Graham’s Law of Diffusion
To understand Graham's law of diffusion, we must first understand the definition of diffusion and rate of diffusion. Though diffusion and Effusion are interchangeably used many times, they have a completely different meaning. The process through which the particles from one gas move to another gas is diffusion. It causes significant disorder in the entire system. We can also observe diffusion at slower rates in liquids as well as solids. The leading cause of this phenomenon is the concentration levels. When the particles of a material are in an area of low concentration, they tend to move to the content with a high area of concentration. A straightforward example of this process is when we use perfume or a scented spray in one part of the room, and then we can smell it in the entire room. Diffusion is involved in this whole scenario.
The change in diffusing molecules over time is called the rate of diffusion. The diffusion rate of a gas is inverse to the square root of the volume (density). Hence, the rate of diffusion formula is:
rate of diffusion \[\alpha \frac{1}{\sqrt{density}}\]
We can also rewrite this equation in terms of molar mass since gases with different volumes have the same number of particles.
rate of diffusion\[\alpha \frac{1}{\sqrt{M}}\]
Here the molar mass of the gas is denoted by M.
Rate of Effusion
When the gaseous particles move from a tiny opening into the vacuum of space or open container, then the process is called Effusion. This space can be a vacuum, any other gas or atmosphere. In this process, the molecules of material try to escape from a closed container through the aperture. The best example of you can observe Effusion in balloons. When we make an opening in the balloon, the gas inside starts escaping into the atmosphere, and it deflates. We can call this Effusion of gas into the atmosphere.
The process by which particles of material from closed space escapes with time is known as the rate of Effusion. Now let us discuss the rate of effusion formula. Since the Effusion is inversely proportional to density and the molar mass of the gas (M), we can write the equation as follows:
Rate of effusion \[\alpha \frac{1}{\sqrt{density}}\alpha \frac{1}{\sqrt{M}}\]
Graham’s Law
Graham's law of diffusion was one of the breakthroughs in the field of chemistry. Thomas Graham discovered this law in 1848, and it is also known as the graham's law of Diffusion. His experimentation with the rate of effusion process unveiled that gas with heavier molecules travels slower than gas with lighter particles. Graham's law of Effusion or diffusion states that when the temperature and pressure are constant than atoms with high molar mass effuse slower than atoms with low molar mass. He also gave the rate at which molecules would escape, i.e. the rate of diffusion.
Moreover, it states that the square root of the molar mass is inversely proportional to the rate of Effusion. This statement gives us the Grahams law of diffusion formula. We can use it to compare two gasses with their rates at constant temperature and pressure. Let us assume r1 and r2 are the rates of Effusion of two gases, and M1 and M2 are the molar masses respectively. Hence, we can write the formula as follows.
r1/r2 = M2/M1
or
\[\frac{r_{1}}{r_{2}}=\sqrt{\frac{M_{2}}{M_{1}}}\]
Solved Examples
Example 1: Calculate the molar mass of a given gas whose diffusion rate is 2.92 times the diffusion rate of NH₃.
Answer:
We know that the diffusion rate is 2.92 times of ammonia; hence we understand that the ratio of diffusion rates of the given gases should be 1/2.92. So,
r1/r2 = 1/2.92
Since we know that the molar mass of ammonia is 17.0307.
We can use Graham’s law. Accordingly,
\[\frac{r_{1}}{r_{2}}=\sqrt{\frac{M_{2}}{M_{1}}}\]
Substituting the values
\[\frac{1}{2.92}=\sqrt{\frac{M_{2}}{17.0307}}\]
Squaring both sides we have,
0.11728 = M2/17.0307
Hence,
M2 = 2.0 g/mol
M2 is the molar mass of the given gas.
Example 2: find the relative diffusion rate of water (molar mass=18.0152) as compared to hard water (molar mass=20.0276).
Answer:
We know that,
The molar mass of water(M1)=18.0152
The molar mass of hard water(M2)=20.0276
Let us assume the rate of diffusion formula of heavy water as one since it has a slower diffusion rate.
r2=1
According to graham’s law
\[\frac{r_{1}}{r_{2}}=\sqrt{\frac{M_{2}}{M_{1}}}\]
Squaring both sides
r1²/r2² = M2/M1
Substituting the values in the above equation
r1²/1 = 20.0276/18.0152
r1² = 1.111705
r1 = 1.05
Hence the relative diffusion rate is 1.05.
FAQs on Grahams Law
1. Why is Thomas Graham famous ?
Thomas Graham (1805-1869) is known as the author of colloidal chemistry and for his abecedarian exploration on the nature of phosphoric acid and phosphates, prolixity of feasts, liquids, and results, adsorption of feasts by essence, dialysis, osmosis, mass transfer through membranes, and the constitution of matter.
In 1829, he was appointed speaker in the Handyperson’s Institute, succeeding Thomas Clark (1801-1867) who had been appointed to the chemistry president at Marischal College (Aberdeen’s alternate university). At the same time Graham submitted to the university’s medical faculty an essay on gassy prolixity (Graham, 1829). Johann Wolfgang Döbereiner (1780-1849) had observed this miracle before, while studying the escape of feasts through cracks in an essence wall (Döbereiner, 1823), but Graham’s study was the first methodical approach to the subject. The significance of this work was similar in that it gained him an appointment as professor of chemistry at Anderson’s College ( latterly the Royal College of Science and Technology), succeeding Alexander Ure (1810-1866), who had moved to London to exercise drug and education at the North London Medical School. This creation was sufficient for his father to yield and for conciliation between them. At Anderson, Graham tutored theoretical and applied chemistry to medical scholars as needed by the Royal College of Surgeons of Edinburgh and as recommended by the Medical Boards (Russell, 2005).
2. What is the history of Graham ?
Graham's exploration on the prolixity of feasts was started by his reading about the observation of German druggist Johann Döbereiner that hydrogen gas diffused out of a small crack in a glass bottle briskly than the girding air diffused in to replace it. Graham measured the rate of prolixity of feasts through cataplasm entrapments, through veritably fine tubes, and through small perforations. In this way he broke down the process so that it could be studied quantitatively. He first stated in 1831 that the rate of effusion of a gas is equally commensurable to the square root of its viscosity, and latterly in 1848 showed that this rate is equally commensurable to the square root of the molar mass. Graham went on to study the prolixity of substances in result and in the process made the discovery that some apparent results actually are dormancies of patches too large to pass through a diploma sludge. He nominated these accouterments colloids, a term that has come to denote an important class of finely divided accouterments.
Around the time Graham did his work, the conception of molecular weight was being established largely through the measures of feasts. Daniel Bernoulli suggested in 1738 in his book Hydrodynamica that toast increases in proportion to the haste, and therefore kinetic energy, of gas patches. Italian physicist Amedeo Avogadro also suggested in 1811 that equal volumes of different feasts contain equal figures of motes. Therefore, the relative molecular weights of two feasts are equal to the rate of weights of equal volumes of the feasts. Avogadro's sapience together with other studies of gas geste handed a base for latterly theoretical work by Scottish physicist James Clerk Maxwell to explain the parcels of feasts as collections of small patches moving through largely empty space.
3. State some examples of Graham’s Law ?
Graham’s law of effusion or prolixity is generally used to calculate the effusion or prolixity rate of a particular gas. It also helps to compare the effusion or prolixity rates of two different feasts. Thereby, helping the scientists to estimate the time needed by a particular gas to escape the vessel or girding in which it's present. This estimation of effusion or prolixity rate is necessary to form the safety measures in case of a gas leak.
One can fluently observe the operation of Graham’s law in real life by lighting an incense stick and observing the geste of the bank motes generated by it. This is because the bank coming out of the burning incense stick spreads in the surroundings snappily with the help of the prolixity process.
4. How does Graham's Law help in construction of chimneys ?
The engineers and masterminds make use of Graham’s law to estimate the proper height of the artificial and domestic chimneys. The bank and poisonous feasts must be released into the upper atmosphere to avoid health hazards and accidents. With the help of Graham’s law, the prolixity and effusion rate of the feasts can be estimated in advance. This helps to determine the applicable height of the chimneys needed to insure the escape of bank and poisonous gas patches down from the ménage and mortal contact.
5. What is Uranium Enrichment ?
Another practical operation of Graham's law is uranium enrichment. Natural uranium consists of an admixture of isotopes with slightly different millions. In gassy effusion, uranium ore is first made into uranium hexafluoride gas, also constantly enthused through a previous substance. Through each effusion, the material passing through the pores becomes more concentrated inU-235 (the isotope used to induce nuclear energy) because this isotope diffuses at a faster rate than the heavierU-238.
6. Are there any Applications of Graham's Law in Real Life?
As we know, today, Graham's law has several uses in daily life. The main application of graham's law is in the separation process. We can separate multiple gases with varying density using this law. Using the formula of Graham's law, we can compare the rates of diffusion and calculator molar masses of an unknown gas using given gas. Furthermore, we can even separate the isotopes of a given gas utilising this law. The typical example of this process is the isotopes of uranium. We mainly use the heavy and light isotopes of uranium that we get from the natural uranium found on the planet.
7. What are the Limitations of Graham's Law?
Graham's law has a significant limitation that everyone should be aware of today. This law holds for Effusion, but in case of diffusion, we only take it as an approximation in the rate of diffusion formula. When the temperature rises the rate increases as well. And when density nses then the rate decreases. So if the material is lighter, then it will have faster rates of diffusion. The main reason behind this phenomenon is that the velocity of atoms or molecules directly affects the rates of diffusion. Due to high temperatures, the speed of molecules increases, as a result of this increasing the diffusion rates with time.