Spontaneity: Meaning, Types, Reference to Entropy, Enthalpy, Gibbs Energy

Spontaneity: When water is kept in an open vessel its volume decreases due to evaporation. Hot coffee becomes cold when it is kept open for some time. Do you apply any energy to these processes? No. What do you call such a process in thermodynamics? These processes are called spontaneous processes, i.e., the changes that take place on their own. The condition is called spontaneity. In this article, you will explore the meaning, types, examples for spontaneity and spontaneous reactions. You are indulging in the condition of entropy, enthalpy and Gibbs energy for spontaneity.

What is Spontaneity?

The term spontaneity means the feasibility of a process. A process that can take place either on its own or under some initiation under the given set of conditions is called a spontaneous process. In other words, a spontaneous process is a process that can occur without work being done on it. Spontaneous processes are also called feasible or probable processes.

It may be noted clearly that a spontaneous process need not be instantaneous, i.e., capable of taking place at once. Its actual speed may vary from very slow to extremely fast. Thus, spontaneity gives no idea about the time taken to bring about the change. Spontaneous processes include both physical changes and chemical changes.

Spontaneous Reaction in Real Life

Some examples of spontaneous reaction in real life are:

1. Evaporation of water
2. The flow of water down the hill
3. Dissolution of sugar or salt in water

Types of Spontaneous Processes

1. Spontaneous processes where no initiation is needed:

Example:

1. Sugar dissolves in water and forms a solution.
2. Evaporation of water from water bodies.
3. Nitric oxide and oxygen react to form nitrogen dioxide.
4. The reaction between hydrogen and iodine gives hydrogen iodide.
5. \({{\text{H}}_2} + {{\text{I}}_2} \to 2{\text{HI}}\)

2. Spontaneous processes where some initiation is required:

Example:

1. Lightning of a candle involving the burning of wax is initiated by ignition.
2. The heating of calcium carbonate to give calcium oxide and carbon dioxide is initiated by heat.
3. \({\rm{CaC}}{{\rm{O}}_3} \to {\rm{CaO}} + {\rm{C}}{{\rm{O}}_2}\)
4. The combination of hydrogen and oxygen to form water was initiated by passing an electric spark.
5. \(2{{\text{H}}_2} + {{\text{O}}_2} \to 2{{\text{H}}_2}{\text{O}}\)
6. The reaction between methane and oxygen to form carbon dioxide and water is initiated by ignition.
7. \({\text{C}}{{\text{H}}_4} + 2{{\text{O}}_2} \to {\text{C}}{{\text{O}}_2} + 2{{\text{H}}_2}{\text{O}}\)

Spontaneity in Terms of Entropy Change

Entropy \(\left({\text{S}}\right)\) is defined as a measure of randomness or disorder of the system. The greater the randomness, the higher is the entropy. The order of randomness or entropy of solid, liquid, and gas is Gas \( > \) Liquid \( > \) Solid.

1. For spontaneous processes in isolated systems (i.e., a system which can neither exchange matter nor energy with the surrounding), the entropy change is positive.
2. Example: Mixing of two gases on opening the stopcock, spreading of a drop ink in a beaker filled with water, etc.
3. For spontaneous processes in open systems (i.e., a system which can exchange matter as well as energy with the surrounding), the total entropy change \(\left({\Delta {{\text{s}}_{{\text{total}}}}} \right)\) must be positive.
4. \(\Delta {{\text{S}}_{{\text{total}}}}\,{\text{or}}\,\Delta {{\text{S}}_{{\text{Universe}}}} = \Delta {{\text{S}}_{{\text{system}}}} + \Delta {{\text{S}}_{{\text{surroundings}}}} > 0\)
5. Example: Cooling down of a cup of tea, the water vapour and energy from the teacup exchange with the surroundings.
6. In all the spontaneous reactions, entropy increases until an equilibrium is reached. Thus, entropy is maximum at equilibrium, and there is no further change in entropy, i.e., \(\Delta {\text{S}} = 0.\) Hence for a process in equilibrium, \(\Delta {{\text{S}}_{{\text{total}}}}\,{\text{or}}\,\Delta {{\text{S}}_{{\text{Universe}}}} = 0.\)

Second Law of Thermodynamics and Spontaneity

The relationship between entropy and spontaneity put forward in terms of the second law of thermodynamics as follows

1. All spontaneous processes or naturally occurring processes are thermodynamically irreversible. Example: Non-reactive gases mix with each other to increase the entropy of constituent molecules. But these cannot be separated from the mixture.
2. Without the help of an external agency, a spontaneous process cannot be reversed. Example: Heat energy can flow from a hot body to the cold of its own but not from the cold body to the hot body unless the cold body is heated.
3. The entropy of an isolated system must increase if it is to be spontaneous in a particular direction, i.e., \(\Delta {{\text{S}}_{{\text{system}}}} > 0\)(Positive).
4. Since the isolated system is cut off from the surrounding, no exchange of energy is possible. In this case, it is to be spontaneous, then the entropy must increase
5. In a non-isolated system, the total entropy of both the system and surroundings must increase or must be positive.
6. \(\Delta {{\text{S}}_{{\text{system}}}} + \Delta {{\text{S}}_{{\text{surroundings}}}} > 0\left( {{\text{Positive}}} \right).\)

What is Enthalpy?

The enthalpy is also called heat content and is denoted by \({\text{H}}{\text{.}}\) The enthalpy of a system may be defined as the sum of the internal energy \(\left({\text{U}} \right)\) and pressure volume \(\left({\text{PV}} \right)\) energy, under a set of conditions.

\({\text{H}} = {\text{U}} + {\text{PV}}\)

In the exothermic process (energy is released by the system), \(\Delta {\text{H}}\) is negative, and in the endothermic process (energy is absorbed by the system), \(\Delta {\text{H}}\) is positive.

What is Energy or Gibbs Energy?

J. Willard Gibbs has introduced the term energy to predict the direction of spontaneity. energy \(\left({\text{G}} \right)\) is defined as the amount of energy available for doing useful work under conditions of constant temperature and pressure.

\({\text{G}} = {\text{H}} – {\text{TS}}\)

Here, \({\text{H}}\) is the enthalpy of the system, \({\text{S}}\) is the entropy of the system, and \({\text{T}}\) is the temperature of the system on the Kelvin scale.

The Gibbs energy, \({\text{G}} = {\text{H}} – {\text{TS}}\)

We know that enthalpy, \({\text{H=U + PV}}\)

Therefore, \({\text{G=U + PV-TS}}\)

The change in Gibbs energy can be expressed as

\(\Delta {\text{G}} = \Delta {\text{U}} + \Delta \left({{\text{PV}}} \right) – \Delta \left( {{\text{TS}}} \right)\)

\(\Delta {\text{G}} = \Delta {\text{U}} + {\text{P}}\Delta {\text{V}} + {\text{V}}\Delta {\text{P}} – {\text{T}}\Delta {\text{S}} – {\text{S}}\Delta {\text{T}}\)

If the change is carried out at a constant temperature and constant pressure then \(\Delta {\text{T=0}}\) and \(\Delta {\text{P=0}}{\text{.}}\)

Therefore, \(\Delta {\text{G}} = \Delta {\text{U}} + {\text{P}}\Delta {\text{V}} – {\text{T}}\Delta {\text{S}}\)

Since, \(\Delta {\text{H}} = \Delta {\text{U}} + {\text{P}}\Delta {\text{V}}\)

\(\Delta {\text{G}} = \Delta {\text{H}} – {\text{T}}\Delta {\text{S}}\)

The equation \(\Delta {\text{G}} = \Delta {\text{H}} – {\text{T}}\Delta {\text{S}}\) is called Gibbs- Helmholtz equation.

Gibbs Energy and Spontaneity

According to Gibbs- Helmholtz equation

\(\Delta {\text{G}} = \Delta {\text{H}} – {\text{T}}\Delta {\text{S}}\)

For reaction to be spontaneous \(\Delta {\text{G}}\) should be negative \(\left({\Delta {\text{G}} < 0} \right).\Delta {\text{G}}\) can be negative under following conditions:

1. \(\Delta {\text{H}}\) is negative and \({\text{T}}\Delta {\text{S}}\) is positive.
2. Both \(\Delta {\text{H}}\) and \({\text{T}}\Delta {\text{S}}\) are negative. In this case, \(\Delta {\text{H}}\) favours while \({\text{T}}\Delta {\text{S}}\) opposes the spontaneous process. Thus, the process can be spontaneous if \(\Delta {\text{H > T}}\Delta {\text{S}}.\)
3. Both \(\Delta {\text{H}}\) and \({\text{T}}\Delta {\text{S}}\) are positive. In this case, \({\text{T}}\Delta {\text{S}}\) favours the spontaneous process and \(\Delta {\text{H}}\) opposes the spontaneous process. Thus, the process can be spontaneous if \(\Delta {\text{H < T}}\Delta {\text{S}}.\)

If \(\Delta {\text{H}}\) is zero, the process does not occur, or the system is in equilibrium.

Effect of Temperature on Spontaneity

According to Gibbs Helmholtz equation, \(\Delta {\text{G=}}\Delta {\text{H}} – {\text{T}}\Delta {\text{S}}.\) The magnitude of ∆H does not change much with rise in temperature, but \({\text{T}}\Delta {\text{S}}\) changes a lot with change in temperature.

1. For endothermic process, \(\Delta {\text{H}}\) is positive and \(\Delta {\text{S}}\) is also positive. Thus, \(\Delta {\text{H}}\) opposes the spontaneous reaction but \({\text{T}}\Delta {\text{S}}\) tends to favour it. Thus, an endothermic process may be non-spontaneous at low temperature and spontaneous at high temperature.
2. For exothermic process, \(\Delta {\text{H}}\) is negative and \(\Delta {\text{S}}\) is also negative. Thus, \(\Delta {\text{H}}\) favours the spontaneous reaction but \({\text{T}}\Delta {\text{S}}\) opposes it. Thus, an exothermic process may be spontaneous at low temperature and non-spontaneous at high temperature.

Summary

In this article, you have learnt the meaning of spontaneity, its types with a good number of examples. You can also identify the spontaneous processes observed in daily life. You are able to recall the meaning of entropy, enthalpy and energy. This article is helpful to understand what are the values of entropy \(\left({\text{S}} \right),\) enthalpy \(\left({\text{H}} \right)\) and energy \(\left({\text{G}} \right),\) for which a reaction to be spontaneous with reference to the Gibbs- Helmholtz equation, i.e.,

\(\Delta {\text{G}} = \Delta {\text{H}} – {\text{T}}\Delta {\text{S}}\)

FAQs on Spontaneity

Q.1. What is entropy and enthalpy?
Ans: Entropy \(\left({\text{S}} \right)\) is defined as a measure of randomness or disorder of the system. The enthalpy of a system may be defined as the sum of the internal energy \(\left({\text{U}} \right)\) and pressure volume \(\left({\text{PV}} \right)\) energy, under a set of conditions.
\({\text{H=U + PV}}\)

Q.2. What is the difference between spontaneity and disorder?
Ans: The term spontaneity means the feasibility of a process. A process which can take place either on its own or under some initiation under the given set of conditions is called a spontaneous process. The disorder is also called randomness or entropy. Entropy \(\left({\text{S}}\right)\) is defined as a measure of randomness or disorder of the system. The greater the randomness, the higher is the entropy.

Q.3. What does spontaneity mean in chemistry?
Ans: The term spontaneity means the feasibility of a process. A process which can take place either on its own or under some initiation under the given set of conditions is called a spontaneous process.
Example: Reaction between hydrogen and iodine to give hydrogen iodide.
\({{\rm{H}}_2}{\rm{ + }}{{\rm{I}}_2} \to 2{\rm{HI}}\)

Q.4. What is the spontaneity of a reaction?
Ans: The spontaneity of a reaction is the feasibility of reaction, i.e., whether the process can take place by itself or under some initiation, under the given set of conditions.

Q.5. What is the relation between spontaneity and entropy?
Ans: For spontaneity, the entropy of the isolated system should be positive. For spontaneous processes in open systems, the total entropy change
\(\left({\Delta {{\text{S}}_{{\text{total}}}}} \right)\) must be positive. \(\Delta {{\text{S}}_{{\text{total}}}}\,{\text{or}}\,\Delta {{\text{S}}_{{\text{Universe}}}} = \Delta {{\text{S}}_{{\text{system}}}} + \Delta {{\text{S}}_{{\text{surroundings}}}} > 0\)

Q.6. How can entropy be used to predict spontaneity?
Ans: If entropy is positive, then the reaction is spontaneous.

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