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# Moles and Molar Mass

Let's say you work at a candy store and a customer asks for different amounts of candy (100, 250, 1000…), so you count out each order. This is a very long and tedious way to do business! Instead, you utilize the average mass of the candy. If you know the mass, you can multiply that by the desired quantity and add the candy to a scale until you reach that weight.

We treat atoms the same way! To find out how many atoms are in a sample, we can relate the mass of the sample to the number of atoms. However, we first need to know the average mass of each atom.

In this article, we will discuss how chemists measure and group the masses of atoms and molecules.

• First, we will define a mole and explain why that unit is used
• Next, we will explain the concepts of atomic mass and molar mass and the differences between the two
• Then, we will explain the concept of molecular mass and explain the differences between it and molar mass
• Lastly, we will look at the link between molar mass and boiling point.

## The Mole

How are chemists able to measure things when everything is made up of different atoms and, to make this more difficult, different isotopes of those atoms? With moles, of course! Not with the small subterranean mammal (though they are cute), but the unit moles.

A mole is a unit used to denote the number of particles, atoms, and compounds. It refers to 6.022x1023 units of a substance, which is Avogadro's number (after Italian chemist Amedeo Avogadro).

Atoms are incredibly small, so if you were to try and count the number of atoms just in a drop of water, you would be there for a while. Moles are used as a way to count atoms/molecules in "bundles", like how we count eggs in a dozen.

## Atomic Mass and Molar Mass

When we measure things in bulk by grams, we refer to the molar mass.

The molar mass is the mass of a substance (in grams) divided by the amount of the substance (in moles). The molar mass is the average of weights, which usually vary due to isotopes. The formula is $$M=\frac{m}{n}\,\,\text{where m is mass and n is the number of moles}$$

Isotopes are elements with the same number of protons, but a different number of neutrons. (Ex: Carbon-14 has 6 protons and 8 neutrons, while Carbon-12 has 6 protons and 6 neutrons)

Molar mass is an "umbrella term" as it can refer to either the atomic weight or molecular weight (which we will discuss later).

The atomic weight of an element is an average of the weight of its isotopes with respect to their relative abundances (Ex: If chlorine-37 makes up 24.33% of all chlorine atoms, then it makes up that percentage of the atomic weight)

The atomic weight is the mass listed in amu (atomic mass units) below an element on the periodic table. It's common for this to be referred to as the atomic mass, even though that is something slightly different (confusing, I know).

As an example, here is what lithium looks like on the periodic table.

Periodic table entry for Lithium. Wikimedia Commons.

The atomic number (number of protons) is listed at the top, the element symbol in the center, and the atomic weight at the bottom. How exactly was this number determined? The atomic weight is determined by taking the known abundance and mass of each isotope and solving for the average.

For Lithium, there are two isotopes: Lithium-6 (7.59 %) and Lithium-7 (92.41 %). So, we can calculate the atomic weight: $$(7.59\%*6.015\,amu)+(92.41\%*7.016\,amu)=6.94\,amu$$

So what is atomic mass, then?

The atomic mass is the mass of a single atom/isotope. It is calculated by adding the number of protons and neutrons (electrons are considered too light and are negligible).

When we calculated the atomic weight, we were using the atomic masses of each isotope. For example, when we refer to lithium-6, we mean the specific isotope with an atomic mass of 6.015 amu. However, when we refer to lithium as a whole (weighted average of both of the known isotopes), we refer to its atomic weight of 6.94 amu.

Just remember that you may find sources that refer to atomic weight as atomic mass, just keep in mind the difference, so you don't get confused!

## Difference Between Molar Mass and Atomic Mass

To summarize, molar mass is an umbrella term referring to either the average masses of an element per mole (atomic weight) or compound per mole (molecular weight). The atomic mass does not fall under the molar mass umbrella since it is not an average, but the mass of a single element/isotope.

## Molecular Mass and Molar Mass

Using atomic masses, we can calculate the molecular mass.

The molecular mass is the sum of the atomic masses of the elements present in the molecule.

Molecular mass is different from molecular weight.

Molecular weight is the sum of the atomic weights of the elements present in the molecule.

As I mentioned before, atomic mass and atomic weight are often used interchangeably, so molar mass, molecular mass, AND molecular weight are also often used interchangeably. Thus, the context and questions must be clear when discussing these terms! Always be careful when reading textbooks and problems to see if when "molecular mass" is mentioned they actually mean "molecular mass" or if they mean "molecular weight" instead.

As a guide to get you used to this, if I am using a term with its original definition, it will be in green, if I am using it with its colloquial definition it will be in red.

The molecular weight of water can be calculated by adding together the atomic masses of the elements in it. Water is made up of 2 hydrogens and 1 oxygen, and the atomic mass of hydrogen is 1.01 g/mol and the atomic mass of oxygen is 16.00 g/mol. The molecular mass would then be: $$(2*1.01\frac{g}{mol})+16.00\frac{g}{mol}=18.02\frac{g}{mol}$$

It is important to remember that atomic weights used in the calculations above are averages for their respective element. Our calculated value, therefore, represents an average molecular mass for a given molecule of water. There are 2 stable isotopes of hydrogen and 3 for oxygen, which makes the exact molecular mass for 1 molecule of water vary greatly!

## Difference Between Molar Mass and Molecular Mass

The amount of swapping between terms can make it hard to tell the difference between them. The main thing to remember is that the molecular mass is the mass of that specific instance of the molecule, while the molar mass is the average of all instances of that molecule based on their abundance. Molecular weight is the term that is synonymous with molar mass.

Chart showing the relationship between terms. StudySmarter Original.

## Molar mass and boiling point

Several factors affect a substance's boiling point, one of them being the molar mass. In general, the larger the molar mass, the larger the boiling point.

Boiling point is also dependent on atomic mass. Since isotopes have different masses, they will also have different boiling points. Like with the general trend, the greater the atomic mass, the greater the boiling point.

Molecules follow the same general trend, however, just because a molecule is heavier, doesn't necessarily mean it will have a higher boiling point. For example, the boiling point of ethanol (CH3CH2OH, molar mass=46.07 g/mol) is 78.4 °C, however, water (molar mass=18.02 g/mol) has a boiling point of 100 °C. This is due to intermolecular forces, which are the forces that exist between molecules. The stronger these forces are, the harder it is for molecules to "pull away" from each other and enter the gas phase.

It is more accurate to compare the molar masses of like molecules, such as in the graph below:

Relationship between molar mass and boiling point for different molecule types. Wikimedia Commons.

Here we see that when molecules are in the same "class", an increase in molar mass means an increase in boiling point.

## Moles and Molar Mass - Key takeaways

• A mole is a unit used to denote the number of particles, atoms, and compounds. It refers to 6.022×1023 units of a substance. This number is referred to as Avogadro's number.

• The molar mass is the mass of a substance (in grams) divided by the amount of the substance (in moles). The molar mass is the average of weights, which usually vary due to isotopes. The formula is $$M=\frac{m}{n}\,\,\text{where m is mass and n is the # of moles}$$

• The atomic weight of an element is an average of the weight of its isotopes with respect to their relative abundances.

• The atomic mass is the mass of a single atom/isotope. It is calculated by adding the number of protons and neutrons (electrons are considered too light and are negligible).

• The molecular mass is the sum of the atomic masses of the elements present in the molecule. While the molecular weight is the sum of the atomic weights of the elements present in the molecule.

• For elements, the greater the molar mass, the greater the boiling point. Molecules of the same type follow this trend.

#### Flashcards in Moles and Molar Mass 10

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How do I find molar mass with moles and grams?

Molar mass is defined as the number of grams per 1 mole.

Are atomic mass and molar mass the same?

No, as molar mass refers to the average weight of all isotopes, while atomic mass refers to the mass of a specific instance of that element.

Are molar mass and molecular mass the same?

No, as molar mass is an average of all instances of a molecule, while the molar mass is the mass of one specific instance of a molecule.

What are the molar masses of magnesium and atomic oxygen?

The molar masses for magnesium and oxygen are 24.31g/mol and 16.00 g/mol, respectively.

What is the formula molar mass and color of potassium?

Using the periodic table, we see that the molar mass of potassium is 39.1 amu. Potassium metal is silver in color.

## Test your knowledge with multiple choice flashcards

Silicon (Si) has three stable isotopes: Si-28 (27.98 amu, 92.23 % abundance), Si-29 (28.98 amu, 4.67 % abundance), and Si-30 (29.98 amu, 3.10 % abundance). What is the atomic weight of silicon?

Calculate the molar mass of acetanilide (C8H9NO). The molar masses are: C=12.01 g/mol, H=1.01 g/mol, N=14.01 g/mol, O=16.00 g/mol.

Fill in the blanks: ___ is the mass of a single atom/isotope, while ___ is the weighted average mass of all isotopes of that element.

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