Pharmacy Calculations## How to Calculate Molecular Weights and Moles

**Pharmacy students are expected to have a rounded knowledge of pharmaceutical calculations. Topics include concentrations, dilutions, isotonicity and displacement values. **

Here, we’ve put together a rapid review of molecular weights and moles; an essential topic that comes up time and time again.

In this guide, we review the fundamentals of the following topics:

- Calculating molecular weights
- Calculating moles
- Calculating the number of molecules in a sample

Let’s begin right away, then, with how to calculate molecular weights.

**What is the molecular weight of methane, CH _{4}?**

**First** – find how many atoms of each element in the formula.

In this case, there is 1 atom of carbon and 4 atoms of hydrogen.

**Second** – consult the periodic table to find each element’s relative atomic mass. The relative atomic mass accounts for all isotopes of the element as they naturally occur.

**Third** – multiple the relative atomic mass value by the number of atoms of each element.

In the case of methane, then:

- 1 atom of carbon = 12
- 4 atoms of hydrogen = 4 x (1) = 4

Adding the two values together, then, we find the molecular weight of methane is 16.

Let’s review at one more example.

**What is the molecular weight of glucose? **

The chemical formula of glucose is C_{6}H_{12}O_{6}.

Following the three steps above, we find that glucose has:

- 6 atoms of carbon = 6 x (12) = 72
- 12 atoms of hydrogen = 12 x (1) = 12
- 6 atoms of oxygen = 6 x (16) = 96

The molecularweight of glucose is, then, 180.

Calculating the number of moles in a sample is simple. Here are the fundamental steps you must take.

**Calculate the number of moles in 30 grams of sodium sulfate.**

The chemical

formula of sodium sulfate is Na_{2}SO_{4}.

**Step 1** – calculate the molecular weight of the compound. For now, forget the number of grams of the compound. We use that

value later.

For this, we follow the same procedure that we did for examples 1 and 2.

- 2 atoms of sodium = 2 x (23) = 46
- 1 atom of sulfur = 1 x (32) = 32
- 4 atoms of oxygen = 4 x (16) = 64

The total molecular weight of sodium sulfate is 142.

**Step 2** – divide the mass of the sample by its molecular weight.

In this case, the question states the sample mass is 30 grams.

- 30 grams of sodium sulfate divided by its molecular weight – which we found to be 142 – gives us a value of 0.2113 moles.

There are 0.2113 moles in 30 grams of sodium

**Find the number of molecules in 30 grams of sodium sulfate.**

This is an extension of example 3 – this time, it asks us to calculate the number of molecules in 30 grams of sodium sulfate.

To calculate the number of molecules, we must first know the total number of moles in 30 grams of sodium sulfate. We learned that figure to be 0.2113.

To find the number of molecules, we simply need to go one step further – multiplying that value by Avogadro’s number – 6 x 10^{23}.

0.2113 x (6 x 10^{23}) = 1.27 x 10^{23} molecules in 30 grams of sodium

**How many millimoles of chloride are in 300mg of calcium chloride?**

The chemical formula of calcium chloride is CaCl_{2}.

This means there is 1 mole of calcium ions and 2 moles of chloride ions.

First, we must discover how many moles are in the total compound. The molecular weight of calcium chloride is 110.

We have 300mg of calcium chloride. We must convert this to grams – 0.3 grams.

Like before, we divide the sample mass by the molecular weight – in this case, 0.3 divided by 110 – to give us 0.0027 moles.

300mg of calcium chloride contains 0.0027 moles – or 2.7 millimoles.

**Conclusion** – there are 2.7 millimoles of calcium and 5.4 millimoles of chloride in 300mg of calcium chloride.

**How many millimoles of sodium are found in 0.9% sodium chloride?**

0.9% refers to 9 grams per 1000mL.

The molecular weight of sodium chloride is 58.5 (consult periodic table for values).

As the sample has 9 grams of sodium chloride, we divided 9 grams by its molecular weight – 58.5 – to find the total number of moles.

9 grams NaCl / 58.5 = 0.154 moles

0.154 moles is the same as 154 millimoles.

This means there is 154 millimoles of sodium ions and 154 millimoles of chloride ions.

We hope that these six examples nourish your understanding of molecular weights and moles; a fundamental concept that comes up time and time again in pharmacy calculations.

If you’re still unsure how to calculate molecular weights and moles, we encourage you to check out three additional articles we’ve covered on this topic:

Calculations