What is Parachor Definition Formula Derivation and Uses
The Greek words "para" which means "aside" and "chor" which means "space" are thought to have been combined to create the term parachor. S. Sugden suggested the parameter parachor, is related to surface tension, in 1924. Parachor definition can be given by the following equation,
$P\,=\,{{\gamma}^{1/4}}\frac{M}{({{\rho}_{L}}-{{\rho}_{V}})}\,=\,{{\gamma }^{1/4}}V$
Where,
$\gamma $ = surface tension
$M$ = molar mass
${{\rho }_{L}}$ = liquid density
${{\rho }_{V}}$ = vapour density in equilibrium with the liquid
Because of the volume multiplier in parachor, it may be extended from components to mixtures hence numerous structure-related problems can be solved with parachor. The conventional units of measurement for the parachor and its group contributions are ${{(erg/c{{m}^{2}})}^{1/4}}\,\times \,(c{{m}^{3}}/mol)$, which is equivalent to ${{(mJ/{{m}^{2}})}^{1/4}}\,\times \,(c{{m}^{3}}/mol)$.
History of Parachor
Sugden demonstrated in earlier articles that every chemical has a distinctive parachor value. Since Sugden's breakthrough, parachor has been employed to "correlate" the surface tension data of a number of different pure liquids and liquid mixtures.
A general molecular theory for parachor that is applicable to all temperature ranges was proposed by Boudh-Hir and Mansoori in 1990.
Escobedo and Mansoori (1996) developed an analytical solution for parachor as a function of temperature that is valid in all temperatures ranging from the melting point to the critical point using the molecular theory of Boudh-Hir and Mansoori.
Additionally, they predicted surface tensions of various liquids in all temperature ranges, from melting point to critical point, using the resultant analytic equation.
Applications of Parachor
The parachor, which is generally constant throughout a large range of temperatures, is defined as the molecular weight of the liquid multiplied by the fourth root of its surface tension divided by the difference between the densities of the liquid and the vapour in equilibrium with it.
It is a molecule's constitutive property that is additive and connected to both surface tension and molar volume. It is an empirical constant for a liquid that connects the surface tension to the molecular volume.
Under conditions where the liquids have similar surface tension, it can be used to estimate molecular volumes and identify incomplete compounds by adding values for the atoms of the ingredients and structural characteristics. Numerous compounds and their structures have been identified using the parachor value. P-benzoquinone, for which the two alternate structures listed below were proposed, is a notable example.
It should be noted that discrepancies in the parachor readings have been found in several instances, including those involving organometallic compounds. Since the development of spectroscopic techniques that produce better readings, the parachor is no longer widely utilized.
A physiologically active molecule's parachor is related to its capacity to penetrate hydrophobic cell structures, notably cellular membranes. From the atoms and bonds that make up a steroid, the parachor may be computed. Analyzing the parachor values of several steroids reveals that these values are linked to a variety of biological processes from various separate sources that are distinct from one another. Numerous analytical techniques have shown that the parachors of steroids directly correlate with their respective anti-inflammatory potencies.
The surface tension of pure ionic liquids based on imidazolium is calculated using the parachor technique at various temperatures. A corresponding-states group-contribution approach is suggested to estimate the surface tension of ionic liquids for this prediction, covering a wide range of temperature and chain length.
Important Questions
Mention the application of parachor value.
Ans: Parachor value can be used to estimate molecular volumes and to identify incomplete compounds by adding values for the atoms of the ingredients and structural characteristics
How is parachor value related to surface tension and density of a liquid?
Ans: Parachor is directly proportional to the fourth root of a liquid’s surface tension and inversely proportional to the liquid’s density.
Summary
Parachor, also known as molar parachor or molecular parachor, is an empirical constant for a liquid that relates the surface tension to the molecular volume. It can be used to compare molecular volumes when the liquids have the same surface tension and to determine the partial structure of compounds by adding values for constituent atoms and structural features. This is the parachor definition in chemistry
Practice Questions
Which of the properties is parachor related to?
Surface tension
Molar volume
Both a and b
None of the above
Who developed an analytical solution for parachor as a function of temperature that is valid in all temperatures ranging from the melting point to the critical point?
Escobedo and Mansoori
S. Sugden
Boudh-Hir and Mansoori
None of the above
Answers
(c)
(a)
FAQs on Parachor in Surface Chemistry and Molecular Structure
1. What is parachor in chemistry?
The parachor is a physical constant that relates the surface tension of a liquid to its molar volume and is used to study molecular structure and constitution. It is defined by the relation:
P = (M/ρ) γ1/4
Where:
- P = parachor
- M = molar mass
- ρ = density of the liquid
- γ = surface tension
2. What is the formula for parachor?
The formula for parachor is P = (M/ρ) γ1/4, where M is molar mass, ρ is density, and γ is surface tension.
In expanded form:
- M is expressed in g mol-1
- ρ in g cm-3
- γ in dyne cm-1 (or N m-1 in SI)
3. Why is parachor considered both additive and constitutive?
Parachor is considered additive because it equals the sum of atomic parachors, and constitutive because it depends on structural features like double bonds and rings.
- Additive property: Total parachor = sum of atomic parachors of all atoms in a molecule.
- Constitutive property: Structural elements such as double bonds, triple bonds, and rings contribute additional parachor values.
4. How do you calculate parachor of a compound?
The parachor of a compound is calculated using P = (M/ρ) γ1/4 or by summing atomic and structural parachors.
Method 1: Experimental calculation
- Measure density (ρ) of the liquid.
- Measure surface tension (γ).
- Substitute values along with molar mass (M) into the formula.
- Add atomic parachors of all atoms.
- Add structural increments for double bonds or rings.
5. What are the units of parachor?
Parachor has units derived from molar volume and surface tension and is commonly expressed in cm3 (dyne)1/4 cm-1/4 mol-1.
From the formula P = (M/ρ) γ1/4:
- M/ρ gives molar volume (cm3 mol-1).
- γ1/4 contributes (dyne cm-1)1/4.
6. How is parachor related to surface tension?
Parachor is directly related to surface tension through the equation P = (M/ρ) γ1/4, meaning it varies with the fourth root of surface tension.
This implies:
- If surface tension (γ) increases, parachor increases proportionally to γ1/4.
- The relationship connects intermolecular forces (via γ) to molecular size and structure.
7. What is the significance of parachor in chemistry?
The significance of parachor lies in its use for determining molecular structure, identifying double bonds, and distinguishing isomers.
Applications include:
- Estimating structural features like rings and multiple bonds.
- Confirming molecular formulas.
- Studying intermolecular forces and surface properties.
8. How does parachor help in detecting double bonds?
Parachor helps detect double bonds because each double bond contributes an additional structural parachor value beyond atomic contributions.
- First calculate theoretical parachor from atomic values only.
- Compare with experimentally determined parachor.
- An excess value indicates the presence of double bonds or ring structures.
9. What is the difference between parachor and molar volume?
The key difference is that molar volume depends only on density and molar mass, while parachor also includes surface tension.
- Molar volume (Vm) = M/ρ
- Parachor (P) = (M/ρ) γ1/4
10. Can you give an example of parachor calculation?
Yes, parachor can be calculated using P = (M/ρ) γ1/4 by substituting experimental values.
Example: Suppose a liquid has:
- M = 46 g mol-1
- ρ = 0.80 g cm-3
- γ = 22 dyne cm-1
Step 2: Calculate γ1/4 = (22)1/4.
Step 3: Multiply values to obtain parachor.
This demonstrates how density and surface tension data are used to determine parachor experimentally.
