Once upon a time, in the quirky town of Physicsville, there was a peculiar competition called the “Density Derby.” In this contest, residents had to create the smallest and heaviest object possible, all while considering density, gravity, and volume.
One day, Professor Dotty, a brilliant scientist with a penchant for mischief, decided to participate. She concocted a plan to win the derby in a rather unusual way. Instead of crafting a tiny, dense object, she created a helium-filled balloon in the shape of a hippopotamus. The balloon was enormous and lightweight, defying the laws of density and gravity.
During the competition, when everyone else was struggling to balance density and volume, Professor Dotty released her helium hippopotamus into the sky. As it gracefully floated upwards, the townsfolk watched in awe. It turned out that volume, when filled with the right gas, could indeed defy gravity, leaving the entire town amused and bewildered.
And that day, Physicsville learned an important lesson: Sometimes, in the world of science, the most unexpected and humorous outcomes can teach us the most valuable lessons about the laws of nature!
Aims/Objectives
- define density, specific gravity and specific volume
- recall relevant equations involving density, specific gravity and specific volume
- calculate the density of an ingredient given the mass and volume using appropriate equation
- calculate the volume or mass given the specific gravity using appropriate equation
- calculate specific volume given the volume of the substance using appropriate equation
- calculate the specific volume given the specific gravity using appropriate equation
- solve application problems involving density, specific gravity and specific volume for pharmaceutical preparations with 100% accuracy without assistance
Foreword
Pharmacists and pharmacy technicians often need to calculate drug dosages and formulations. Density, which represents the mass of a substance per unit volume, is essential for converting between different forms of medications, such as liquid to solid or vice versa. Pharmacists are responsible for formulating medications for specific patient needs. Knowledge of density and specific volume is vital for compounding medicines accurately. Compounding pharmacists need to calculate ingredient quantities based on their density to ensure the final product’s quality, efficacy, and safety. Pharmacists must accurately measure and dispense medications to patients. Understanding specific gravity (the ratio of the density of a substance to the density of a reference substance, usually water) is important when dealing with liquid medications. Specific gravity helps pharmacists determine if a liquid medication will sink, float, or remain suspended, affecting how it should be dispensed and administered. Knowledge of specific volume (reciprocal of density) is crucial for understanding the volume occupied by a given mass of a substance. This is important in pharmaceutical manufacturing, especially in ensuring the proper storage and packaging of medications. Understanding specific volume helps in determining appropriate container sizes, which can influence the stability and shelf life of drugs.
In pharmaceutical manufacturing, maintaining the correct density and specific gravity of formulations is essential for quality control. Deviations from the expected values can indicate errors in the manufacturing process, potentially leading to ineffective or unsafe medications. Incorrect calculations related to density, specific gravity, and specific volume can lead to dosing errors, which can pose serious risks to patients. Pharmacists must ensure that the prescribed medications are accurately prepared and dispensed to avoid adverse effects and enhance patient safety.
Density
Density is a measure of how much mass is contained in a given volume. It quantifies how tightly packed the particulate matter in a substance is.
Density information is more useful than just converting between mass and volume. In fact a high-density indicates the particles within the substance are densely packed, leaving them with limited freedom of movement. This restriction on their ability to move and flow freely mean this is a solid substance or semisolid substance requiring high shearing force during compounding. A higher density often implies higher mass, which means particles have greater inertia. This increased mass results in reduced kinetic energy, making the particles move more slowly and sometimes might require the addition of energy for example heating on a water bath to facilitate compounding.
High-density substances have tightly packed particles, making it more challenging for them to intermingle with other substances. The particles are less likely to spread out and mix thoroughly with substances of lower density. Pharmacists and Technicians in compounding needs to understand these physical properties and determine when pharmaceutical aids are required to facilitate mixing. For example oil is less dense than water, when compounding an emulsion an emulsifying agent is required to break the interfacial tension between the two substances allowing them to mix and form an emulsion. Due to the close arrangement of particles, there is limited intermolecular space in high-density substances. This limitation reduces the opportunities for other substances to permeate and integrate with the high-density material.
Specific Gravity
Specific gravity is a dimensionless quantity that compares the density of a substance to the density of a reference substance, usually water at a specific temperature. It provides a measure of how much denser or lighter a substance is compared to water. Since specific gravity is a ratio of densities, it has no units. Water at 4 degrees Celsius (39.2 degrees Fahrenheit) is commonly used as the reference substance for calculating specific gravity. If a substance has a specific gravity greater than 1, it is denser than water and will sink in water. If the specific gravity is less than 1, the substance is less dense than water and will float.
Specific gravity is widely used in various fields, including chemistry, pharmaceutical manufacturing, physics, engineering, and other industries, to characterize and compare the density of substances, particularly liquids and solids. Using the previous example, we can calculate the specific gravity of Glycerin.
If 30 mL of Glycerin weighs 24 g what is the specific gravity of Glycerin?
Since we need to find the specific gravity, we need to firstly convert the volume of the substance to weight of equal volume of water.
Since 1 mL of water = 1 g of water = 1 g of Glycerin
Therefore 30 mL of Glycerin = 30 g of Glycerin.
Specific Volume
This is the number of cubic meters occupied by one kilogram of a particular substance. The standard unit is the meter cubed per kilogram. Water at a temperature of 4 degrees Celsius is usually used as the standard for both liquid and solid. In other words, it quantifies how much space a given amount of a substance occupies.
Note, the unit of specific volume in the International System of Units (SI) is cubic meters per kilogram (m³/kg) as previously mentioned. Specific volume helps in understanding the amount of space a substance occupies per unit mass. Reviewing the example above, it means that one kilogram of aerogel occupies 0.33 cubic meter of space. Specific volume is particularly useful in thermodynamics, fluid mechanics, and engineering applications where understanding the spatial distribution of mass is important. Alternatively, we could calculate specific volume using the following formula.
Similarly to specific gravity, specific volume is dimensionless in this second example. Recall, Specific volume = 1/Density, meaning inverse proportionality. If you compare the previous response SG of Glycerin = 0.8 and V of Glycerin 1.25 you will also realize that these two are inversely proportional. It gets even more interesting, the product of specific gravity and specific volume must always be equal to 1 since the reference standard is water and the specific gravity of water is 1 at 4 degrees Celsius.
Make sure you work all the examples before viewing the answers below!
References
Ansel H.C & Stoklosa M.J (2010). Pharmaceutical Calculations (13th ed). Lippincott Williams & Wilkins
Winfield, A. J., Rees, J. A., & Smith, I. (2009). Pharmaceutical practice (4th ed.) Churchill Livingstone Elsevier.
Published: 2023- 10- 3