Thermodynamic equilibrium: A fate decider for a chemical process

The success of a chemical reaction hinges on the position of equilibrium. Thermodynamic equilibrium is a concept of thermodynamics. It is an internal state of a single thermodynamic system or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium, there are no net macroscopic flows of matter or of energy, either within a system or between systems. As a consequence, at the thermodynamic equilibrium, the rates of all reactions proceeding in two opposite directions are equal. At thermodynamics equilibrium, the existence of gradients of various types within or across a thermodynamic system comes to zero. Effectively thermodynamic equilibrium stops a thermodynamic process.

Thermodynamic equilibrium is a thermodynamic state of rest

All thermodynamic gradients cease to exist at equilibrium. In general change of state of a thermodynamic system results from the existence of gradients of various types within or across its boundary. Thus a gradient of pressure results in momentum or convective transport of mass. Temperature gradients result in heat transfer, while a gradient of concentration promotes diffusive mass transfer. Thus, as long as internal or cross-boundary gradients of any form as above exist with respect to a thermodynamic system it will undergo a change of state in time. The result of all such changes is to annul the gradient that in the first place causes the changes. This process will continue till all types of gradients are nullified. In the ultimate limit, one may then conceive of a state where all gradients (external or internal) are non-existent and the system exhibits no further changes. Under such a limiting condition, the system is said to be in a state of thermodynamic equilibrium.

Types of equilibrium

A thermodynamic system may exist in various forms of equilibrium: stable, unstable, and metastable. Consider the body to be initially in state ‘1’. If disturbed by a mechanical force of a very small magnitude the body will return to its initial state. However, if the disturbance is of a large magnitude, the body is unlikely to return to its initial state. In this type of situation, the body is said to be in unstable equilibrium. Consider next the state ‘2’; even a very small disturbance will move the body to either position ‘I’ or ‘3’. This type of original equilibrium state is termed metastable. Lastly, if the body is initially in the state ‘3’, it will tend to return to this state even under the influence of relatively larger disturbances. The body is then said to be in a stable equilibrium state. If ‘E’ is the potential energy of the body and ‘x’ is the effective displacement provided to the body in the vertical direction, the three equilibrium states may be described by the following equations:

 Stable equilibrium = ?^2E/?X^2 > 0

Unstable equilibrium = ? ^2E/?X^2< 0

Meta stable equilibrium = ?^2E/?X^2 = 0

The disturbances in these cases could be mechanical, thermal or chemical in nature.

Zeroth law of thermodynamics

This is an outstanding example of thermodynamic equilibrium

The experience of touch, in relation to body temperature, is common to all. It leads directly to what is known as the zeroth law of thermodynamics. This can be stated as follows: Two systems that are each in thermal equilibrium with a third system are in thermal equilibrium with each other. In practice, this principle has enabled the development of solid, liquid, and gas thermometers, which use the size variations of substances in relation to various scales, one of the most common being temperature measured in degrees Celsius (°C). Over time, the measurement process has made use of many other thermophysical properties, such as thermoelectric properties (Seebeck effect), which are exploited in thermocouples.

Thermodynamics

Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:

A= [U-TS]

Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:

G= [U-TS+PV], where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.

 Conditions that prevail at thermodynamic equilibrium

-For a completely isolated system, S is maximum at thermodynamic equilibrium.

-For a system with controlled constant temperature and volume, A is minimum at thermodynamic equilibrium.

-For a system with controlled constant temperature and pressure, G is minimum at thermodynamic equilibrium.

 How equilibrium sets in? The points should always be remembered

-Two systems are in thermal equilibrium when their temperatures are the same.

-Two systems are in mechanical equilibrium when their pressures are the same.

-Two systems are in diffusive equilibrium when their chemical potentials are the same.

-All forces are balanced and there is no significant external driving force.

 A fate decider for chemical processes

Typical cases

Production of Methanol

Owing to the equilibrium nature of the methanol synthesis reaction, the conventional fixed-bed reactor provides a low conversion of synthesis gas to methanol. Moreover, the synthesis reaction is exothermic and total moles diminish as the reaction goes to completion

Production of Ammonia

Preparation of ammonia by Haber’s process: In this nitrogen combines with hydrogen to form ammonia, the yield of ammonia is more at low temperature, high pressure and in the presence of iron as catalyst.

Production of sulphuric acid

Preparation of sulphuric acid by contact process: In this process, the fundamental reaction is the oxidation of sulfur dioxide into sulfur trioxide. This is a chemical equilibrium-driven reaction. Conversion of sulfur dioxide to sulfur trioxide is a reversible reaction

Credit: Google