Dilution Calculations and Concepts

Concentrated vs. Dilute Solutions

• Concentrated Solution: A solution with a large amount of solute.
• Dilute Solution: A solution with a small amount of solute.

Visual Representation

• Concentration can be visually assessed by the intensity of color in a solution.
• More color intensity indicates a more concentrated solution with more solute particles.

Molarity Calculation

$M<em>1V</em>1 = M<em>2V</em>2$

• $M_1$ = initial molarity
• $V_1$ = initial volume
• $M_2$ = final molarity
• $V_2$ = final volume
• The number of moles of solute remains the same during dilution, but the volume changes.
• The equation is based on the principle of conservation of mass.

Example Calculation 1

• Problem: Diluting 100 mL of a 2.5 M potassium bromide solution to 0.55 M.
• Goal: Find the final volume ($V_2$).
• Given:
  • $V_1 = 100 \text{ mL}$
  • $M_1 = 2.5 \text{ M}$
  • $M_2 = 0.55 \text{ M}$
• Equation: $M<em>1V</em>1 = M<em>2V</em>2$
• Plug in values:
  • $(2.5 \text{ M}) (100 \text{ mL}) = (0.55 \text{ M}) V_2$
• Solve for $V_2$:
  • $V_2 = \frac{(2.5 \text{ M}) (100 \text{ mL})}{0.55 \text{ M}} = 454.5 \text{ mL}$
• Calculate the amount of water to add:
  • $454.5 \text{ mL} - 100 \text{ mL} = 354.5 \text{ mL}$
  • Final volume: 454.5 mL
  • Water to add: 354.5 mL

Example Calculation 2

• Diluting 18 M sulfuric acid to 1.0 M.
• Goal: Determine the volume of 18 M sulfuric acid needed to create 500 mL of a 1.0 M solution and the amount of water needed.
• Given:
  • $M_1 = 18 \text{ M}$
  • $V_2 = 500 \text{ mL}$
  • $M_2 = 1.0 \text{ M}$
• Find: $V_1$
• Equation: $M<em>1V</em>1 = M<em>2V</em>2$
• Plug in values:
  • $(18 \text{ M}) V_1 = (1.0 \text{ M}) (500 \text{ mL})$
• Solve for $V_1$:
  • $V_1 = \frac{(1.0 \text{ M}) (500 \text{ mL})}{18 \text{ M}} = 27.777 \text{ mL} \approx 27.8 \text{ mL}$
• Amount of 18 M sulfuric acid needed: 27.8 mL
• Calculate amount of water needed:
  • $\text{Water} = 500 \text{ mL} - 27.8 \text{ mL} = 472.2 \text{ mL}$
• Always add acid to water to dissipate heat of the reaction and prevent boiling or splashing.

Diluting Acids Safely

• Use a volumetric flask.
• Add most of the water first (e.g., 400 mL).
• Carefully add the required amount of concentrated acid (e.g., 27.8 mL).
• Add the remaining water to reach the final desired volume (e.g., add the last bit of water drop wise).