Maintaining Homeostasis - Biology

1. Fundamental Concepts

Definition: Homeostasis is the process by which an organism maintains a stable internal environment despite changes in external conditions.
Diffusion: The movement of molecules from an area of high concentration to an area of low concentration.
Osmosis: A specific type of diffusion involving the movement of water across a semipermeable membrane.

2. Key Concepts

Basic Rule: $${\text{{Net movement of particles}} = \text{{Concentration gradient}}}$$

Osmotic Pressure: $${\text{{Osmotic pressure}} = i \cdot M \cdot R \cdot T}$$ where $i$ is the van't Hoff factor, $M$ is the molarity, $R$ is the gas constant, and $T$ is the temperature.

Application: $${\text{{Maintaining cell volume and function through osmotic balance}}}$$

3. Examples

Example 1 (Basic)

Problem: If a cell is placed in a hypertonic solution, what will happen?

Step-by-Step Solution:

The external solution has a higher solute concentration than the cell.
Water will move out of the cell to the external solution.
The cell will shrink due to water loss.

Validation: This aligns with the principle that water moves from areas of lower solute concentration to areas of higher solute concentration.

Example 2 (Intermediate)

Problem: Calculate the osmotic pressure of a 0.5 M NaCl solution at 298 K.

Step-by-Step Solution:

Identify the components: $i = 2$ (since NaCl dissociates into two ions), $M = 0.5$, $R = 0.0821 \frac{\text{{L atm}}}{\text{{mol K}}}$, $T = 298$ K.
Substitute into the formula: $${\text{{Osmotic pressure}} = 2 \cdot 0.5 \cdot 0.0821 \cdot 298}$$
Calculate: $${\text{{Osmotic pressure}} = 24.7 \text{{ atm}}}$$

Validation: The calculation confirms the expected osmotic pressure for the given conditions.

4. Problem-Solving Techniques

Visual Strategy: Use diagrams to illustrate the movement of water and solutes across membranes.
Error-Proofing: Always check the units and ensure they are consistent throughout the calculations.
Concept Reinforcement: Relate theoretical concepts to real-world examples, such as the effects of salt on plant cells.