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.
Diffusion Formula
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”.