken bonds) - Σ (Bond enthalpies of formed bonds)
Example Calculation:
| Bond | Enthalpy (kJ/mol) | Change |
|---|---|---|
| C-H | 436 | -4(436) (4 C-H bonds broken in CH₄) |
| O=O | 498 | -1(498) (1 O=O bond broken in O₂) |
| C=O | 799 | -(799) (1 C=O bond formed in CO₂) |
| O-H | 463 | 2(463) (2 O-H bonds formed in 2H₂O) |
ΔH ≈ (-4(436) - 498) - (-799 + 2(463)) ≈ -502 kJ/mol
This negative ΔH indicates an exothermic reaction, releasing 502 kJ of energy per mole of methane combusted.
Entropy is a measure of randomness or disorder in a system.
A positive ΔS indicates an increase in disorder, often associated with:
Conversely, a negative ΔS suggests a decrease in disorder, such as:
The magic lies in how ΔG considers both ΔH and ΔS:
ΔG = ΔH - TΔS (where T is temperature)
This equation tells us that a favorable reaction (negative ΔG) can result from either a negative ΔH (exothermic) or a positive ΔS (increased disorder), or ideally, a combination of both. Even an endothermic reaction (positive ΔH) might be spontaneous if the increase in entropy (positive ΔS) is significant enough at a particular temperature (T).
Understanding ΔG, ΔH, and ΔS empowers organic chemists to predict reaction feasibility, optimize reaction conditions, and design new synthetic pathways for organic molecules.
The equilibrium constant (K) is a temperature-dependent constant that reflects the ratio of product concentrations to reactant concentrations at equilibrium. For a general reaction:
\begin{equation} \text{aA} + \text{bB} \leftrightarrow \text{cC} + \text{dD} \end{equation} \begin{equation} K = \frac{[\text{C}]^c [\text{D}]^d}{[\text{A}]^a [\text{B}]^b} \end{equation}where:
A high K value (greater than 1) indicates a product-favored equilibrium, meaning there are more products than reactants at equilibrium. Conversely, a K value less than 1 signifies a reactant-favored equilibrium. If K is equal to 1, the concentrations of reactants and products are equal at equilibrium.
The magic lies in the relationship between ΔG and K, described by the following equation:
ΔG = -RTln(K)
or
K = e(-RT/ΔG)
where:
This equation tells us that the value of K is related tp the sign and magnitude of ΔG:
By calculating ΔG using thermochemical data or estimating it from bond enthalpies, and knowing the temperature, we can predict the equilibrium constant (K) and understand the extent of a reaction at equilibrium in organic chemistry.