Establishment of Chemical Equilibrium

Dynamic Nature of Chemical Equilibrium

In a previous chapter on chemical equilibrium, the basic idea of a reversible reaction and the concept of equilibrium were introduced. Here, the focus is on how such an equilibrium is actually established in time: what happens when reactants (or products) are mixed, why the system does not simply “stop,” and how the balance between forward and reverse reaction rates arises.

We will deliberately stay qualitative here; quantitative relationships (such as the law of mass action and the equilibrium constant) are treated in later chapters.

Time Evolution of a Reversible Reaction

Consider a general reversible reaction in a closed system:

$$
\text{A} + \text{B} \rightleftharpoons \text{C} + \text{D}
$$

Suppose we start with pure reactants (A and B) and no products (C and D).

• At the beginning:
• The forward reaction rate (A + B → C + D) is initially high, because the concentrations of A and B are high.
• The reverse reaction rate (C + D → A + B) is essentially zero, because C and D are not yet present.
• As time passes:
• A and B are consumed, so their concentrations decrease; the forward rate slows down.
• C and D are formed, so their concentrations increase; the reverse rate speeds up.
• After some time:
• The forward and reverse rates become equal.
• At this point, the system has reached chemical equilibrium.

Graphically, if you plot the concentrations of A, B, C, and D versus time, you typically see:

• Reactant concentrations decreasing and then leveling off.
• Product concentrations increasing and then leveling off.
• A “flattening” of curves as equilibrium is approached.

Similarly, if you plot reaction rates versus time:

• The forward rate starts high and falls.
• The reverse rate starts low (often zero) and rises.
• The two curves intersect at equilibrium and then run parallel at the same rate.

This evolution from an initial state to equilibrium is often called the establishment or attainment of chemical equilibrium.

Dynamic vs. Static Equilibrium

When equilibrium has been established, the observable macroscopic properties of the system (such as color, pressure, and total concentrations of reactants and products) no longer change with time. However, this does not mean that nothing is happening at the molecular level.

Dynamic equilibrium

At chemical equilibrium:

• The forward reaction still occurs.
• The reverse reaction still occurs.
• The rates of the forward and reverse reactions are equal.

As a result:

• The net change in the concentrations of reactants and products is zero.
• Individual molecules are continuously converted back and forth, but the overall composition remains constant.

This is why chemical equilibrium is said to be dynamic, not static.

Consequences of dynamic equilibrium

Dynamic equilibrium has several important implications:

• If a small amount of a reactant or product is added or removed, the system can respond (by adjusting reaction rates) to re-establish equilibrium under the new conditions.
• The fact that reactions continue in both directions even at equilibrium is the basis for understanding how external influences (such as concentration, pressure, temperature, catalysts) affect an equilibrium system.

The detailed response of an equilibrium to changes in conditions is discussed elsewhere; here we only need the idea that the system remains reactive when equilibrium is established.

Approaches to Equilibrium from Different Initial Conditions

Chemical equilibrium can be established from a variety of starting points, not just from “all reactants”:

Starting with only reactants

• This is the most intuitive case.
• Only the forward reaction is possible at first.
• Products gradually accumulate; the reverse reaction “turns on” and increases in rate until equilibrium is reached.

Starting with only products

• Now only the reverse reaction can occur at the beginning.
• Reactants are gradually formed; the forward reaction “turns on” and increases until rates balance.

Starting with a mixture of reactants and products

• Both forward and reverse reactions are possible from the start.
• One of the directions is usually favored initially, depending on the starting composition.
• The system adjusts until the characteristic equilibrium composition at that temperature and pressure is reached.

An important insight:

• Regardless of how you start, as long as the system is closed and conditions (temperature, pressure, volume) remain the same, the system approaches the same equilibrium state.
• This independence from initial composition is one of the defining features of chemical equilibrium and a basis for defining an equilibrium constant.

Molecular-Level Picture of Establishing Equilibrium

On the microscopic level, the establishment of equilibrium can be understood in terms of molecular collisions and probabilities.

From reactants to equilibrium

Imagine we have a gas-phase reversible reaction:

$$
\text{A(g)} + \text{B(g)} \rightleftharpoons \text{C(g)}
$$

• Initially, there are many A and B particles and no C particles.
• Collisions between A and B often have enough energy and correct orientation to produce C.
• As C accumulates, C particles now collide with each other or with other species, which can lead to the reverse process (e.g., C breaking back into A and B, depending on the mechanism).
• Eventually, the frequency of successful A + B → C events matches the frequency of successful C → A + B events.

On a molecular level, “establishing equilibrium” means that the relative frequencies of forward and backward elementary processes have adjusted to a steady balance.

Role of reaction pathways

Real reactions can proceed through multiple steps and intermediate species. Even in multistep mechanisms:

• Several forward and reverse elementary steps occur.
• Some intermediates might rapidly interconvert.
• The overall forward and reverse reaction rates for the net reaction eventually become equal.

The internal details of the path do not change the central idea: equilibrium corresponds to a steady state of macroscopic composition where forward and reverse processes are balanced.

Equilibrium in Closed vs. Open Systems

To establish and maintain chemical equilibrium in the simplest sense, certain conditions must be met.

Closed systems

• In a closed system, matter does not enter or leave, but energy (as heat or work) may be exchanged with the surroundings.
• Under fixed temperature, fixed total amounts of substances, and fixed volume (or pressure), a reversible reaction tends to approach a definite equilibrium state.
• The composition at equilibrium is stable over time (as long as external conditions are unchanged).

Most basic discussions of chemical equilibrium assume such closed, well-defined systems.

Open systems and flow systems (brief qualitative view)

• In an open system, matter can be added or removed.
• If reactants are continuously supplied and products are continuously removed (as in a flow reactor), the system might reach a steady state where concentrations remain constant, but:
• This steady state is not necessarily a true thermodynamic equilibrium.
• Net conversion in one direction may occur continuously.
• In contrast, thermodynamic equilibrium in a closed system involves no net macroscopic flux of matter in any direction, and forward and reverse reaction rates are equal.

In this chapter, “establishment of chemical equilibrium” always refers to the closed-system, true-equilibrium case.

Factors Affecting How Fast Equilibrium Is Established

The time it takes for a system to reach its equilibrium composition can vary from fractions of a second to years or longer. The equilibrium state itself is defined thermodynamically, but the path and speed of approach to that state are matters of kinetics.

Kinetic vs. thermodynamic perspectives

• Thermodynamics:
• Determines whether a particular composition is more stable.
• Determines what the equilibrium composition should be under given conditions.
• Kinetics:
• Determines how quickly the system moves toward equilibrium.
• Controls the time scale over which equilibrium is established.

In this chapter, we do not calculate rates, but we qualitatively note what influences them.

Key influences on the speed of establishment

1. Nature of the reactants and products
• Some bonds are easier to break or form than others.
• Simple ionic reactions in solution can reach equilibrium almost instantaneously.
• Reactions involving strong covalent bonds, large molecules, or complex rearrangements can be very slow.
2. Temperature
• Higher temperature increases the fraction of collisions with enough energy to overcome activation barriers.
• As temperature rises, the system approaches equilibrium faster (though the actual equilibrium position may also shift).
3. Concentrations and physical state
• Higher concentrations (or partial pressures) generally increase collision frequency in gases and solutions.
• Reactions in homogeneous phases (all gases or all in solution) often equilibrate faster than those involving solids or phase boundaries, where diffusion can be limiting.
4. Catalysts
• A catalyst provides an alternative reaction pathway with a lower activation energy for both forward and reverse directions.
• This speeds up the establishment of equilibrium but does not change the final equilibrium composition.
• At equilibrium, the rates of forward and reverse reactions are increased by the same factor.

Detailed, quantitative treatment of reaction rates and catalysis is covered in chemical kinetics; here only their qualitative role in establishing equilibrium is emphasized.

Partial Equilibria and Multistep Systems

Many systems involve multiple simultaneous equilibria or multi-step reactions. The establishment of overall equilibrium can be more subtle in such cases.

Sequential reactions

Consider:

$$
\text{A} \rightleftharpoons \text{B} \rightleftharpoons \text{C}
$$

• The A ⇌ B equilibrium might be established quickly.
• The B ⇌ C equilibrium might be slower.
• For some time, A and B may be in near-equilibrium with each other while C is still changing.

Eventually:

• All steps reach a common state where the forward and reverse rates of each individual step are equal.
• The entire system has reached overall equilibrium.

Competing equilibria

In more complex systems, a substance may participate in several equilibria simultaneously. Establishing equilibrium then involves the mutual adjustment of all reactions:

• The system moves through a sequence of composition changes.
• Individual partial equilibria can be temporarily established and then readjusted as other reactions proceed.
• Only when all coupled reactions have balanced forward and reverse rates is the full equilibrium state attained.

This idea underlies many important chemical systems, such as acid–base buffers and metal–ligand complexes, but the quantitative treatment belongs to later chapters.

Experimental Observations of Equilibrium Establishment

In practice, how do chemists know that equilibrium has been reached?

Monitoring a property over time

A property that depends on composition is measured as a function of time, for example:

• Color intensity (for colored species).
• pH (for acid–base systems).
• Pressure (for gas-phase reactions at fixed volume).
• Conductivity (for ionic reactions in solution).

Typically:

• The measured property changes rapidly at first.
• The rate of change slows.
• Eventually, the measured value becomes constant within experimental error.

When the measured property stops changing under constant external conditions, it is an indication that the system has reached equilibrium.

Reversibility test

Another practical check is to start:

• Once from a reactant-rich mixture.
• Once from a product-rich mixture.

If, under identical conditions, both experiments end at the same final composition (and thus same measured properties), this supports the conclusion that:

• A true equilibrium state has been established.
• The reaction is reversible under those conditions.

This empirical observation connects directly to the concept that equilibrium is independent of the path and initial mixture, depending only on conditions such as temperature and pressure.

Summary

• A reversible reaction in a closed system evolves over time toward a state where the concentrations of all species become constant.
• This establishment of chemical equilibrium is the result of:
• A decreasing forward reaction rate (as reactants are consumed).
• An increasing reverse reaction rate (as products are formed).
• At equilibrium, the forward and reverse reaction rates are equal, so the net change in composition is zero, even though reactions continue at the microscopic level.
• The same equilibrium composition is reached from different starting mixtures, provided conditions (temperature, pressure, total amounts) are the same.
• The speed with which equilibrium is established is governed by kinetics (nature of the reaction, temperature, catalysts, etc.), while the position of equilibrium is determined by thermodynamics.
• In complex systems with multiple steps or reactions, partial equilibria can form and adjust until a global balance of all forward and reverse rates is reached.

The next chapters will use this qualitative understanding to introduce quantitative relationships, particularly the law of mass action and the equilibrium constant, which describe equilibrium compositions numerically.