Question

Which is correct for parachor? (a) \(\frac{M}{D} \cdot \gamma^{1 i 8}\) (b) \(\frac{M}{D} \cdot \gamma^{1 / 2}\) (c) \(\frac{M}{D} \cdot \gamma^{1 / 6}\) (d) \(\frac{M}{D} \cdot \gamma^{1 / 4}\)

Short answer

The correct formula for parachor is option (d): \( \frac{M}{D} \cdot \gamma^{1 / 4} \).

Step-by-step solution

Understanding Parachor

Parachor is defined as the product of the molar volume and the surface tension to the power of 1/4. The formula for parachor (\(P\)) is \(P = M/D \cdot \gamma^{1/4}\), where \(\gamma\) is the surface tension, \(M\) is the molar mass, and \(D\) is the density.

Compare with the Given Options

Now, compare the correct formula for parachor with the options given in the question. The option that matches with the correct formula for parachor is option (d): \( \frac{M}{D} \cdot \gamma^{1 / 4} \).

Key concepts

Surface Tension

Surface tension is a fundamental concept in physics and physical chemistry that describes the elastic tendency of a fluid surface to acquire the least surface area possible. This property arises due to the cohesive forces between liquid molecules at the surface which are greater than those in the interior, as surface molecules lack neighboring molecules on one side. These forces create a 'film' that makes it more difficult to move an object on the surface or to penetrate the surface.

For liquids, surface tension allows them to resist external forces, and it is the reason why certain small insects can walk on water or how water droplets form perfect spheres. In real-life applications, surface tension is crucial in various industries, ranging from pharmaceuticals to manufacturing, involving processes like spraying, coating, and printing.

In the case of parachor, surface tension (\(\gamma\)) plays a critical role as it is raised to the power of 1/4 in the formula, linking it intrinsically to the parachor value. A deeper understanding of surface tension will also aid in comprehending how changes in temperature, purity, and other factors can affect a liquid's parachor.

Molar Volume

Molar volume is a concept used primarily in chemistry to describe the volume occupied by one mole of a substance at a given temperature and pressure. It is derived from the molar mass (\(M\)) of the substance and its density (\(D\)). The molar volume is inversely proportional to density, as can be deduced from the formula \(V_m = M/D\), where \(V_m\) is the molar volume.

Understanding the molar volume is imperative when discussing solutions and mixtures, where the concentration and proportion of components are critical. In relation to parachor, molar volume is integrated with surface tension within the formula. Given that parachor is defined as the product of the molar volume and the surface tension to the power of 1/4, as seen in the problem, we are reminded that both volumetric and interfacial properties are key to this concept.

Moreover, the molar volume aids scientists and engineers in designing and controlling processes such as distillation and crystallization, where specific volume changes are crucial for efficiency and product quality.

Physical Chemistry

Physical chemistry is a branch of chemistry that deals with the study of how matter behaves on an atomic and molecular level and how chemical reactions occur. It bridges the gap between physics and chemistry, merging the principles of both to understand the physical properties of molecules, the forces that act upon them, and the energy changes that accompany chemical processes.

Concepts such as energy, thermodynamics, kinetics, and quantum mechanics are all within the purview of physical chemistry. These concepts are not only essential for theoretical understanding but also have practical applications in areas such as materials science, biotechnology, and environmental science. For a concept like parachor, physical chemistry provides the theoretical foundation to comprehend why certain mathematical relationships, like the one involving surface tension and molar volume, exist and how they can be applied in practical scenarios.

Students studying this field gain a comprehensive view of chemical systems that is critical for innovation and problem-solving in industries such as pharmaceuticals, petrochemicals, and materials development. Fostering a strong grasp of physical chemistry is crucial for accurately calculating and predicting phenomena like parachor, which can be significant in characterizing chemical compounds and their interactions.