Diffusion - Biology | Scholardog

1. Fundamental Concepts

Definition: Diffusion is the net movement of molecules from an area of high concentration to an area of low concentration until equilibrium is reached.
Concentration Gradient: The difference in concentration that drives diffusion.
Passive Transport: Movement of substances across a cell membrane without the use of energy.

2. Key Concepts

Fick's First Law of Diffusion: $J = -D \cdot \frac{\partial C}{\partial x}$

Where $ J $ is the flux, $ D $ is the diffusion coefficient, and $ \frac{\partial C}{\partial x} $ is the concentration gradient.

Factors Affecting Diffusion:

Temperature: Higher temperatures increase molecular motion.
Molecular Size: Smaller molecules diffuse faster.
Distance: Greater distances require more time for diffusion.

Application: Diffusion plays a crucial role in cellular processes such as nutrient uptake and waste removal.

3. Examples

Example 1 (Basic)

Problem: Consider two chambers separated by a permeable membrane. Chamber A has a concentration of glucose ($ C_A = 0.5 \text{ M} $) and Chamber B has a concentration of $ C_B = 0.1 \text{ M} $. If the diffusion coefficient ($ D $) is $ 1 \times 10^{-9} \text{ m}^2/\text{s} $ and the distance between the chambers is $ 0.001 \text{ m} $, calculate the flux ($ J $).

Step-by-Step Solution:

Calculate the concentration gradient: $ \frac{\partial C}{\partial x} = \frac{C_A - C_B}{x} = \frac{0.5 - 0.1}{0.001} = 400 \text{ M/m} $.
Apply Fick's First Law: $ J = -D \cdot \frac{\partial C}{\partial x} = -(1 \times 10^{-9}) \cdot 400 = -4 \times 10^{-7} \text{ M/s} $.

Validation: The negative value indicates the direction of diffusion from high to low concentration.

Example 2 (Intermediate)

Problem: In a biological system, the concentration of oxygen in blood is $ C_1 = 0.2 \text{ M} $ and in tissue is $ C_2 = 0.05 \text{ M} $. Given the diffusion coefficient $ D = 2 \times 10^{-10} \text{ m}^2/\text{s} $ and the thickness of the tissue layer $ x = 0.002 \text{ m} $, find the rate of oxygen diffusion.

Step-by-Step Solution:

Calculate the concentration gradient: $ \frac{\partial C}{\partial x} = \frac{C_1 - C_2}{x} = \frac{0.2 - 0.05}{0.002} = 75 \text{ M/m} $.
Apply Fick's First Law: $ J = -D \cdot \frac{\partial C}{\partial x} = -(2 \times 10^{-10}) \cdot 75 = -1.5 \times 10^{-8} \text{ M/s} $.

Validation: The calculated flux matches the expected direction and magnitude for oxygen diffusion in biological systems.

4. Problem-Solving Techniques

Visual Strategy: Use diagrams to represent concentration gradients and diffusion paths.
Error-Proofing: Double-check units and ensure consistent use of SI units throughout calculations.
Concept Reinforcement: Relate theoretical concepts to real-world examples, such as gas exchange in lungs or nutrient absorption in cells.