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# Moles and Molar Mass

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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.

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

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.

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.

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

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

## Moles and Molar Mass Quiz - Teste dein Wissen

Question

C2H5N(CH2CH2Cl)is a type of nitrogen mustard mainly which was used in World War I to kill a lot of soldiers. However, I use it in the lab to create catalysts. I forgot to write up the molar mass. Can you help me figure it out?

Well, first you have to count up all the elements in the molecule.  Remember everything in the brackets is counted as many times as the subscript of the brackets. So, there are 6 carbons, 13 hydrogens, 2 chlorines and 1 nitrogen. This gives us a molar mass of 170.08 g/mol.

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Question

Calculate the molar mass of water H2O and heavy water D2O.

Hint: The atomic weight of Deuterium (D) is not in the periodic table. You can google it or treat it as 2.0 for this exercise.

Water consists of 2 hydrogens and one oxygen while heavy water consists of 2 deuteriums and one oxygen. Now we have to add up the atomic weights ( 1+1+16 for water and 2+2+16 for heavy water). So, you end up with 18 g/mol for water while for heavy water you get 20g/mol.

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Question

What is the molar mass of H2?

It is 2 g/mole. You can get this by adding up the atomic mass 1 twice.

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What is the atomic weight of Li2S?

It is 45.95 g/mol. You can get this by adding up the atomic weights of 2 lithium atoms and 1 sulfur atom.

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Question

One of the most important proteins in Sars-CoV-2 (Covid-19 virus) has the composition of :
Carbon-1499 pieces, Hydrogen-2318 pieces, Nitrogen-402 pieces, Oxygen-445 pieces, Sulfur-22 pieces.

Yes, this is just one big molecule. Can you tell me the molar mass of this monstrosity?

Just like with any other compound, we can simply add up everything.
1499 * 12 + 2318 * 1 + 402 * 14 + 445 * 16 +22 * 32 = 33758 g/mol

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Question

If you consume 4 coffees at once, this is equivalent to 400mg of caffeine. You can survive up to 10 millimoles at once. (fictional value, don't try this!)

The molar mass of caffeine is 194.19 g/mol. Will you be okay?

Dividing 400 milligrams by 194.19 grams per mole gives us 0.0021 moles or 2.1 mmoles, so most likely you will be okay.

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Question

How much do 2 moles of NaCl ( table salt) weigh?

First, we have to calculate the molar mass which is found to be 58,44 g/mol. Now, multiply this by the number of moles to get 116.88 grams.

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Question

Calculate the molar mass of HCl.

The molar mass of HCl is calculated like this:

1 Cl and 1 H builds up the molecule.
M(HCl) = 1*35.45 +1 *1.01 = 36.46 g/mol

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Question

UFis used to enrich uranium for reactors. Can you calculate the molar mass of this gas?

The molar mass can be calculated like this :
M(UF6) = 6* 19.0 + 1* 238.0 = 352.0 g/mol

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Question

What is the molar mass of acetic acid? The formula is C2H5OH it is often abbreviated as AcOH.

Acetic acid weighs 46.0  g/mol.

M(AcOH) = 6*1.0 +2*12.0+16.0 = 46.0 g/mol

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Question

Porphyrin is a very important structure in nature it is present in almost all lifeforms in some way or another. The basic structure has the formula of :
C20H14N4

What is the molar mass of it?

The molar mass can be calculated as :

20* 12.0 + 14*1.0 + 4*14.0 = M(Porphyrin) = 310 g/mol

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Question

Calculate the molar mass of glucose:

Structure:  C6H12O6

The molar mass can be calculated like this:

M(Glucose) = 6* 12.0 + 6*16.0+12*1.0 = 180.0 g/mol

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Question

How heavy is a diamond made up of 3.01* 10^23 carbon atoms?

A diamond is solely made out of carbon.
Converting 3.01*10^23 to moles (dividing by Avogadro's number 6.02*10^23) gives us 0.5 moles.

n(diamond) = (3.01*10^23)/ (6.02*10^23) = 0.5 mol

m(diamond) = n(diamond) * M(diamond) =n(diamond) *M(C) = 0.5* 12.0 = 6 g

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Question

How many moles are in 23g of Na metal?

M(Na) = 23.0g/mol

23.0g/23.0g/mol = 1 mol = n(Na)

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Question

Is Avogadro's number connected to the concept of moles?

Yes, Avogadro's number tells you how many atoms are in a mole of a substance. 6.02*10^23 atoms.

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Question

What is the molar mass of HF?

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Question

How many moles are there in 130 g of Chlorobenzene? (C6H5Cl)

That is the equivalent of 1.16 moles

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Question

There are about 1.35g of caffeine in 100 grams of coffee beans. How many moles of caffeine are there in a 1-pound bag of coffee?
Caffeine has the following chemical formula: C8H10N4O2

There are about 450 g in one pound which translates to 6.1 grams of caffeine. Now we need the molar mass to convert this quantity into moles. M = 194.2 g/mol for this one.
Dividing 6.1 / 194.2 gives us 31.41 mmoles

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Question

Can you tell me how many atoms of carbon there are in a 5-carat diamond? ( 1 carat is 0.2g )

5 carat is roughly 1 g. A diamond only contains carbon atoms so the "molar mass" of diamond is 12.0 g/mol. So, the number of atoms is 1 g /  12g/mol * Avogadro's number ( roughly 6.02*1023) .This comes out to about 5*1022 carbon atoms.

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Question

What is the molar mass of NaI ?

149.9 g/mol

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Question

Molar mass of Al2O3?

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Question

_______ is referred to as the number of protons plus the number of neutrons.

Mass number

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Question

______ is the number of protons.

Atomic number

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Question

The elements on the periodic table are ordered by ______ number.

Atomic

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Question

Isotopes are atoms of the same element with the same number of ______ (atomic number), but different numbers of  ______.

Protons; neutrons

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Question

The most abundant isotope of hydrogen is called ______.

protium

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Question

The isotope of hydrogen called deuterium, contains ____ proton and ____ neutrons.

1 ; 1

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Question

The _______ of an isotope is referred to the percentage of atoms with a specific atomic mass found in a naturally occurring sample of an element.

Relative abundance

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Question

The ______ of an element is referred to as the weighted average of all the isotope's individual masses.

Relative atomic mass

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Question

True or false: Radioactive isotopes are those in which the nucleus spontaneously decays, releasing radiation.

True

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Question

The relative stability of the nucleus is determined by the number of _____.

neutrons

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Question

In ______, the atom nucleus gives out an alpha particle (two protons and two neutrons).

alpha decay

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Question

An alpha particle is a ____ nucleus with two protons and two neutrons.

helium

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Question

In beta decay, the atom loses an electron, giving out a beta particle, which is a ____.

electron

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Question

What is the value for Avogadro's number?

6.022x1023

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Question

How many moles of oxygen are in Au(NO3)3?

9

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Question

What the molecular weight of a compound?

The total mass of the compound

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Question

What is the molecular weight of C6H5Br?

157.01 g/mol

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Question

How many molecules are in 3 mols of XeF6? How many atoms of F?

a) 1.807 x 1024 molecules

b) 1.084 x 1025 atoms

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How many grams are in 2 mols of ZnCl2?

272.60 g

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Question

What is the relationship between mols and Avogadro's number?

1 mol is equal to Avogadro's number

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Question

What does amu stand for, and how is it related to moles?

amu stands for atomic mass unit. 1 amu=1 g/mol

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Question

What is the percent composition of Cl in FeCl3?

65.6%

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Question

True or False: Avogadro's number is equal to 6.022 x 1023 atoms

False

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Question

How many atoms of oxygen are in 34.2 g of H2SO4

8.4 x 1023 atoms

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Question

How many grams of fluorine are in a compound with a molar mass of 48.2 g/mol when the percent composition is 36.8%?

17.7 g

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Question

True or False: To convert from molecules to moles, you divide by Avogadro's number

True

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Question

Mass spectrometry is a method used to determine the _______ of atoms/molecules in a sample

atomic mass

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Question

In mass spectrometers that use electron impact ionization (EI)a beam of electrons is used to remove an electron (or electrons) from a molecule, forming a _______, also called a molecular ion.

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Question

True or false: A radical cation has both a positive charge and an unshared electron.

True

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