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Diffusion refers to the movement of a substance from the area of increased concentration to a lower concentration area. In addition, it occurs in gases and liquid as their particles are free to move randomly from one place to another. It is an important process in living beings, due to these substances driving in and out of a cell. Liquid and gases undergo diffusion as the molecules can move randomly.
Diffusion is characterised by a net movement of the particles down their concentration gradient, or in other words from the area of greater concentration to an area of lower concentration.
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Key Terms: Substance, Diffusion, Molecules, Concentration Gradient, Solutes, Semipermeable Membrane
Read More: Number of Moles Formula
What is Diffusion?
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Diffusion is the net passive activity of molecules or particles from areas of higher to the lower area of concentration. For diffusion to take place there must be a concentration gradient. The inequality in the amounts of solutes between the two regions will cause them to move between the two regions.
- To describe diffusion in the natural context, the ions, respiratory gases, glucose, or other particles move randomly between the congested and the less-crowded regions (fluids), often across a semipermeable membrane.
- The unequal concentration of the particles between two fluids will generate a gradient that will incite them to move to equalise the disparity in concentrations unless the movement of solutes during the diffusion procedure is not a one-way route.
- The net movement of oxygen and carbon dioxide across the alveolar-capillary membrane of mammalian lungs and the net movement of glucose down the concentration gradient are diffusion examples in biological systems.
Diffusion Process
Fick’s Laws of Diffusion
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Fick’s law of diffusion was derived by Adolf Fick in the early 19th century. He explained the law of diffusion as when the molar flux due to diffusion is proportionate to the concentration gradient, the absorption rate of change is a point in space which is proportional to the second derivative of concentration with the area. The diffusion process that justifies Fick’s laws is called Fickian diffusion while the diffusion process that does not obey Fick’s laws is called Anomalous diffusion or non-Fickian diffusion.
Fick’s First Law of Diffusion
According to Fick’s first law of diffusion, “The molar flux which results from diffusion is proportional to the concentration gradient”. At a point in space, the rate of change of concentration in the solution is proportionate to the second derivative of concentration with the space.
Graphical Representation of Fick’s First Law of Diffusion
Mathematically,
where, J represents diffusion flux, D represents diffusivity, φ represents concentration and x represents position.
Fick’s Second Law of Diffusion
The second law of Fick is a linear equation in which the dependent variable is the concentration of the chemical species under consideration. Also, the diffusion of each chemical type occurs independently. It determines the relation between the change in concentration gradient of the particles and time.
Graphical Representation of Fick’s Second Law of Diffusion
Mathematically,
Diffusion Formula
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Diffusion is referred to the movement of substance towards the region with lower concentration. Its equation can be defined as the equation of partial differentiation which indicates the dynamics in a material undergoing diffusion. The diffusion equation is
Where, Φ(r, t) represents density of diffusing material, D(Φ, r) represents collective diffusion coefficient and ∇ represents the vector differential operator del.
Read More: Dalton’s atomic theory
Types of Diffusion
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There exist mainly two classifications of diffusion as mentioned below:
- Simple Diffusion: Simple diffusion is generally the movement of molecules along their concentration slope without any direct involvement of other molecules. It involves both, the spread of a material through a medium or the transport of a particle across a membrane. In most biological systems, diffusion occurs across a semipermeable membrane made by a lipid bilayer.
- Facilitated Diffusion: Facilitated diffusion, on the other hand, requires the presence of another molecule (the facilitator) for diffusion to take place. Facilitated diffusion is essential for the motion of large or polar molecules across the hydrophobic lipid bilayer. Facilitated diffusion is crucial for the biochemical operations of every cell since there is contact between various subcellular organelles.
Simple Diffusion vs Facilitated Diffusion
Causes of Diffusion
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Some of the causes of diffusion are:
- Diffusion is a natural and physical procedure, which takes place on its own, without stirring or shaking the solutions. The liquids and gases undergo diffusion as the molecules can move randomly.
- Diffusion takes place as a consequence of a difference in concentration from a medium with greater concentration to a medium at a smaller concentration. Hence, the causes of diffusion are the movement of molecules of solids, liquids, and gases from a region of their higher concentration to a region of their lower concentration until both the regions achieve uniform concentration.
Read More: Rate Determining Step
Things to Remember
- The method of diffusion is described as the net motion of molecules from an area with more concentration to an area with lesser concentration.
- The molecules in the gas, liquid, or solid are in steady motion due to their kinetic energy and may collide with each other.
- Random motion is expressed as the movement that occurs by chance since there is no concept of occurrence by which the direction of the particles shifts in a solution or gas.
- Several factors influencing the rate of diffusion of a solute comprise the mass of the solute, the atmosphere temperature, the density of solvent, and the distance travelled.
- There are majorly two factors affecting the method of diffusion: Temperature, and the type of substance. The hotter the gas or fluid, the more rapid diffusion takes place. On the other hand, the substances diffuse more rapidly in gases than in liquids. This is due to the particles in a gas which are more scattered and move faster than the particles in a fluid.
Read More: Relation between Molarity and Molality
Sample Questions
Ques. Give the formula of Maxwell-Stefan diffusion? (2 marks)
Ans. The formula of Maxwell-Stefan diffusion is:
∑ixi =1,∑iωi=1
Besides, they are associated with the concentration and each other as:
Xi = c ∑jci
Wi = Mici ∑jMjci
Xi = ωiMi ∑jωjMj
Ques. What are the applications of Fick’s Law of diffusion? (2 marks)
Ans. According to Fick’s First Law of Diffusion,
Flux =−P ( c2−c1 ) F=−P(c2−c1 )
where, P represents permeability, F represents Flux and C2 - C1 is the difference in concentration.
Fick’s law applies to two miscible fluids or liquids when they come in contact and diffusion takes place at a macroscopic level. The diffusion equations from Fick’s law are being used in fabricating integrated circuits. It has many applications in pharmaceutical and food industries.
Ques. Explain the terms dialysis and osmosis. What are the major forms of dialysis? (4 marks)
Ans. Dialysis is the diffusion of solutes across a selectively permeable membrane. A selectively permeable membrane permits only the specific ions and molecules to pass through, while it blocks the movement of other molecules or ions. Dialysis is generally a treatment that extracts or removes water and toxins from the body. Dialysis is typically used for those patients having acute or chronic kidney failure.
There are major two forms of dialysis are:
- Hemodialysis: Hemodialysis involves the reduction of fluid & toxin from the blood by diffusion and convection across a semipermeable membrane by pumping the patient’s blood via an exterior filter.
- Peritoneal Dialysis: Peritoneal dialysis involves the disposal of fluid & toxin by diffusion and convection by infusing and extracting fluid into the peritoneal cavity via an abdominal catheter.
Osmosis on the other hand is the movement of solvent molecules from the region of lower concentration to the region of higher concentration via a semipermeable membrane. Since water is solvent in every living being, biologists describe osmosis as the diffusion of water across a selectively permeable membrane. For instance, plants take water and minerals from roots with the assistance of osmosis.
Ques. Explain which two gasesâ??under similar conditions of temperature (T) and pressure (P) have similar diffusion rates? (3 marks)
Ans. According to Graham's diffusion law, under similar conditions of temperature and pressure, the diffusion rates of various gases are directly proportional to the pressure of gases and are inversely proportional to the square root of their molar masses or mass densities i.e. r = (1÷√d).
Since the gram molar mass of both carbon dioxide and nitrous oxide is similar i.e. 44g. Thus, both CO2 and N2O will diffuse at the same rate under similar conditions of temperature and pressure or will have similar diffusion rates. Whereas, CO and N2 having masses 28gmol-1 will have the highest diffusion rate, and NO2 with molecular mass 48 g mol-1 will have the least diffusion at similar conditions of temperature and pressure.
Ques. What are some examples of diffusion? (3 marks)
Ans. We can observe various examples of diffusion in our day-to-day life, a few of which have been mentioned below:
- The fragrance of perfumes or Incense Sticks
- Opening the bottle of soda or cold drinks and the CO2 diffuses in the air
- The dipping of tea bags in hot water diffuses the tea
- Tiny dust particles or vapour diffuse into the atmosphere, causing air pollution
- Breathing or intake of oxygen into the body and diffuses in our blood
- Transportation of biomolecules & minerals in Plants and Animals
- The sugar gets dissolved with the water evenly and sweetens it without having to stir the water.
- The disposal of waste substances & toxins from our body is also an example of diffusion.
Ques. State the significance of diffusion? (3 marks)
Ans. Diffusion helps in the movement of substances in and out of the cells. The molecules shift towards a region with lower concentration from the region with higher concentration till the concentration becomes equivalent in both the regions.
- Diffusion is essential to cells as it lets them acquire the useful substances required to obtain energy and grow, and helps them get rid of waste products.
- Diffusion is an important procedure for photosynthesis in plants where carbon dioxide from the stomata diffuses into the leaves and finally into the cells.
- The diffusion helps in attracting insects and different animals for pollination.
Ques. Among carbon dioxide and bromine gas, which one will diffuse faster? (3 marks)
Ans. The diffusion rate relies on the molecular mass, temperature, and concentration gradient. In terms of molecular mass, carbon dioxide (CO2) has the highest molecular mass and should be expected to diffuse slowest as according to Graham's diffusion law, under similar conditions of temperature (T) and pressure (P), the diffusion rates of gases are inversely proportional to the square root of their molar masses. In terms of temperature, CO2 also has the lowest heat capacity. It should be the slower diffusing gas in the atmosphere. The lesser the relative molecular mass of a gas molecule, the faster it will diffuse. CO2 has the smallest relative molecular mass, followed by bromine gas. Therefore, carbon dioxide (CO2) will diffuse faster than bromine gas.
Ques. On what factors does the rate of diffusion depend? (4 marks)
Ans. The rate of diffusion depends on the nature of the interaction between the medium and material. For instance, a gas diffuses rapidly in another gas. For instance, the way the noxious odour of ammonia gas spreads in the atmosphere. Likewise, if a canister of liquid nitrogen leaks a little, nitrogen gas that escapes would quickly diffuse into the atmosphere whereas it would diffuse slightly more slowly in a fluid like water and slowest in a solid.
The other factors on which the rate of diffusion relies are:
- Concentration: The higher the concentration difference, the faster will be the diffusion rate.
- Temperature: The higher the temperature, the more kinetic energy the particles will possess. Hence, the particles will move and merge more quickly.
- Surface Area: The rate of diffusion also relies on the surface area as, the greater the surface area, the faster will be the rate of diffusion.
Ques. Solve the following diffusion formula: (3 marks)
∂ψ / ∂t = kΔ2ψ with u(x, 0) = f(x), u(0, t) = 0 and u(L, t) = 0
F(x) = 12 sin (π x / L)
Ans. According to the given question,
u(x, 0) = f(x), u(0, t) = 0 and u(L, t) = 0
Let, n = 1
B1 = 12
From the formula,
Un(x, t) = Bn sin (n π x / L) e –k(2 π / L)2 t
U(x, t) = 12 sin(π x / L) e –k(π/L)2 t
Ques. A specific application needs to raise the volume of 80 cm3 of a certain gas by 20% without altering the pressure. Find out to what temperature should the gas be heated if its initial temperature is 25° C? (4 marks)
Ans. As per the question given, the desired increase in the volume of gas is
20% of 80 cm3 = (20/100) × 80 = 16 cm3
Thus, the final volume of the gas will be 80 + 16 = 96 cm3
We’re given that V1 = 80 cm3, V2 =96 cm3
Given that, T1 = 25 oC = (273 + 25) K = 298 K, T2 = ?
Applying the Charles's law, we will get:
V1/T1 = V2/T2
80/298 = 96/T2
T2 = 357.6 K
=> 357.6 - 273
= 83.4 oC
Therefore, the gas should be heated at 83.4 oC to change the 80 cm3 volume of a gas by 20%.
Ques. Distinguish between diffusion and effusion of gases? (5 marks)
Ans. The major differences between the diffusion and effusion have been mentioned in the table below:
| Effusion | Diffusion |
|---|---|
| It takes place when the gas molecules escape via a pinhole into a vacuum | During diffusion, one gas combines with another by thermal random motion resulting in the collision between each other while discharging molecular energy. |
| In simple words, gas can travel via a small opening. | It is the ability of gases to merge together in the absence of barriers. |
| It usually takes place when the hole's size/ aperture is smaller in comparison to the mean free path of the molecules. | It happens either when there are no holes or if holes in the barrier are greater than the mean free path. |
| It either occurs or is facilitated by a difference of pressures. | It occurs due to differences in concentration. |
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