Passive Transport - Biology

1. Fundamental Concepts

Definition: Passive transport is the movement of substances across a cell membrane without the use of energy, driven by the concentration gradient.
Types: Includes diffusion and osmosis.
Concentration Gradient: The difference in concentration of a substance between two regions.

2. Key Concepts

Basic Rule: $${\text{{Substance}}} \cdot {\text{{moves from high to low concentration}}}$$

Molecular Movement: $${\text{{Molecules move randomly but net movement is down the gradient}}}$$

Application: $${\text{{Used in various biological processes such as nutrient uptake and waste removal}}}$$

3. Examples

Example 1 (Basic)

Problem: Explain how oxygen moves into a red blood cell.

Step-by-Step Solution:

Oxygen has a higher concentration outside the cell than inside.
Oxygen molecules move randomly but there is a net movement from the area of high concentration to low concentration.
The oxygen enters the cell through passive transport until equilibrium is reached.

Validation: Oxygen concentration decreases outside the cell and increases inside until both sides are equal.

Example 2 (Intermediate)

Problem: Calculate the rate of diffusion of glucose across a cell membrane if the concentration on one side is 0.5 M and on the other side is 0.1 M. Assume the diffusion constant $D$ is $1 \times 10^{-9} \text{{m}}^2/\text{{s}}$ and the thickness of the membrane is $1 \times 10^{-7} \text{{m}}$.

Step-by-Step Solution:

Use Fick's first law of diffusion: $J = -D \frac{\Delta C}{\Delta x}$.
Calculate the concentration gradient: $\Delta C = 0.5 \text{{M}} - 0.1 \text{{M}} = 0.4 \text{{M}}$.
Calculate the thickness of the membrane: $\Delta x = 1 \times 10^{-7} \text{{m}}$.
Substitute values into Fick's law: $J = -(1 \times 10^{-9} \text{{m}}^2/\text{{s}}) \cdot \frac{0.4 \text{{M}}}{1 \times 10^{-7} \text{{m}}}$.
Simplify: $J = -4 \times 10^{-2} \text{{M/s}}$.

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

4. Problem-Solving Techniques

Visual Strategy: Use diagrams to represent concentration gradients and movement of molecules.
Error-Proofing: Always check the units and ensure they are consistent throughout the calculation.
Concept Reinforcement: Relate the concept of passive transport to real-world examples like water moving through a semipermeable membrane.