Thermodynamics and kinetics of a molecule's birth

A molecule's birth: How does a molecule decide whether to be solid, liquid, or gas?

A + B [ reactants] = C [product]

For a product to be born, there must be at least two atoms. Whether C is formed in nature or in a laboratory, it requires a certain amount of energy at a specific temperature and pressure in order for A and B to react and form a new molecule C. This is one part of the story.

The next step is to determine whether C will be solid, liquid, or gas when it is born. A and B have no say over whether C should be solid, liquid, or gas. The environment, including temperature and pressure, as well as the structure or shape of C, determine which state of matter C will be delivered in.

The fundamentals are introduced here. Until now, the kinetics of the reaction had played the most important role. Thermodynamics now takes over.

Every molecule is stable when it has the lowest free energy and highest entropy, dG = dH - TdS.?C would be born in the given temperature and pressure conditions as a solid, liquid, or gas with the lowest Gibbs free energy. ?A + B will not react until product C has less free energy than its parents, A and B. ?Simply adding A and B will not result in C; the reaction will be the opposite. It is technically referred to as an endothermic reaction.

Briefly, let us look at the energy of four states of the matter

The energy of different states of matter

Solids

The bonds between individual molecules are much stronger (and require more energy to break) in solids than in liquids. As a result, the molecules form a relatively rigid structure in which molecules "stay in place."

Liquids

The bonds between individual molecules in a liquid are strong enough to maintain a surface. They are weak enough that random heat effects continuously break and reform the bonds, allowing the molecules to move freely rather than being held in place by the rigid structure of a solid. They don't have a macroscopic shape, but their volume is fairly constant. This is true in both directions: they do not expand like gases and barely compress.

Gas

The bonds between individual molecules are no longer strong enough to give the gas structure. Because individual molecules barely interact with one another, gases easily expand and compress. When you compress a gas enough, it becomes a liquid (and then a solid) - you're basically forcing the individual molecules to get close enough to each other and reinforcing the intramolecular forces with external pressure.

Plasma

The heat is so intense that it not only breaks down molecules but also breaks them apart and strips electrons from individual atoms. Overall, plasma behaves similarly to a gas, with a few additional intriguing properties.

Solids are the least mobile phase of a substance and therefore, they have the minimum energy and the most stable state of a matter. The most important concept is a substance has its maximum stability when it is at the ground state of energy level at ambient pressure.

If you look at tabulated standard thermodynamic data at 25° C, H2O(l) has a Gibbs free energy of?237.13kJ?mol?1. While for melting of ice:?H2O(s) → H2O(I)??ΔH? = +6.03 kJ mol–1???ΔS?= +22.1 J K–1 mol–1, = 6.03 – 273.15x22.1 = 0.00 kj/mol

This is hugely lower free energy than water and as you can see there is no free energy. Of ice at 0 degc.

?What does it mean? Given an option, water [liquid] will transit to ice

The next important point is the phase transition

The journey of a molecule from one state to another is very interesting.

In one line, the phase transition is the breaking and formation of intermolecular bonds in a substance. It is a kind of competition between minimizing energy and maximizing entropy.

A phase transition is the transition of a thermodynamic system from one phase to another. A phase is a macroscopic system with uniform composition and physical properties.

A 'matter' is more than the sum of its constituent parts.

Atoms have a strong interaction with one another and the ability to form different phases of matter. In short, a phase of matter is a collection of interacting constituents with macroscopic properties that cannot be obtained through constituent study. So, how do they choose a specific phase to form when there is a large collection of constituents? Understanding this will necessitate an understanding of the competition in a large system between energy and entropy, between order and disorder.

How does Phase Transition work?

There are two variables to consider when looking at the phase transition, pressure (P) and temperature (T). For the gas state, the relationship between temperature and pressure is defined by the equations below:

Ideal Gas Law:

PV=nRT

van der Waals Equation of State:

(P+ a?n^2V^2)(V?nb) =nRT

Where V is volume, R is the gas constant, and n is the number of moles of gas.

The ideal gas law assumes that no intermolecular forces are affecting the gas in any way, while the van der Waals equation includes two constants, a and b, that account for any intermolecular forces acting on the molecules of the gas.

Temperature

Temperature can change the phase of a substance. One common example is putting water in a freezer to change it into ice.

Pressure

Pressure can also be used to change the phase of the substance. Imagine, a container fitted with a piston that seals in a gas. As the piston compresses the gas, the pressure increases. Once the boiling point has been reached, the gas will condense into a liquid. As the piston continues to compress the liquid, the pressure will increase until the melting point has been reached. The liquid will then freeze into a solid. This example is for an isothermal process where the temperature is constant and only the pressure is changing.

A phase transition occurs when the two phases have the same free energy

The conditions under which phase transitions occur essentially depend on the system being considered, and the thermodynamic free energy of the system. A phase transits to another when [1] the two phases have the same free energy, dG =0. This means the two phases are in thermodynamic equilibrium. This further means that the phase is at its maximum entropy and it is looking for more space where it can dump its entropy like water to vapor transition.

Example:

Water to vapor phase transition

If this process is carried out at 1 atm and the normal boiling point of 100 degc (373.15 K), we can calculate ΔG from the experimentally measured value of ΔHvap (40.657 kJ/mol). For vaporizing 1 mol of water, ΔH=40,657; J , so the process is highly endothermic. From the definition of ΔS, we know that for 1 mol of water,

ΔSvap = ΔHvap / Tb= 40,657J/ 373.15 K=108.96 J/K

Hence there is an increase in the disorder of the system. At the normal boiling point of water,

ΔG100 degc =ΔH100 degc ?TΔS100 degc =40,657 J?[(373.15 K)(108.96 J/K)] =0 J

Therefore, at the phase transition point at 100 degc, ΔG =0

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Credit: Google