DENSITY AND SG - 2nd PPT of EXAM II - Comprehensive Study Notes on Density and Specific Gravity

Objectives of the Class

• Converting between weights and wattage.

  • Calculate densities and specific gravities.

  • Use findings to convert between mass and volume.

  • Application in pharmaceutical scenarios.

Density

• Definition: Density is mass per unit volume.

  • Expressed as:
    $\text{Density (D)} = \frac{\text{mass}}{\text{volume}}$

• Example:

  • Water density: 1 g/mL means that 1 mL of water weighs 1 gram.

• Unit of density: Weight per unit volume, typically in grams per cubic centimeters (g/cc) or grams per milliliter (g/mL).

  • Example Calculation:

  • 10 mL of water weighs 18 grams.

  • Therefore, Density of Sulfuric Acid:
    $\text{Density} = \frac{18\, \text{grams}}{10\, \text{mL}} = 1.8\, \text{g/mL}$

• Example of a material (Copper):

  • Weight: 53.6 grams and volume: 6 mL

  • Calculation:

  • 
    $\text{Density} = \frac{53.6\, \text{grams}}{6\, \text{mL}} = 8.93\, \text{g/mL}$

Specific Gravity

• Definition: Specific gravity is the ratio of a substance's weight to the weight of an equal volume of a standard substance (usually water).

  • Formula:
    $\text{Specific Gravity} = \frac{\text{Weight of Substance}}{\text{Weight of Equal Volume of Water}}$

• No units in specific gravity; the units cancel out.

• Examples:

  • Calculation of specific gravity for a substance weight of 18 grams at a volume of 10 mL:
    $\text{Specific Gravity} = \frac{18\, \text{grams}}{10\, \text{grams}} = 1.8$

• Implications:

  • Specific gravity < 1 indicates substance is lighter than water.

  • Specific gravity > 1 indicates substance is heavier than water.

Calculation Examples

• Example 1:

  • Given: 150 mL of sorbitol weighs 170 grams. What is the specific gravity?

  • Weight of equal volume of water = 150 grams.

  • Calculation:
    $\text{Specific Gravity} = \frac{170\, \text{grams}}{150\, \text{grams}} = 1.1333$

• Example 2:

  • 2 fluid ounces of glycerol weighs 74.1 grams. What is the specific gravity?

  • Use 29.57 or 30 for fluid ounce to ml conversion.

  • Calculation leads to $\text{Specific Gravity} \approx 1.253$.

Mixing and Effects on Density/S.G.

• Dilution Concept:

  • Adding more water reduces density (the solution becomes lighter).

• Instrument to measure density: Pycnometer.

  • Glass bottle used for measuring specific gravity and density in laboratory settings.

  • Comes in sizes like 50 mL, fitted with a glass stopper to release trapped air.

Using a Pycnometer Example

1. Empty Weight: 120 grams.

2. Weight Filled with Water: 171 grams.

3. Calculating Weight of Water:
   $\text{Weight of Water} = 171 - 120 = 51\, \text{grams}$

4. Weight of Unknown Liquid: (after filling pycnometer with new liquid)
   $\text{Weight of New Liquid} = 160 - 120 = 40\, \text{grams}$

5. Specific Gravity Calculation:
   $\text{Specific Gravity} = \frac{40\, \text{grams}}{51\, \text{grams}} \approx 0.784\; (lighter than water)$

Pharmaceutical Applications

• Example: Cost calculation using specific gravity.

  • Glycine specific gravity = 1.25, price = $5.43/pound.

  • Calculate mass of 1000 mL of glycine (1.25 g/mL):
    $1000 mL \times 1.25\, \text{g/mL} = 1250\, \text{grams}$

  • Convert to pounds:
    $\text{Pounds} = \frac{1250}{454} \approx 2.75\, \text{pounds}$

  • Determine cost:
    $\text{Total Cost} = 2.75\, \text{pounds} \times 5.43 = 14.93\, \text{dollars}$

• Additional pharmacological example where specific gravity helps solve mass and volume combinations for drug solutions.

  • Example: Addition of a drug to syrup

    • Initial syrup: 60 mL, specific gravity = 1.2.

    • Weight before drug addition = 1.2 * 60 = 72 grams.

    • Drug added = 1.2 grams.

    • New volume = 60.2 mL.

    • New total mass = 72 + 1.2 = 73.2 grams.

    • New density (or specific gravity calculation):
      $\text{Density} = \frac{73.2\, \text{grams}}{60.2\, \text{mL}} \approx 1.216 \; (unitless)$

Conclusion

• Key Differences Between Density and Specific Gravity:

  • Density has units (g/mL), while specific gravity is unitless.

• Importance of understanding density and specific gravity in the context of pharmaceutical applications, especially in dispensing and determining proper dosage and concentrations of solutions.

• Encouragement to practice calculations and concepts in upcoming sessions and assessments.