UPSC Exam  >  UPSC Notes  >  Chemistry Optional Notes for UPSC  >  Graham’s Law of Effusion & Intermolecular Collisions

Graham’s Law of Effusion & Intermolecular Collisions | Chemistry Optional Notes for UPSC PDF Download

Introduction

  • An important consequence of the kinetic molecular theory is what it predicts in terms of effusion and diffusion effects. Effusion is defined as a loss of material across a boundary. A common example of effusion is the loss of gas inside of a balloon over time.
  • Graham’s Law of Effusion & Intermolecular Collisions | Chemistry Optional Notes for UPSCThe rate at which gases will effuse from a balloon is affected by a number of factors. But one of the most important is the frequency with which molecules collide with the interior surface of the balloon. Since this is a function of the average molecular speed, it has an inverse dependence on the square root of the molecular weight.
    Rate of effusion ∝ = 1/√MW
    This can be used to compare the relative rates of effusion for gases of different molar masses.

Question for Graham’s Law of Effusion & Intermolecular Collisions
Try yourself:
Which of the following factors has the most significant effect on the rate of effusion from a balloon?
View Solution

The Knudsen Cell Experiment

  • A Knudsen cell is a chamber in which a thermalized sample of gas is kept, but allowed to effuse through a small orifice in the wall. The gas sample can be modeled using the Kinetic Molecular Theory model as a collection of particles traveling throughout the cell, colliding with one another and also with the wall. If a small orifice is present, any molecules that would collide with that portion of the wall will be lost through the orifice.

Graham’s Law of Effusion & Intermolecular Collisions | Chemistry Optional Notes for UPSC

Figure 2.5.1: Effusion of gas particles through an orifice. (CC BY-SA 3.0; Astrang13).

This makes a convenient arrangement to measure the vapor pressure of the material inside the cell, as the total mass lost by effusion through the orifice will be proportional to the vapor pressure of the substance. The vapor pressure can be related to the mass lost by the expression
Graham’s Law of Effusion & Intermolecular Collisions | Chemistry Optional Notes for UPSC
where g is the mass lost, A is the area of the orifice,  Δt is the time the effusion is allowed to proceed, T is the temperature and  MW  is the molar mass of the compound in the vapor phase. The pressure is then given by  p. A schematic of what a Knudsen cell might look like is given below.

Graham’s Law of Effusion & Intermolecular Collisions | Chemistry Optional Notes for UPSC

Intermolecular Collisions

  • A major concern in the design of many experiments is collisions of gas molecules with other molecules in the gas phase. For example, molecular beam experiments are often dependent on a lack of molecular collisions in the beam that could degrade the nature of the molecules in the beam through chemical reactions or simply being knocked out of the beam.
  • In order to predict the frequency of molecular collisions, it is useful to first define the conditions under which collisions will occur. For convenience, consider all of the molecules to be spherical and in fixed in position except for one which is allowed to move through a “sea” of other molecules. A molecular collision will occur every time the center of the moving molecule comes within one molecular diameter of the center of another molecule.

Graham’s Law of Effusion & Intermolecular Collisions | Chemistry Optional Notes for UPSCOne can easily determine the number of molecules the moving molecule will “hit” by determining the number of molecules that lie within the “collision cylinder”. Because we fixed the positions of all but one of the molecules, we must use the relative speed of the moving molecule, which will be given by
vrel = √2 – v
The volume of the collision cylinder is given by
Vcol = √2 – v Δt A
The collisional cross section, which determined by the size of the molecule is given by
σ = πd2
Some values of σ are given in the table below:

Table 2.6.1: Collisional cross-section of Select Species
Graham’s Law of Effusion & Intermolecular Collisions | Chemistry Optional Notes for UPSC

Since the number of molecules within the collision cylinder is given by
Graham’s Law of Effusion & Intermolecular Collisions | Chemistry Optional Notes for UPSC
and since the number density ( N/V) is given by
Graham’s Law of Effusion & Intermolecular Collisions | Chemistry Optional Notes for UPSC
the number of collisions is given by
Graham’s Law of Effusion & Intermolecular Collisions | Chemistry Optional Notes for UPSC
The frequency of collisions (number of collisions per unit time) is then given by
Graham’s Law of Effusion & Intermolecular Collisions | Chemistry Optional Notes for UPSC
Perhaps a more useful value is the mean free path (λ), which is the distance a molecule can travel on average before it collides with another molecule. This is easily derived from the collision frequency. How far something can travel between collisions is given by the ratio of how fast it is traveling and how often it hits other molecules:
λ = ⟨v⟩/Z
Thus, the mean free path is given by
Graham’s Law of Effusion & Intermolecular Collisions | Chemistry Optional Notes for UPSC
The mere fact that molecules undergo collisions represents a deviation from the kinetic molecular theory. For example, if molecules were infinitesimally small (σ≈) then the mean free path would be infinitely long! The finite size of molecules represents one significant deviation from ideality. Another important deviation stems from the fact that molecules do exhibit attractive and repulsive forces between one another. These forces depend on a number of parameters, such as the distance between molecules and the temperature (or average kinetic energy of the molecules.)

Question for Graham’s Law of Effusion & Intermolecular Collisions
Try yourself:
What is the purpose of a Knudsen cell experiment?
View Solution

The document Graham’s Law of Effusion & Intermolecular Collisions | Chemistry Optional Notes for UPSC is a part of the UPSC Course Chemistry Optional Notes for UPSC.
All you need of UPSC at this link: UPSC
308 docs

Top Courses for UPSC

FAQs on Graham’s Law of Effusion & Intermolecular Collisions - Chemistry Optional Notes for UPSC

1. What is Graham's Law of Effusion?
Ans. Graham's Law of Effusion states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. In other words, lighter gases will effuse or escape through a small opening faster than heavier gases.
2. How are intermolecular collisions related to Graham's Law of Effusion?
Ans. Intermolecular collisions play a crucial role in Graham's Law of Effusion. The rate of effusion is determined by the frequency of collisions between gas molecules and the size of the opening through which they are escaping. The more frequent the collisions, the higher the rate of effusion. Therefore, intermolecular collisions directly affect the effusion rate.
3. How can Graham's Law of Effusion be applied practically?
Ans. Graham's Law of Effusion has several practical applications. One important application is in gas separation techniques, such as in the production of enriched oxygen for medical purposes. By utilizing the different effusion rates of gases, it is possible to separate them based on their molar masses. Additionally, this law is used in the study of diffusion and the calculation of diffusion rates in various gases.
4. What factors influence the rate of effusion according to Graham's Law?
Ans. According to Graham's Law of Effusion, the rate of effusion is influenced by two main factors: the molar mass of the gas and the size of the opening through which the gas is escaping. Lighter gases with lower molar masses will effuse faster, while smaller openings will restrict the effusion rate.
5. Can Graham's Law of Effusion be applied to all gases?
Ans. Graham's Law of Effusion is applicable to ideal gases under certain conditions. It assumes that the gases behave ideally, meaning they have no intermolecular forces and occupy negligible volumes. Real gases may deviate from this behavior due to factors such as high pressure or low temperature. Therefore, while Graham's Law is a useful approximation, it may not hold true for all gases in all situations.
Explore Courses for UPSC exam

Top Courses for UPSC

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

MCQs

,

Important questions

,

Exam

,

Summary

,

video lectures

,

Extra Questions

,

Free

,

Previous Year Questions with Solutions

,

shortcuts and tricks

,

past year papers

,

Semester Notes

,

practice quizzes

,

pdf

,

Viva Questions

,

study material

,

Graham’s Law of Effusion & Intermolecular Collisions | Chemistry Optional Notes for UPSC

,

Objective type Questions

,

Graham’s Law of Effusion & Intermolecular Collisions | Chemistry Optional Notes for UPSC

,

mock tests for examination

,

Graham’s Law of Effusion & Intermolecular Collisions | Chemistry Optional Notes for UPSC

,

ppt

,

Sample Paper

;