Pharmaceutical Calculations
Density:
• Def.: It is a mass per unit volume of substance (1.8 g/ml).
• Calculated by dividing mass by volume.
Example: If 10 ml of sulfuric acid weight 18 g,
18 (g)
Density = = 1.8 g per ml (g/ml)
10 (ml)
Specific gravity: (sp.gr.)
• Def.: Weight of substance / weight of equal volume of standard
substances have the same temperature.
• For specific gravity of liquids and solids, water used as standard.
• It is a ratio between like quantities (no dimension).
Example: in the above example, calculate the specific gravity?
10 ml of H2O (with same conditions) = 10 g (weight)
Specific gravity of acid:
wt of 10 ml of acid 18 (g)
= = 1.8
wt of 10 ml of water 10 (g)
• It is a constant value for each substance.
Specific Gravity of Liquids
• Calculate specific gravity by three methods (liquids):
1- Weight and volume known.
2- Specific gravity bottle (pycnometer).
3- Displacement or plummet method.
,1- Specific gravity by known weight and volume of liquids:
Ex: If 54.96 ml of oil weight 52.8 g
wt of 54.96 ml of oil = 52.78 = 0.9603
Specific gravity of oil =
wt of 54.96 ml of water 54.96
N.B.:
54.96 ml of water weight 54.96 gm (under similar conditions).
2- Specific gravity of liquids by pycnometer (specific gravity bottle):
1- Wt of container (specific gravity bottle) (empty) → (1).
2- Filled the container with water and weight → (2).
3- Filled the container with liquid and weight → (3).
4- Wt of water = (2) – (1) → (4)
5- Wt of liquid = (3) – (1) → (5)
wt of liquid = (5)
Specific gravity =
wt of water (4)
Example
• Specific gravity bottle weights = 23.66 g (1)
• Filled with water weights = 72.95 g (2)
• Filled with liquid weights = 73.56 g (3)
Specific gravity →?
• Wt of water = 72.95 – 23.66 = (2) – (1) = 49.29 gm
• Wt of liquid = 73.56 – 23.66 = (3) – (1) = 49.90 gm
49.90
Specific gravity = = 1.012
49.29
, Specific Volume
• Specific volume of substance = volume of substance
volume of equal wt of water
• Specific gravity: comparison Wts of equal volumes
• Specific volume: comparison Vs of equal weights
• Are reciprocals of each other (specific gravity = 1/ specific volume)
(Specific volume= 1/specific gravity)
• If multiplied together = 1
Specific volume calculation (liquid):
1- Given volume of specified Wt.
2- Given its specific gravity
3- Calculate specific gravity by having specific volume.
Example:
1- Determine specific volume of syrup, 91.0 ml (its wt = 107.16 g)
91.0 91.0
Specific volume = = = 0.850
volume of standard (water) 107.16
107.16 g of water = 107.16 g ml (volume)
2- What is specific volume of phosphoric acid having sp. gr. 1.71?
1
sp. volume = = 0.585
1.71
3- What is sp. gr. of liquid has sp. volume 1.396
1
sp. gr. = = 0.716
1.396
Calculations of weight (liquid):
• Calculation the weight of liquid when given
- Volume - specific gravity
Density:
• Def.: It is a mass per unit volume of substance (1.8 g/ml).
• Calculated by dividing mass by volume.
Example: If 10 ml of sulfuric acid weight 18 g,
18 (g)
Density = = 1.8 g per ml (g/ml)
10 (ml)
Specific gravity: (sp.gr.)
• Def.: Weight of substance / weight of equal volume of standard
substances have the same temperature.
• For specific gravity of liquids and solids, water used as standard.
• It is a ratio between like quantities (no dimension).
Example: in the above example, calculate the specific gravity?
10 ml of H2O (with same conditions) = 10 g (weight)
Specific gravity of acid:
wt of 10 ml of acid 18 (g)
= = 1.8
wt of 10 ml of water 10 (g)
• It is a constant value for each substance.
Specific Gravity of Liquids
• Calculate specific gravity by three methods (liquids):
1- Weight and volume known.
2- Specific gravity bottle (pycnometer).
3- Displacement or plummet method.
,1- Specific gravity by known weight and volume of liquids:
Ex: If 54.96 ml of oil weight 52.8 g
wt of 54.96 ml of oil = 52.78 = 0.9603
Specific gravity of oil =
wt of 54.96 ml of water 54.96
N.B.:
54.96 ml of water weight 54.96 gm (under similar conditions).
2- Specific gravity of liquids by pycnometer (specific gravity bottle):
1- Wt of container (specific gravity bottle) (empty) → (1).
2- Filled the container with water and weight → (2).
3- Filled the container with liquid and weight → (3).
4- Wt of water = (2) – (1) → (4)
5- Wt of liquid = (3) – (1) → (5)
wt of liquid = (5)
Specific gravity =
wt of water (4)
Example
• Specific gravity bottle weights = 23.66 g (1)
• Filled with water weights = 72.95 g (2)
• Filled with liquid weights = 73.56 g (3)
Specific gravity →?
• Wt of water = 72.95 – 23.66 = (2) – (1) = 49.29 gm
• Wt of liquid = 73.56 – 23.66 = (3) – (1) = 49.90 gm
49.90
Specific gravity = = 1.012
49.29
, Specific Volume
• Specific volume of substance = volume of substance
volume of equal wt of water
• Specific gravity: comparison Wts of equal volumes
• Specific volume: comparison Vs of equal weights
• Are reciprocals of each other (specific gravity = 1/ specific volume)
(Specific volume= 1/specific gravity)
• If multiplied together = 1
Specific volume calculation (liquid):
1- Given volume of specified Wt.
2- Given its specific gravity
3- Calculate specific gravity by having specific volume.
Example:
1- Determine specific volume of syrup, 91.0 ml (its wt = 107.16 g)
91.0 91.0
Specific volume = = = 0.850
volume of standard (water) 107.16
107.16 g of water = 107.16 g ml (volume)
2- What is specific volume of phosphoric acid having sp. gr. 1.71?
1
sp. volume = = 0.585
1.71
3- What is sp. gr. of liquid has sp. volume 1.396
1
sp. gr. = = 0.716
1.396
Calculations of weight (liquid):
• Calculation the weight of liquid when given
- Volume - specific gravity
