Concentration and Dilution

Introduction to Dilution

• Dilution: This is the process of decreasing the concentration of a solute by adding more solvent while keeping the quantity of solute unchanged. Visualise it as increasing the number of people sharing the same space, similar to solute in a solvent.

Key Formula and Components

• Formula: $M_1V_1 = M_2V_2$ This expression calculates the amount of solvent needed to attain a desired final concentration.
• $M_1$: Initial concentration
• $V_1$: Initial volume
• $M_2$: Final concentration
• $V_2$: Final volume

Calculations and Worked Examples

Example 1: Calculating Final Concentration

• Known Data:
  • $M_1 = 2 \, \text{M}$, $V_1 = 50 \, \text{mL}$, $V_2 = 200 \, \text{mL}$
• Calculation:
  • $M_2 = \frac{M_1 \times V_1}{V_2} = \frac{2 \times 50}{200} = 0.5 \, \text{M}$

Example 2: Adjusting Volume

• Task: Modify a 100 mL solution from 1 M to 0.5 M.
• Solution:
  • Using $M_1V_1 = M_2V_2$
  • $1 \text{ M} \times 100 \text{ mL} = 0.5 \text{ M} \times V_2$
  • $V_2 = \frac{1 \times 100}{0.5} = 200 \text{ mL}$
  • Therefore, we need to add 100 mL of solvent to the original solution.

Serial Dilutions

• Definition: This involves stepwise diluting a stock solution to produce a series of concentration levels while maintaining consistent dilution ratios.

Procedure Example:

• Begin with a 1 M solution, mix 1 mL with 9 mL of water:
  • $C = \frac{1 \, \text{mL} \times 1 \, \text{M}}{10 \, \text{mL}} = 0.1 \, \text{M}$
• Repeat for further dilutions.

Laboratory Techniques

• Stock Solutions:
  • These are concentrated solutions used to prepare dilutions, allowing for efficiency and consistency.

Equipment and Methodology

• Employ calibrated pipettes and flasks to ensure precision.
• Meniscus Reading: Ensure the meniscus is aligned at eye level for accuracy.

Practice Problems

1. Dilute a 1 M solution to 0.5 M, starting with 100 mL. Calculate each step. Solution: Using $M_1V_1 = M_2V_2$ $1 \text{ M} \times 100 \text{ mL} = 0.5 \text{ M} \times V_2$ $V_2 = \frac{1 \times 100}{0.5} = 200 \text{ mL}$ You need to add 100 mL of solvent to the original solution to achieve the desired concentration.

2. Change a 200 mL solution from 0.5 M to 0.25 M. Solution: Using $M_1V_1 = M_2V_2$ $0.5 \text{ M} \times 200 \text{ mL} = 0.25 \text{ M} \times V_2$ $V_2 = \frac{0.5 \times 200}{0.25} = 400 \text{ mL}$ You need to add 200 mL of solvent to the original solution to achieve the desired concentration.

Quick Review

• Apply $M_1V_1 = M_2V_2$ for dilutions.
• Maintain consistent units in calculations.
• Preparation Tip: Always double-check your steps, ensure precise measurements, and document your work meticulously.