6.7 Describing a Reaction: Equilibria, Rates, and Energy Changes

Equilibria, Rates, and Energy Changes in Organic Reactions

Every organic reaction involves two fundamental questions: will this reaction happen, and how fast will it happen? Thermodynamics answers the first question through equilibrium constants and free energy. Kinetics answers the second through reaction rates and activation energy. Keeping these two ideas separate is one of the most important things you can do in this course.

Equilibrium Constants and Free Energy

The equilibrium constant ($K$) tells you where a reaction "settles" once it has had enough time. For a general reaction $aA + bB \rightleftharpoons cC + dD$, the equilibrium constant is:

$K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

• A large $K$ (much greater than 1) means products dominate at equilibrium. The reaction is product-favored.
• A small $K$ (much less than 1) means reactants dominate. The reaction is reactant-favored.
• When $K \approx 1$, you'll have a significant mixture of both.

The equilibrium constant connects directly to Gibbs free energy change ($\Delta G$) through this relationship:

$\Delta G = -RT\ln K$

where $R$ is the gas constant (8.314 J/mol·K) and $T$ is the absolute temperature in Kelvin. This equation is the bridge between thermodynamics and the equilibrium expression. A negative $\Delta G$ corresponds to $K > 1$ (product-favored), and a positive $\Delta G$ corresponds to $K < 1$ (reactant-favored). When $\Delta G = 0$, the system is at equilibrium.

You can also calculate $\Delta G$ from enthalpy and entropy:

$\Delta G = \Delta H - T\Delta S$

This is where the two driving forces of a reaction come together.

Enthalpy and Entropy in Reactions

Enthalpy ($\Delta H$) measures the heat exchanged during a reaction at constant pressure. In organic chemistry, you can think of it as the net energy change from breaking and forming bonds.

• Exothermic reactions release heat ($\Delta H < 0$). Combustion of hydrocarbons is a classic example. Stronger bonds form in the products than were broken in the reactants.
• Endothermic reactions absorb heat ($\Delta H > 0$). Bond breaking costs more energy than bond forming returns.

Entropy ($\Delta S$) measures the disorder or randomness of a system.

• Reactions that produce more molecules (especially gas molecules) from fewer tend to have positive $\Delta S$ and are entropically favored.
• Reactions that produce fewer molecules from more tend to have negative $\Delta S$ and are entropically disfavored.

Together, $\Delta H$ and $\Delta S$ determine whether $\Delta G$ is negative (favorable) or positive (unfavorable):

Most organic reactions you'll encounter are driven primarily by enthalpy (favorable bond changes), with entropy playing a secondary role. But when $\Delta H$ is small, entropy and temperature can tip the balance.

Reaction Rates vs. Equilibrium Positions

This distinction trips up a lot of students: thermodynamics tells you where a reaction ends up, kinetics tells you how fast it gets there. These are independent properties.

Reaction rates describe how quickly reactants convert to products.

• The rate depends on the rate-determining step (RDS), which is the slowest step in the mechanism.
• Rates are influenced by temperature, reactant concentration, and catalysts.
• A catalyst speeds up both the forward and reverse reactions equally. It helps the system reach equilibrium faster but does not shift where that equilibrium lies.

Equilibrium position describes the ratio of products to reactants once the system has settled.

• Determined entirely by thermodynamic quantities: $K$, $\Delta G$, $\Delta H$, and $\Delta S$.
• Reached when the forward and reverse reaction rates become equal, so there's no net change in concentrations.

Here's why this matters in organic chemistry: a reaction can be thermodynamically favorable (large $K$, negative $\Delta G$) but incredibly slow if the activation energy is high. Conversely, a fast reaction isn't necessarily one that goes to completion. You need to consider both factors when predicting what actually happens in the flask.

Reaction Energy Profile

A reaction coordinate diagram plots energy on the y-axis against the progress of a reaction on the x-axis. It gives you a visual summary of both the thermodynamics and kinetics of a reaction.

Key features of the diagram:

• Reactants sit at the starting energy level on the left.
• Products sit at the ending energy level on the right. If products are lower in energy than reactants, the reaction is exothermic; if higher, endothermic.
• The transition state is the highest energy point along the pathway. It represents a fleeting, unstable arrangement of atoms where bonds are partially broken and partially formed. You cannot isolate a transition state.
• Activation energy ($E_a$) is the energy difference between the reactants and the transition state. It's the energy barrier that must be overcome for the reaction to proceed.

According to collision theory, a reaction occurs when molecules collide with both sufficient energy (at least $E_a$) and proper orientation. Most collisions don't meet both criteria, which is why reactions aren't instantaneous.

A few practical points:

• A catalyst lowers $E_a$ by providing an alternative reaction pathway. The starting and ending energies stay the same, so $\Delta G$ is unchanged.
• Raising the temperature increases the fraction of molecules with enough energy to overcome the barrier, which is why reactions speed up when heated.
• For multi-step reactions, each step has its own transition state and activation energy. The step with the highest $E_a$ is the rate-determining step.