What is Spontaneity? – Definition, Types, Gibbs Energy

Thermodynamics is a discipline of physics that studies heat, work, and temperature, as well as their relationships with energy, radiation, and matter’s physical characteristics. The four principles of thermodynamics regulate the behaviour of these quantities, which provide a quantitative description using quantifiable macroscopic physical characteristics but may be described by statistical mechanics in terms of microscopic elements. Thermodynamics is used in a wide range of science and engineering areas, including physical chemistry, biochemistry, chemical engineering, and mechanical engineering, as well as more sophisticated fields like meteorology.

Thermodynamics arose from a desire to improve the efficiency of early steam engines, notably via the work of French scientist Nicolas Léonard Sadi Carnot (1824), who felt that increasing engine efficiency would help France win the Napoleonic Wars. Lord Kelvin, a Scots-Irish scientist, was the first to define thermodynamics succinctly in 1854, stating, “Thermo-dynamics is the science of the connection of heat to forces operating between contiguous portions of substances, and the relation of heat to electrical action.”

What Is Spontaneity?

The phrase spontaneity refers to a process’s viability. A spontaneous process is one that can occur on its own or as a result of some kind of initiation under certain conditions. In other terms, a spontaneous process is one that may happen without any intervention. Feasible or probable processes are other names for spontaneous processes.

Some real-life instances of spontaneous reactions:

• Water vaporisation
• The water flowed down the slope.
• Sugar or salt dissolves in water.

Types of Spontaneous Processes

• Processes that occur without the requirement for an initiator:
  • Sugar makes a solution when it dissolves in water.
  • The evaporation of water from bodies of water.
  • Nitrogen dioxide is formed when nitric oxide and oxygen combine.
  • Hydrogen iodide is formed when hydrogen and iodine react.

H₂ + I₂ → 2HI

• Processes that occur spontaneously but require some initiation:
  • Ignition starts the process of lighting a candle that is burning wax.
  • The heat initiates the heating of calcium carbonate to produce calcium oxide and carbon dioxide. CaCO₃  → CaO + CO₂
  • An electric spark was used to start the reaction between hydrogen and oxygen, which resulted in the formation of water. 2H₂ + O₂  →  2H₂O
  • Ignition starts the reaction between methane and oxygen, which produces carbon dioxide and water. CH₄ + 2O₂  →  CO₂ + 2H₂O

Spontaneity in Terms of Entropy Change

The entropy (S) of a system is defined as a measure of its unpredictability or disorder. The entropy increases as the unpredictability increases. The order of randomness or entropy of solid, liquid, and gas is Gas > Liquid > Solid.

• The entropy change is positive for spontaneous processes in isolated systems (i.e., a system that cannot interchange matter or energy with its surroundings).

For example, mixing two gases when the stopcock is opened, spreading a drop of ink in a beaker filled with water, and so on.

• The total entropy change (Δs_total) must be positive for spontaneous processes in open systems (i.e., a system that may interchange matter and energy with the environment).

ΔS_total or ΔS_Universe=ΔS_system + ΔS_surroundings>0

• When a cup of tea cools down, the water vapour and energy from the teacup exchange with the environment.
• Entropy grows in all spontaneous reactions until an equilibrium is established. As a result, at equilibrium, entropy is at its maximum, and there is no further change in entropy.  i.e., ΔS=0. Hence for a process in equilibrium, 

ΔS_total or ΔS_Universe=0

Second Law of Thermodynamics and Spontaneity

In terms of the second law of thermodynamics, the following is the connection between entropy and spontaneity:

• Thermodynamically, all spontaneous or spontaneously occurring reactions are irreversible. Non-reactive gases, for example, react with one another to increase the entropy of constituent molecules. These, however, cannot be separated from the rest of the combination.
• A spontaneous process cannot be reversed without the assistance of an outside entity. Heat energy may move from a hot body to its own cold, but not from a cold body to a hot one unless the cold body is heated first.
• If an isolated system is to be spontaneous in a certain direction, its entropy must grow, i.e., 

S_system>0 (Positive)

• Because the isolated system is blocked off from the rest of the world, no energy exchange is conceivable. If it is to be spontaneous in this scenario, the entropy must rise.
• The total entropy of both the system and its surroundings must grow or be positive in a non-isolated system.

ΔS_system+ΔS_surroundings>0(Positive)

Enthalpy

The enthalpy, often known as heat content, is represented by the letter H. Under certain conditions, a system’s enthalpy may be defined as the sum of its internal energy (U) and pressure-volume (PV) energy.

H=U+PV

H is negative in exothermic processes (energy is released by the system) and positive in endothermic processes (energy is absorbed by the system).

Gibbs Energy

To forecast the direction of spontaneity, J. Willard Gibbs used the phrase “free energy.” The quantity of energy available for accomplishing productive work under constant temperature and pressure is known as free energy (G).

G=H–TS

H stands for the system’s enthalpy, S for the system’s entropy, and T for the system’s temperature on the Kelvin scale.

The Gibbs free energy, G=H–TS

We know that enthalpy, H=U + PV

Therefore, G=U + PV-TS

Gibbs free energy changes can be represented as:

ΔG=ΔU+Δ(PV)–Δ(TS)

ΔG=ΔU+PΔV+VΔP–TΔS–SΔT

ΔT=0 and ΔP=0 if the change is carried out at a constant temperature and constant pressure.

Therefore, ΔG=ΔU+PΔV–TΔS

Since, ΔH=ΔU+PΔV

ΔG=ΔH–TΔS

The equation ΔG=ΔH–TΔS is called Gibbs- Helmholtz equation.

Gibbs Energy and Spontaneity: According to Gibbs- Helmholtz equation, 

ΔG=ΔH–TΔS

ΔG should be negative (ΔG<0) for the response to be spontaneous. Under the following circumstances, ΔG can be negative:

• TΔS is positive while ΔH is negative.
• TΔS and ΔH are both negative. In this situation, ΔH favours the spontaneous process whereas TΔS opposes it. If ΔH > TΔS, the process can be spontaneous.
• TΔS and ΔH are both positive. TΔS is in favour of the spontaneous process in this situation, whereas ΔH is against it. As a result, if ΔH <TΔS, the process can be spontaneous.

The process does not occur if ΔH is 0, or the system is in equilibrium.

Effect of Temperature on Spontaneity: ΔG=ΔH–TΔS, according to Gibbs Helmholtz equation. The magnitude of H does not vary much as the temperature rises, while TΔS changes a lot as the temperature rises.

• ΔH is positive for endothermic processes, while ΔS is likewise positive. As a result, whereas ΔH opposes the spontaneous reaction, TΔS favours it. At low temperatures, an endothermic reaction may be non-spontaneous, but at high temperatures, it may be spontaneous.
• ΔH is negative for exothermic processes, and ΔS is also negative. As a result, whereas ΔH favours the spontaneous reaction, TΔS opposes it. Exothermic processes can therefore be spontaneous at low temperatures and non-spontaneous at high temperatures.

Sample Questions

Question 1:  What is the difference between spontaneity and disorder?

Answer:

The phrase spontaneity refers to a process’s viability. A spontaneous process is one that can occur on its own or as a result of some kind of initiation under certain conditions. Randomness or entropy are other terms for disorder. The entropy (S) of a system is defined as a measure of its unpredictability or disorder. The entropy increases as the unpredictability increases.

Question 2: What is spontaneity?

Answer:

The phrase spontaneity refers to a process’s viability. A spontaneous process is one that can occur on its own or as a result of some kind of initiation under certain conditions.

Example: Reaction between hydrogen and iodine to give hydrogen iodide.

H₂+I₂→2HI

Question 3: What is the relation between spontaneity and entropy?

Answer:

The isolated system’s entropy should be positive for spontaneity. The total entropy change (ΔS_total) for spontaneous processes in open systems must be positive.

ΔS_total or ΔS_Universe=ΔS_system+ΔS_surroundings>0

Question 4: What are the types of spontaneity?

Answer:

• Processes that occur without the requirement for an initiator.
• Processes that occur spontaneously but require some initiation.

Question 5:  What is the spontaneity of a reaction?

Answer:

The feasibility of a reaction is its spontaneity, i.e., whether the process can occur on its own or with some initiation, given a set of conditions.