In a glass tube of uniform cross section, a mixture of \(\mathrm{HCl}\) and \(\mathrm{He}\) gases are sent from one end and a mixture of \(\mathrm{NH}_{3}\) and Ar gases are sent from the another end, at the same time. The white fumes of \(\mathrm{NH}_{4} \mathrm{Cl}\) will appear first (a) at the middle of the tube (b) closer to \(\mathrm{NH}_{3}\) end (c) closer to \(\mathrm{HCl}\) end (d) at the \(\mathrm{NH}_{3}\) end

When it comes to predicting how gases will behave under certain conditions, Graham's Law of Diffusion is a crucial concept in physical chemistry that is commonly assessed in competitive exams. This law states that the rate at which a gas will diffuse or effuse is inversely proportional to the square root of its molar mass. In simpler terms, lighter gases will diffuse more rapidly than heavier ones.

This relationship can be mathematically expressed as: \[ \frac{Rate_1}{Rate_2} = \sqrt{\frac{Molar\, Mass_2}{Molar\, Mass_1}} \] where \( Rate_1 \) and \( Rate_2 \) are the diffusion rates of two different gases, and the molar masses are that of the respective gases. When you see a problem involving the diffusion of gases, such as the one involving \( \mathrm{HCl} \), \( \mathrm{NH}_{3} \), \( \mathrm{He} \), and Ar, think of Graham's law to help you solve it.

In our exercise, the white fumes of \( \mathrm{NH}_{4} \mathrm{Cl} \) appearing indicate where the gases meet. Understanding Graham's law helped us predict that \( \mathrm{NH}_{3} \) and \( \mathrm{He} \), being lighter, diffuse faster, leading to the observed reaction closer to the \( \mathrm{HCl} \) end of the tube.

Going beyond diffusion, the chemical reaction rate is another fundamental aspect to consider in physical chemistry, particularly important if you're preparing for competitive exams. This rate is the speed at which reactants are converting into products in a chemical reaction. It depends on several factors like concentration of reactants, temperature, and the presence of catalysts or inhibitors.

A practical understanding of reaction rates is crucial when predicting outcomes of reactions, as seen in the glass tube experiment with \( \mathrm{NH}_{4} \mathrm{Cl} \). While Graham's law predicts where gases will meet, the actual formation of fumes is a matter of how fast the reaction occurs. Rapid diffusion leads to a quick reaction, while slower diffusion can result in a slower reaction and a delayed appearance of fumes.

In our exercise, the reaction rate is intertwined with diffusion rates—a faster diffusion of \( \mathrm{NH}_{3} \) not only ensured it met \( \mathrm{HCl} \) closer to the latter's end but also that the reaction occurred promptly to form the white fumes of \( \mathrm{NH}_{4} \mathrm{Cl} \) at that location.

Understanding molar mass is another essential piece in the puzzle of physical chemistry problems and is frequently tested in competitive exams. The molar mass is the mass of one mole of a substance, typically measured in grams per mole (g/mol). It's a collective measure of the atomic masses of the atoms that make up a molecule and plays a pivotal role in various aspects of chemistry, including stoichiometry, gas laws, and reaction rates.

Calculating the molar masses of the involved gases is the initial step in solving our exercise. It guides us to predict the diffusion rates according to Graham's Law, as seen with \( \mathrm{HCl} \), \( \mathrm{NH}_{3} \), \( \mathrm{He} \), and Ar. The concept of molar mass also translates into practical situations like determining the amount of a chemical needed for a reaction or understanding the properties of gases.

For students, grasping molar mass is fundamental because it lays the groundwork for not only solving problems related to diffusion but also for a wide range of other chemical calculations. Remembering that molar mass can be directly linked to molecular weight allows you to quickly correlate the two when working through your chemistry problems.