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# Tutorial: Density and Specific Gravity.

Mar 31st, 2024

### Density and Specific Gravity on the PTCB Exam

Both density and specific gravity calculations are tested on the PTCB exam.

Whilst you are unlikely to encounter challenging questions on either of these two topics, you should nonetheless be familiar with the definitions of both terms as well as how to calculate simple density and specific gravity questions.

In this tutorial, we will learn more about both density and specific gravity – and why an understanding of these two concepts is essential in pharmacy.

### What is Density?

Density is a property of matter that measures how much mass is contained in a given volume.

An object with high density has more mass within a contained volume compared to an object with low density. Wood has a lower density than iron, for example, because the atoms in iron are more tightly packed together. This means that wood can float on water whereas iron nails are likely to sink.

Understanding density in the pharmacy setting is essential because some ingredients must be converted from solid to liquid, and knowing the density of the liquid is very useful.

Mathematically, density (ρ) is calculated as the mass (m) of an object divided by its volume (V):

Density = Mass / Volume

Density is an intensive property, meaning it doesn’t change with the quantity of the substance, unlike extensive properties like mass or volume. This means that regardless of the amount of material present, the density of a substance remains constant under given conditions of temperature and pressure.

Sample Question 1.

Find the density of 250 mL of alcohol that weighs 203 grams.

Density = Mass / Volume

Density = 203 g / 250 mL

Density = 0.812 g/mL

Sample Question 2.

A pharmacy has a stock solution of medication with a density of 1.05 g/mL. The prescription calls for a 200 mg / 5 mL concentration of the active ingredient. How much stock solution is needed to prepare 300 mL of the prescribed concentration?

Step 1: Calculate the amount active ingredient needed for the prescription:

Mass of active ingredient = Desired concentration × Volume

(200mg / 5 mL)  × 300mL = 2000 mg

In other words, we need 300 mL of final solution.

Each 5 mL of this solution must have 200 mg of active ingredient. Therefore, we multiply both together to find out the total amount of active ingredient needed.

In this case, the 300 mL solution must have 2,000 mg of active ingredient.

Step 2: Convert to grams (since density is measured in g/mL):

2000mg = 2 grams

Step 3: Calculate volume of stock solution needed to obtain 2 grams of the active ingredient:

We learned earlier than Density = Mass / Volume.

We have density and mass, but we are looking for volume. So, by re-arranging the equation, we can establish that:

Volume = Mass / Density

Volume = 2 / 1.05 = 1.9 mL

1.9 mL of stock solution is needed to prepare 300 mL at the prescribed concentration.

### What is Specific Gravity?

Like density, every substance has a specific gravity. Specific gravity is not only useful in pharmacy but also medicine generally. For instance, the concept is widely applied as a diagnostic tool in urine samples.

Specific gravity is the ratio of the weight of a substance compared to the weight of the same amount of water. In other words, specific gravity is how heavy a substance is compared to water.

Specific Gravity = Weight / Weight of Equal Volume of Water

For example:

• If a substance has a specific gravity of 0.8, it is 20% lighter than water.
• If a substance has a specific gravity of 1.5, it is 50% heavier than water.
• If a substance has a specific gravity of 1, it is the same weight as water.

Let’s review some sample questions.

Sample Question 3.

Calculate the specific gravity of 200 mL of sorbitol solution that weighs 227 grams?

Specific Gravity = Weight / Weight of Equal Volume of Water

Specific Gravity = 227 grams / 200 mL

Specific Gravity = 1.13

As we learned above, we can conclude that this solution is approximately 13% heavier than water.

Sample Question 4.

In the pharmacy, you are presented with 3 fl. oz. of glycerol weighing 111.15 grams. Find its specific gravity.

1 fl. oz = 29.57 mL

Therefore 3 fl. oz. is the same as 88.71 mL

Now that we have the volume, we can complete the equation:

Specific Gravity = Weight / Weight of Equal Volume of Water

Specific Gravity = 111.15 grams / 88.71 mL

Specific Gravity = 1.25

Therefore, the glycerol weighs 25% more than water.

### Similarities

You may have noticed the core similarity between both density and specific gravity – namely, that both equations involve dividing mass by volume:

Density = Mass / Volume

Specific Gravity = Weight / Weight of Equal Volume of Water

Furthermore, both equations use grams for mass and mL for volume.

For this reason and given their conceptual equivalence, both terms are often used interchangeably in compounding.

When answering PTCB calculation questions, it’s important that you keep an eye on units. Anything other than grams or mL means you will need to perform a conversion.

### Tutorial Review

Over the course of this tutorial, we have learned:

• Density is a property of matter, defined as how much mass is contained within a defined volume.
• Substances with higher densities (such as iron) have atoms more tightly packed together (such as gas or wood).
• Density can be calculated using the formula:

Density = Mass / Volume

Where mass is in grams and volume is in milliliters.

• Specific gravity is the ratio of the weight of a substance compared to the weight of the same amount of water.
• Specific gravity can be calculated using the following formula:

Specific Gravity = Weight / Weight of Equal Volume of Water

• Water has a specific gravity of 1, and so substances with a specific gravity less than 1 are lighter than water, and substances with a specific gravity more than 1 are heavier than water.
• Both density and specific gravity are similar and are often used interchangeably in the pharmacy setting.

The PTCB exam questions in this tutorial are the standard and style of density and specific gravity questions you can expect to encounter on the day of your exam. More complex examples are highly unlikely to appear.

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