Diffusion Formula is the mathematical expression to calculate the rate of diffusion which is explained in detail in this article. As we know, diffusion is defined as the movement of molecules from a higher concentration to a lower concentration. The concept of diffusion plays an important role in some natural and artificial phenomena.
Diffusion is responsible for various phenomena in everyday life such as the mixing of two or more substances, the exchange of gases etc. This article deals with a formula for the rate of diffusion, while also discussing the basics of diffusion as well. Other than that, we will also discuss how to calculate the rate of diffusion and the factors affecting the rate of diffusion as well. Let’s start our learning journey on the topic named “Diffusion Formula”.
What is Diffusion?
Diffusion is a fundamental process by which particles, molecules, or substances spread out or disperse from an area of high concentration to an area of low concentration. It occurs due to the random motion of particles, driven by their kinetic energy. As particles move, they collide and interact with one another, leading to the gradual equalization of concentration across a given space. This phenomenon is observed in various natural and man-made systems, such as the diffusion of gases in the atmosphere, the spreading of dyes in a liquid, or the movement of substances across cell membranes.
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Examples of Diffusion
Examples, where the concept of Diffusion is observed, are:
- When you spray perfume in one corner of a room, the scent molecules diffuse through the air, gradually spreading out and becoming detectable in other areas of the room.
- When you breathe in, the oxygen molecules from the air diffuse into the tiny air sacs of your lungs. From there, they cross the lung membranes and enter the bloodstream, where they can be transported to cells throughout your body.
- If you drop a few drops of food colouring into a glass of water, the coloured molecules will diffuse and gradually spread throughout the water, creating an evenly coloured solution.
What is Rate of Diffusion?
The speed or rate at which particles or molecules spread and move from an area of higher concentration to an area of lower concentration. It is measured as how quickly diffusion occurs.
What is Diffusion Rate Formula?
Diffusion is defined as the net movement of anything from a higher concentration to a lower concentration, whereas the diffusion rate formula describes the rate at which particles spread out or move from an area of higher concentration to a lower concentration. it measures the process of diffusion by considering factors such as the diffusion coefficient, surface area, concentration difference, and distance over which diffusion occurs. It is a mathematical representation of the phenomenon of diffusion.
How to Calculate Rate of Diffusion?
To calculate the rate of diffusion, we can use the following formula:
Rate of Diffusion = (D × A × ΔC) / Δx
Where,
- D is the diffusion coefficient, which depends on the nature of the substance and the medium it is diffusing through.
- A is the surface area across which diffusion occurs.
- ΔC is the concentration difference between the two regions.
- Δx is the distance over which diffusion takes place.
Factors Affecting Rate of Diffusion
There are four factors that are affecting the rate of diffusion.
- Concentration Gradient: The difference in concentration between the two regions will affect the rate of diffusion. A steeper concentration gradient leads to faster diffusion.
- Temperature: As the temperature increases that will increase the kinetic energy of molecules, thereby the molecules move faster and collide with each other which will lead to an increase in diffusion
- Molecular Size: If the molecular size is smaller then larger will be the diffusion, because they can move through gaps in the medium more easily
- Nature of Medium: The nature of the medium will play a key role in diffusion because the impact rate of diffusion depends on the factors such as density, solubility, etc influence the ease of diffusion.
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Solved Examples on Diffusion Rate Formula
Example 1: A gas with a diffusion coefficient of 0.02 cm2/s spreads through a container with a surface area of 50 cm2. The concentration difference between the two sides of the container is 0.1 mol/cm3, and the distance over which diffusion occurs is 2 cm. Calculate the rate of diffusion.
Solution:
Given:
D = 0.02 cm2/s,
A = 50 cm2,
ΔC = 0.1 mol/cm3, and
Δx = 2 cm.
Thus, Rate of Diffusion = (D × A × ΔC) / Δx
⇒ Rate of Diffusion = (0.02 cm2/s) × (50 cm2) × (0.1 mol/cm3) / (2 cm)
⇒ Rate of Diffusion = 0.05 mol/s
Therefore, the rate of diffusion of the gas through the container is 0.5 moles per second.
Example 2: A dye diffuses through a liquid medium with a diffusion coefficient of 0.05 mm^2/min. The liquid has a surface area of 1000 mm^2. The concentration difference between the initial position of the dye and the rest of the liquid is 0.02 g/mL. If the distance over which diffusion occurs is 5 mm, calculate the rate of diffusion.
Solution:
Given:
D = 0.05 mm2/min
A = 1000 mm2
ΔC = 0.02 g/mL = 0.02 g/cm3
Δx = 5 mm
As we know, Rate of Diffusion = (D × A × ΔC) / Δx
and, 1 mm2 = 0.01 cm2 (since 1 mm = 0.1 cm)
Thus, A = 1000 mm2 = 1000 × 0.01 cm2 = 10 cm2,
1 mm = 0.1 cm (since 1 cm = 10 mm), and
Δx = 5 mm = 5 × 0.1 cm = 0.5 cm
Thus, Rate of Diffusion = (0.05 mm2/min × 10 cm2 × 0.02 g/mL) / 0.5 cm
And as 1 min = 60 seconds
Therefore, Rate of Diffusion = (0.05 mm2/min × 10 cm2 × 0.02 g/mL) / 0.5 cm
⇒ Rate of Diffusion = (0.05 cm2/min × 10 cm2 × 0.02 g/mL) / 0.5 cm
⇒ Rate of Diffusion = (0.01 cm2/min × 0.02 g/mL) / 0.5 cm
⇒ Rate of Diffusion = 0.0002 g/min
Therefore, the rate of diffusion of the dye through the liquid is 0.0002 grams per minute.
Example 3: A solute diffuses through a membrane with a diffusion coefficient of 0.1 cm^2/s. The membrane has a surface area of 20 cm^2, and the concentration difference between the two sides of the membrane is 0.05 mol/L. If the distance across the membrane is 0.5 cm, calculate the rate of diffusion.
Solution:
Given:
D = 0.1 cm2/s
A = 20 cm2
ΔC = 0.05 mol/L = 0.05 × 10-3 mol/cm3
Δx = 0.5 cm
Thus, Rate of Diffusion = (D × A × ΔC) / Δx
⇒ Rate of Diffusion = (0.1 cm2/s × 20 cm2 × 0.05 mol/L) / 0.5 cm)
⇒ Rate of Diffusion = (0.1 cm2/s × 20 cm2 × 0.05 mol/L) / 0.5 cm
⇒ Rate of Diffusion = (0.1 cm2/s × 20 cm2 × 0.05 mol/L) / 0.5 cm
⇒ Rate of Diffusion = (0.1 × 20 × 0.05) mol/s
⇒ Rate of Diffusion = 0.1 mol/s
⇒ Rate of Diffusion = 0.1 mol/s
Therefore, the rate of diffusion of the solute through the membrane is 0.1 moles per second.
Example 4: A substance diffuses through a gel with a diffusion coefficient of 0.02 mm^2/min. The gel has a surface area of 10 mm^2, and the concentration difference between the two sides of the gel is 0.1 g/cm^3. If the distance across the gel is 1 mm, calculate the rate of diffusion.
Solution:
Given:
D = 0.02 mm2/min
A = 10 mm2
ΔC = 0.1 g/cm3
Δx = 1 mm
Thus, Rate of Diffusion = (D × A × ΔC) / Δx
⇒ Rate of Diffusion = (0.02 mm2/min × 10 mm2 × 0.1 g/cm3) / 1 mm
As, 1 mm2 = 0.01 cm2 (since 1 mm = 0.1 cm)
and A = 10 mm2 = 10 × 0.01 cm2 = 0.1 cm2
1 mm = 0.1 cm (since 1 cm = 10 mm)
Thus, Δx = 1 mm = 1 × 0.1 cm = 0.1 cm
⇒ Rate of Diffusion = (0.02 mm2/min × 0.1 cm2 × 0.1 g/cm3) / 0.1 cm
⇒ Rate of Diffusion = (0.002 mm2/min × 0.1 g/cm3)
⇒ Rate of Diffusion = 0.0002 g/min
Therefore, the rate of diffusion of the substance through the gel is 0.0002 grams per minute.
Example 5: A scent diffuses through a room with a diffusion coefficient of 0.05 m^2/s. The room has a surface area of 50 m^2, and the concentration difference between the scent’s source and the rest of the room is 0.01 mg/m^3. If the distance across the room is 10 m, calculate the rate of diffusion.
Solution:
Given:
D = 0.05 m2/s
A = 50 m2
ΔC = 0.01 mg/m3
Δx = 10 m
Rate of Diffusion = (D × A × ΔC) / Δx
⇒ Rate of Diffusion = (0.05 m2/s × 50 m2 × 0.01 mg/m3) / 10 m
As 1 mg = 0.001 g (since 1 g = 1000 mg)
and ΔC = 0.01 mg/m3 = 0.01 × 0.001 g/m3 = 0.00001 g/m3
⇒ Rate of Diffusion = (0.05 m2/s × 50 m2 × 0.00001 g/m3) / 10 m
⇒ Rate of Diffusion = (0.0025 g/s) / 10 m
⇒ Rate of Diffusion = 0.00025 g/s
Therefore, the rate of diffusion of the scent through the room is 0.00025 grams per second.
FAQs on Diffusion Formula
1. What is Diffusion?
Diffusion is the process where particles, such as molecules or ions, move from an area of high concentration to an area of low concentration. It’s like spreading or mixing something out evenly.
2. How does diffusion happen?
Diffusion happens because particles are always in constant motion. They naturally move around randomly, and over time, they spread out and become more evenly distributed.
3. What is Diffusion Rate Formula?
The diffusion rate formula describes the rate at which particles or molecules move from an area of high concentration to an area of low concentration and Diffusion Rate is given by (D × A × ΔC)/ΔX.
Where,
- D is the diffusion coefficient, which depends on the nature of the substance and the medium it is diffusing through.
- A is the surface area across which diffusion occurs.
- ΔC is the concentration difference between the two regions.
- Δx is the distance over which diffusion takes place.
4. What does the Diffusion Coefficient (D) Represent?
The diffusion coefficient (D) represents the mobility or the speed at which particles or molecules move through a particular medium. It is a constant that is specific to the substance being diffused and the medium through which it is diffusing. Different substances and different mediums have different diffusion coefficients.
5. What Affects the Rate of Diffusion?
Concentration gradient, temperature, molecular size, medium’s properties are some of the factors that effect the rate of diffusion
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