Density, Specific Gravity, and Specific Volume

1. Density, Specific Gravity, and Specific Volume Dr. Hayder B Sahib PhD., M.Sc., DSc., BSc (Pharmacology)

2. Density: is mass /unit volume • It is usually expressed as gram/cubic centimeter (g/cc) • Density of water expressed 1 g/ml • Density= Mass/volume • Example: if 10ml of sulfuric acid weight 18g, what is its density? • Density = 18/10= 1.8 g/ml • Specific Gravity (sp.gr.): is a ratio expressed decimally of the weight of substance to the weight of an equal volume of substance chosen as a standard, both substances at the same temperature. • Note: water is used as a standard for specific gravity of liquids and solids. The most useful standard for gases is hydrogen.

3. Specific Gravity = weight of substance / weight of equal volume of water • sp. gr has no unit • Example : If 10ml of sulfuric acid weight 18 g and 10ml of water under similar condition weight 10g what is the specific gravity of the acid ? • Sp. gr= 18g/10ml= 1.8 • Substances that have sp.gr. less than 1 are lighter than water • Substances that have higher sp.gr. than one are heavier than water

4. Calculating the specific gravity of liquids • Sp.gr. = weight of substance / weight of equal volume of water • Example: if 54.96 ml of an oil weight 52.78g. what is the sp.gr. of the oil? • 54.96ml of water weight 54.96g • Sp.gr. = 52.78g/54.96= 0.9603 • Example 2 if one pint of a liquid weight 16 fl.oz what is the sp.gr. of the liquid? • 16 fl.oz of water weight 473g • Sp.gr. = 601g/473g=1.27

5. Pycnometer or specific gravity Bottle • A pycnometer is a special glass bottle used to determine sp.gr it is available in the lab. Its volume ranging from 1-50 ml. • In using pycnometer, first weight empty bottle, then weigh it again when filled to capacity with water • Example: A 50ml pycnometer found to weight 120g when empty. 170g when filled with water and 160g when filled with an unknown liquid, calculate the sp.gr of the unknown liquid? • Sp.gr = wt of substance/ wt of equal volum of water • Weight of water = 170-120=50g • Weight of unknown liquid = 160-120=40g • Sp.gr. 40/50 = 0.78

6. Example 2 • A sp.gr. bottle weight 23.66 when filled with water, it weighs 72.95g when filled with another liquid it weight 73.56g what is the sp.gr. of the liquid ? • 73.56-23.66=49.90g • 72.95-23.66=49.29g • Sp.gr. = 49.90/49.29= 1.012

7. Displacement or plummet Method • The specific gravity calculation is based on Archimede’s principles. • The body immersed in a liquid displace an amount of the liquid equal to its own volume and suffer an apparent loss in weight equal to the weight of the displaced liquid. • So weight a plummet then suspended in water and when suspended in a liquid the sp.gr. of which we want to determine. And by subtracting these weight from the weight of the plummet in air.

8. Example • A glass plummet weight 12.64g in air, 8.57g when immersed water and 9.12g when immersed in oil, calculate the sp.gr. of the oil • 12.64-9.12= 3.52g • 12.64-8.57 = 4.07g displaced water • Sp.gr. = 3.52g/4.07g = 0.868 • Note: for the sp .gr of the solid as it has very limited application in the pharmaceutical Sciences so we wont go through it.

9. Specific gravity: is a factor that expresses how much heavier or lighter the substance than water. • If we had50 ml of a liquid with a specific gravity of 1.2 it would weight 1.2 time much as an equivalent volume of water. • 50 ml would weight 50g and therefore the liquid would weight 1.2 times that or 60g

10. Calculate the weight, knowing the volume and specific gravity • Gram = Milliliter X sp.gr • Example: what is the weight in gram of 3620 ml of alcohol having sp.gr. of 0.820 • 3620 ml of water weight 3620 g • 3620g X 0.820 = 2968 • Example: what is the weight in gram of 2 fl.oz of liquid having sp.gr of 1.118? • 2 X 29.57 = 59.14 • 59.14 ml of water weight 59.14 g • 59.14 X 1.118 = 66.12 g

11. Calculating the volume knowing the weight and sp.gr • ml = g/ sp. gr

12. Pharmaceutical Application of Specific Gravity • to convert the weight of an ingredient to volume and vice versa • in preparation of Parentral Nutrition (TPN) Clinical Application • It is important in urine analysis. In normal adult, the sp.gr of urine is usually within the range 1.010 to 1.025 • The specific gravity of urine decrease with age, while in newborn generally within the range of 1.001- 1.020 • The specific gravity is an indicator of both the concentrations of particles in the urine and the patient’s degree of hydration.

13. A higher than normal sp. gr indicates that urine is concentrated this may be due to the presence of excess of waste products and electrolyte. • the presence of glucose (glucose urea), protein (protein urea), low fluid intake and excessive water loss. • Low sp.gr indicates that the urine is dilute which may be a result of Diabetes Insipidus, renal disease, increase fluid intake, IV hydration. In modern clinical lab. The sp.gr. of urine is determined by (refractive • index method) but urine analyses preferred by fully automated equipments that determine in seconds urine chemistry, sp.gr, Ph, color, clarity.

14. Specific volume: • In Pharmaceutical practice, defined as an abstract number representing the ratio, expressed decimally of the volume of substance to the volume of an equal weight of another substance taken as a standard both having the same temperature, water is the standard • ml = g/ sp.gr