Spontaneity In Thermodynamics

Spontaneity in thermodynamics tells us whether a process will naturally occur under given conditions. It is governed by a balance between enthalpy (heat content), entropy (disorder), and temperature, all of which are encapsulated in the Gibbs free energy equation. Understanding these concepts allows us to predict and control chemical and physical processes in both natural and industrial settings.

As we know Thermodynamics is the study of energy changes and the direction of processes. In this context, spontaneity refers to whether a process will occur on its own, without external influence. Understanding spontaneity involves concepts like enthalpy, entropy, and Gibbs free energy. Let’s understand in detail.

1.0Spontaneous Processes

A spontaneous process occurs naturally under a given set of conditions. Examples include ice melting at room temperature or iron rusting when exposed to moisture and oxygen. Once they have started, these processes do not require any external energy to proceed. Here are some points to understand-

• Spontaneity does not imply speed; some spontaneous processes, like the rusting of iron, can be slow.
• A process can be spontaneous in one direction (e.g., water flowing downhill) but non-spontaneous in the reverse direction (water flowing uphill without a pump).

2.0Enthalpy (ΔH) and Spontaneity

Enthalpy is a measure of heat content in a system. It helps us understand the energy changes during chemical reactions.

1. Exothermic Reactions and Spontaneity:

• Many exothermic reactions (ΔH<0) tend to be spontaneous because the release of heat energy lowers the system's energy. However, not all exothermic reactions are spontaneous. Spontaneity also depends on the entropy change (ΔS) and temperature. If ΔS is very negative (large decrease in entropy), the reaction could still be non-spontaneous at certain temperatures.
• For example, fuel combustion releases heat, making it typically spontaneous because it lowers the system's energy.

2. Endothermic Reactions and Spontaneity

• For endothermic reactions (ΔH>0), the process can be spontaneous if:
• • The temperature is high enough to make the TΔS term larger than ΔH.
  • The entropy change (ΔS) is significantly positive, increasing the TΔS term, which can make ΔG negative.

3.0Entropy (ΔS)

Entropy is a measure of disorder or randomness in a system. The Second Law of Thermodynamics states that the total entropy of the universe always increases for a spontaneous process. As we already discussed-

• Increase in Entropy (ΔS>0): Spontaneous processes often involve an increase in entropy. For instance, when a solid turns into a liquid or gas, the molecules gain freedom to move, increasing disorder.
• Decrease in Entropy (ΔS<0): Some processes that decrease entropy can still be spontaneous if the enthalpy change is sufficiently negative.

4.0Gibbs Free Energy and Spontaneity (ΔG)

The spontaneity of a reaction is determined by both enthalpy (ΔH) and entropy (ΔS), as well as temperature, Gibbs free energy combines both enthalpy and entropy into one equation to predict spontaneity:

                                  ΔG = ΔH −TΔS

Where:

• ΔG: Gibbs free energy change
• ΔH: Enthalpy change
• ΔS: Entropy change
• T: Absolute temperature in Kelvin

Interpretation of ΔG:

• ΔG<0: The process is spontaneous.
• ΔG>0: The process is non-spontaneous.
• ΔG=0: The system is in equilibrium.

How ΔG Determines Spontaneity:

• Exothermic Reaction with ΔS>0: Always spontaneous (ΔG<0).
• Exothermic Reaction with ΔS<0: Spontaneous at low temperatures.
• Endothermic Reaction with ΔS>0: Spontaneous at high temperatures.
• Endothermic Reaction with ΔS<0: Never spontaneous.

5.0Temperature and Spontaneity

Temperature can influence spontaneity by affecting the TΔS term in the Gibbs free energy equation. For example:

• Ice melting is non-spontaneous at low temperatures (below 0°C) but becomes spontaneous at room temperature because the positive ΔS overcomes the positive ΔH.

Examples of Spontaneity in Everyday Life:

• Dissolution of Salt in Water: When salt dissolves in water, it breaks into ions, increasing entropy and making the process spontaneous, even though it absorbs heat.
• Combustion of Fuels: Combustion releases a large amount of energy, making it highly spontaneous and energetically favourable.

Here is a table explaining the spontaneity of reactions based on the signs of ΔH and ΔS:

Explanation:

1. Spontaneous at All Temperatures: When ΔH<0 (exothermic) and ΔS>0 (increase in disorder), the reaction is spontaneous at any temperature.
2. Spontaneous at Low Temperatures: When both ΔH and ΔS are negative, the reaction is spontaneous at low temperatures, where the −TΔS term has less impact.
3. Spontaneous at High Temperatures: When both ΔH and ΔS are positive, the reaction becomes spontaneous at high temperatures, where the TΔS term outweighs ΔH.
4. Non-Spontaneous at All Temperatures: When ΔH>0 and ΔS<0, the reaction is non-spontaneous at all temperatures, as both terms contribute to making ΔG positive.

6.0Solved Examples 

Q. The thermodynamic stability of a substance is dependent upon the value of Gibb's function. Explain the stability of solids at low temperatures and the stability of gas at very high temperatures.

Ans.

1. Stability of Solids at Low Temperature

At low temperatures, solids are more thermodynamically stable. This is because of the Gibbs free energy equation:

G = H−TS

favors phases with lower entropy (S).

• Enthalpy (H): Solids generally have low enthalpy due to strong intermolecular forces holding the particles in a fixed, orderly arrangement.
• Entropy (S): Solids have low entropy as the particles are highly ordered.
• Temperature Effect: At low temperatures, the −TS term is small because the temperature (T) is low. This means the Gibbs free energy G is mainly influenced by enthalpy H. Since solids have low enthalpy, their G is low, making them stable.

2. Stability of Gases at High Temperature

At very high temperatures, gases become more thermodynamically stable compared to liquids and solids.

• Enthalpy (H): Gases have relatively higher enthalpy due to weaker intermolecular forces.
• Entropy (S): Gases have high entropy because their particles move freely and are randomly distributed.
• Temperature Effect: At high temperatures, the −TS term becomes very significant because the temperature (T) is high. The large positive entropy (S) of gases multiplied by high temperature (T) results in a substantial negative contribution to G. This lowers the Gibbs free energy of the gas phase, making it more stable at high temperatures.

Q. 100 kJ heat is transferred from a larger heat reservoir at 400 K to another large heat reservoir at 300 K. Suppose there is no change in temperature due to the exchange of heat :

Ans.