Thermodynamic equilibrium: A short note

Thermodynamic 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, a change of state of a thermodynamic system results from the existence of gradients of various types within or across its boundary.

What are the gradients across the boundary?

Examples

-A gradient of pressure results in momentum or convective transport of mass.

-Temperature gradients result in heat transfer

- 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 an 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 does equilibrium set 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.

Difference between equilibrium constant and equilibrium position

The equilibrium constant is the number that gives the relationship between amounts of products and reactants of a reaction mixture at its equilibrium whereas the equilibrium position is the moment at which the forward reaction of the equilibrium is equal to the backward reaction. This is the key difference between equilibrium constant and equilibrium position.

Equilibrium is the state of a system where there is a forward and backward reaction at the same time. This means, there are opposing reactions that balance each other. The equilibrium constant gives a quantitative explanation of the equilibrium state of a system whereas the equilibrium position explains the equilibrium system qualitatively.

What is the equilibrium constant?

The equilibrium constant is the number that gives the relationship between the amounts of products and reactants of a reaction mixture at its equilibrium. An equilibrium state of a reaction mixture is the state approached by the system at which no further changes of the reactants or products take place. The equilibrium constant is the ratio between concentrations of products and the reactants.

?The equilibrium constant is independent of the initial concentrations of reactants. The factors that affect the value of the equilibrium constant are temperature, nature of the solvent, the ionic strength of ions in the reaction mixture, etc. The equilibrium constant is denoted by “K”.

A + B < --- > C

K = [C] / [A] [B]

This is also known as the equilibrium constant of concentrations because the concentrations of reactants and products are used in writing the expression. It is denoted by Kc. If the value of the K is higher than 1, the equilibrium favors the products. But if the value of K is lower than 1 the equilibrium favors reactants.

Gibbs free energy and equilibrium constant

At equilibrium, the forward and reverse reactions proceed at equal rates. The driving force in each direction is equal because the free energy of the reactants and products under equilibrium conditions is equivalent to ΔG = 0.

The key equation

ΔG° = -RT ln K

K = e ^ - dG/RT

R is the gas constant with a value of 8.314 J K-1mol-1. T is the temperature of the reaction in Kelvin.

ΔG° is the standard free energy change here - NOT the free energy change at whatever temperature the reaction was carried out.

Example 1

Suppose you have a fairly big negative value of ΔG° = -60.0 kJ mol-1.

The first thing you have to do is remember to convert it into J by multiplying by 1000, giving -60000 J mol-1.

And let's suppose that we are interested in the equilibrium constant for the reaction at 100°C - which is 373 K.

ΔG° = -RT ln K

-60000 = -8.314 x 373 x ln K

This gives ln K =19.35

Using the ex-function on your calculator gives a value for K = 2.53 x 108.

That is a huge value for an equilibrium constant and means that at equilibrium the reaction has almost gone to completion. In the equilibrium constant expression, there must be lots of products at the top and hardly any reactants at the bottom.

Example 2

Now let's repeat the same exercise with a fairly big positive value of ΔG° = +60.0 kJ mol-1.

And we will keep the same temperature as before - 373 K.

ΔG° = -RT ln K

+60000 = -8.314 x 373 x ln K

This gives ln K = -19.35

Using the ex?function on your calculator gives a value for K = 3.96 x 10-9.

That is a tiny value for an equilibrium constant, and there has been virtually no reaction at all at equilibrium. In the equilibrium constant expression, there must be hardly any products at the top and lots of reactants at the bottom.

What affects the equilibrium constant?

Changing concentrations

Equilibrium constants are not changed if you change the concentrations of things present in the equilibrium. The only thing that changes an equilibrium constant is a change of temperature. The position of equilibrium is changed if you change the concentration of something present in the mixture. According to Le Chatelier's Principle, the position of equilibrium moves in such a way as to tend to undo the change that you have made.

Suppose you have an equilibrium established between four substances A, B, C, and D.

A+2B?C+D

According to Le Chatelier's Principle, if you decrease the concentration of C, for example, the position of equilibrium will move to the right to increase the concentration again.

Changing pressure

This only applies to systems involving at least one gas. Equilibrium constants are not changed if you change the pressure of the system.. The position of equilibrium may be changed if you change the pressure. According to Le Chatelier's Principle, the position of equilibrium moves in such a way as to tend to undo the change that you have made.

That means that if you increase the pressure, the position of equilibrium will move in such a way as to decrease the pressure again - if that is possible. It can do this by favoring the reaction which produces fewer molecules. If there are the same number of molecules on each side of the equation, then a change of pressure makes no difference to the position of equilibrium.

Changing temperature

This is typical of what happens with an equilibrium where the forward reaction is exothermic, increasing the temperature decreases the value of the equilibrium constant. Where the forward reaction is endothermic, increasing the temperature increases the value of the equilibrium constant.

The position of equilibrium also changes if you change the temperature. According to Le Chatelier's Principle, the position of equilibrium moves in such a way as to tend to undo the change that you have made. If you increase the temperature, the position of equilibrium will move in such a way as to reduce the temperature again. It will do that by favoring the reaction which absorbs heat.

Equilibrium constant and rate constant

What is the rate constant?

The rate constant, or the specific rate constant, is the proportionality constant in the equation that expresses the relationship between the rate of a chemical reaction and the concentrations of the reacting substances.

Difference between equilibrium constant and rate constant

There is a simple relationship between the equilibrium constant for a reversible reaction and the rate constants for the forward and reverse reactions if the mechanism for the reaction involves only a single step. The equilibrium constant for a one-step reaction is equal to the forward rate constant divided by the reverse rate constant, K = k forward / k reverse.

Credit: Google