# Spontaneity

SPONTANEITY

Spontaneity is a concept in thermodynamics that refers to the tendency of a process to occur without any external influence. Here are 10 key points to help explain spontaneity:

1. Spontaneous processes are those that occur naturally, without any external input of energy or work.
2. Spontaneity is related to the second law of thermodynamics, which states that the entropy of a closed system always increases over time.
3. Entropy is a measure of the degree of disorder or randomness in a system, and spontaneous processes tend to increase the entropy of the system.
4. Examples of spontaneous processes include the dissolving of salt in water, the melting of ice, and the expansion of a gas into a vacuum.
5. However, not all processes that occur on their own are necessarily spontaneous in the thermodynamic sense. For example, a ball rolling downhill may seem spontaneous, but it is actually due to the influence of gravity, which is an external force.
6. The spontaneity of a process can be determined by calculating the change in free energy, ΔG, which is related to the enthalpy change, ΔH, and the entropy change, ΔS, through the equation ΔG = ΔH - TΔS, where T is the temperature.
7. If ΔG is negative, the process is spontaneous, while if ΔG is positive, the process is non-spontaneous. If ΔG is zero, the system is in equilibrium.
8. The spontaneity of a reaction depends on factors such as temperature, pressure, and concentration.
9. For example, the reaction between hydrogen and oxygen to form water is spontaneous under standard conditions (25°C and 1 atm pressure), but it becomes non-spontaneous at higher temperatures or lower pressures.
10. The concept of spontaneity is important in understanding many natural processes, such as the formation of stars and planets, the evolution of life on Earth, and the behavior of complex systems such as ecosystems and economies.

Enthalpy and spontaneity

Chemical reactions involve a change in energy from reactants to products, and this change in energy can be either exothermic or endothermic. Exothermic reactions release heat, whereas endothermic reactions absorb heat. It is often assumed that exothermic reactions are spontaneous because they involve a decrease in energy, which seems reasonable based on evidence from phenomena like the flow of water down a hill or the fall of a stone on the ground.

For example, the reactions N2(g) + H2(g) → NH3(g), H2(g) + Cl2(g) → HCl(g), and H2(g) + O2(g) → H2O(l) all release heat and have a negative standard enthalpy of reaction (∆rH), indicating a decrease in enthalpy from reactants to products. This decrease in enthalpy can be shown on an enthalpy diagram as a downward slope from reactants to products, as shown in Fig..

However, there are also reactions like N2(g) + O2(g) → NO2(g) and C(graphite, s) + 2 S(l) → CS2(l) that absorb heat and have a positive ∆rH, indicating an increase in enthalpy from reactants to products. These reactions are still spontaneous, despite their positive ∆rH values. The increase in enthalpy can be shown on an enthalpy diagram as an upward slope from reactants to products, as shown in Fig.

Entropy and Spontaneity

• In an isolated system, there is always a tendency for the system's energy to become more disordered or chaotic, which could be a criterion for spontaneous change.
• The manifestation of disorder is called entropy, which is a measure of the degree of randomness or disorder in the system.
• The greater the disorder in an isolated system, the higher is the entropy.
• The change in entropy accompanying a chemical reaction may be estimated qualitatively by a consideration of the structures of the species taking part in the reaction.
• For a given substance, the crystalline solid state is the state of lowest entropy, while the gaseous state is the state of highest entropy.
• Entropy is a state function and ΔS is independent of path.
• ΔS is related to q and T for a reversible reaction.
• The total entropy change (ΔStotal) for the system and surroundings of a spontaneous process is given by ΔStotal = ΔSsys + ΔSsurr> 0.
• When a system is in equilibrium, the entropy is maximum, and the change in entropy, ΔS = 0.
• ΔU does not discriminate between reversible and irreversible processes, whereas ΔS does.

Gibbs free energy change

• Gibbs free energy change (∆G) is a measure of the energy available to do work in a chemical reaction.
• The Gibbs free energy change is related to the change in enthalpy (∆H) and the change in entropy (∆S) of the system, as well as the temperature (T) at which the reaction takes place.
• The equation for Gibbs free energy change is: ∆G = ∆H - T∆S
• A negative value of ∆G indicates that the reaction is spontaneous and can occur without the input of energy, while a positive value of ∆G indicates that the reaction is non-spontaneous and requires energy to occur.
• At constant temperature and pressure, the change in Gibbs free energy (∆G) is related to the maximum non-expansion work (∆Gmax) that can be obtained from the reaction: ∆Gmax = -∆G.
• The equilibrium constant for a chemical reaction can be related to the Gibbs free energy change using the equation: ∆G° = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin. The symbol ∆G° represents the standard Gibbs free energy change for the reaction.

Gibbs Energy and Spontaneity

The change in Gibbs free energy (∆G) of a system at constant temperature and pressure is a measure of the maximum amount of work that can be obtained from the system. A negative ∆G indicates that the process is spontaneous, and the system can perform work on the surroundings. On the other hand, a positive ∆G indicates that the process is non-spontaneous, and work must be done on the system to drive the reaction in the forward direction.

The relation between ∆G and spontaneity can be summarized as follows:

• If ∆G is negative, the process is spontaneous, and the reaction can occur spontaneously without the need for an external driving force. The reaction is exergonic, meaning it releases energy, and the products are more stable than the reactants.
• If ∆G is positive, the process is non-spontaneous, and the reaction cannot occur spontaneously. The reaction is endergonic, meaning it requires an input of energy to proceed, and the products are less stable than the reactants.
• If ∆G is zero, the process is at equilibrium, and the reaction neither proceeds in the forward nor the reverse direction. The reaction is at a state of minimum free energy, and the system is in a state of maximum stability.

Thus, Gibbs free energy is a thermodynamic function that provides a criterion for the spontaneity of a process. The spontaneity of a reaction is determined by the free energy change of the system (∆G) and the conditions under which the reaction takes place.

Second Law of thermodynamics

The Second Law of Thermodynamics states that in any spontaneous process, the total entropy of the system and its surroundings always increases, and the total energy available to do useful work decreases. In other words, the entropy of an isolated system can never decrease over time. This law can be expressed in several different ways, such as:

1. The entropy of a closed system tends to increase over time.
2. Heat flows spontaneously from hot objects to cold objects, never the other way around.
3. Any cyclic process involving heat engines and heat reservoirs cannot be 100% efficient.
4. It is impossible to construct a machine that operates in a cycle and produces no effect other than the transfer of heat from a lower-temperature body to a higher-temperature body.

The Second Law is a fundamental principle of thermodynamics and has many important implications for energy and entropy in physical and chemical systems. It helps to explain why certain reactions occur spontaneously while others do not, and why some forms of energy are more useful than others. It also places limits on the efficiency of energy conversion processes, and provides a basis for understanding the behavior of systems at low temperatures.

Third Law of thermodynamics

The Third Law of Thermodynamics states that as the temperature of a pure, perfect crystalline solid approaches absolute zero (0 Kelvin), the entropy of the crystal approaches a minimum value specific to that crystal. This minimum value of entropy is zero at 0 Kelvin. The third law of thermodynamics helps in the calculation of the absolute entropy values of substances at any given temperature. It provides an absolute reference point for the determination of the entropy changes accompanying chemical and physical processes. However, achieving a temperature of absolute zero is impossible, so the third law is more of a theoretical concept than something that can be practically demonstrated.