The Mole and Avogadro’s Constant

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The Mole and Avogadro’s Constant

If you were searching for methods to get rid of the moles that are ruining your garden, then unfortunately this is the wrong place. Nor is it the mole that you may see on someone’s chin. But the mole we will be talking about is also very important and infests throughout chemistry. It is the international unit for the amount of substance. And if you came exactly for this mole, then “Welcome”.

Which came before? The mole or Avogadro’s constant? This is a question harder than “Which came first, the egg or the chicken?” Let’s look a bit at the history. Oh, if you are still wondering about the egg and the chicken, the answer is “The egg”.

Origin of Avogadro’s Law and The Mole

The Avogadro’s constant and the mole have an intertwined history.

In the year 1803, English chemist John Dalton revitalized the idea of Democritus that every substance is made up of tiny atoms. And this got Amedeo Avogadro, an Italian scientist, thinking about the relation between the amount of substance and the number of atoms.

He observed many things, like the electrolysis of water produced hydrogen gas and oxygen gas in a 2:1 volume ratio. From his observations, in the year 1811, he proposed that an equal volume of gasses contains an equal number of atoms or molecules under the same condition regardless of the nature of the gas. Which is known as Avogadro’s law or hypothesis. But he could not calculate the number of molecules in an amount of gas yet.

Not much was done about this number of atoms or molecules after that for a while. But the concept of the mole was developing. Because, by that time, the term relative mass was already familiar to scientists and they calculated in terms of mass. Relative mass is in the end, the ratio of masses of atoms that has no unit. So, even if you expressed these relative masses in other units their ratio would hold.

And this relative mass expressed in gram was called a mole of that substance. It is not as complex as it sounds. Let’s look at an example. The relative mass of the carbon atom is 12. So 12g carbon means 1mole carbon. Similarly,

1 mole of hydrogen= 1g hydrogen

1 mole of aluminum= 27g aluminum

I know what you’re thinking: “How did it get the name mole?” German chemist Ostwald coined the unit Mol from the word Molekül in the year 1894. Mole is the translated form of mol.

Note that the number of atoms in a mole is the same for every element, the same as Avogadro’s law.  But the value of this number could not be obtained for a long time. No, its approximate value was actually determined by Joseph Loschmidt in 1865 albeit indirectly and the term, Avogadro’s constant, was still not there. And so, people were still unaware of this discovery.

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This term was first introduced by Jean Perrin in 1909 who defined it as the number of molecules in 32 grams of oxygen as it was the standard of the relative mass at that time. But as said earlier, they had yet to know the value.

Perrin finally had a breakthrough when Robert Millikan determined the charge of an electron through his oil-drop experiment. And the value of the total charge of 1mole of electrons, the Faraday constant, was already known to scientists since 1834. Although you read a bit earlier that the term mole was introduced in 1894, there was already a term known as the equivalent mass which is similar to the mole but depends on valency. For electrons the mole and the equivalent mass have the same value and so is the total charge.

You might now wonder how did the scientists manage to determine the total charge of a mole of electrons without knowing their number. The answer is electrolysis. Faraday is the pioneer in this case. He determined the Faraday constant by measuring the amount of electricity needed to obtain one mole of mono-valent metal through electrolysis.

The value of Faraday constant= 96485 C = Total charge of one mole of electrons.

Charge of an electron= 1.602×10−19 C

So, Avogadro’s constant NA= 96485 C1.602×10-19 C = 6.022×1023

Jean Perrin later calculated the value of Avogadro’s constant in many different ways and was awarded the nobel prize for his work in 1926.

Knowing the past helps us learn new things from the people that came before us. We can learn both from their success and failure. Although you will not need history to do calculations involving moles or Avogadro’s constant, this story teaches us how the things we need might be in front of us and be never noticed.

This should be enough about history. Let’s look at the exact information you need to know.

Avogadro’s Constant or Avogadro’s Number

You have seen that the Avogadro’s constant is defined as the number of atoms in 16g of oxygen or the number of molecules in 32g of oxygen. We have to clarify because oxygen is found as O2 in nature which contains 2 atoms per molecule.

But this definition changed over time. Carbon-12 isotope replaced oxygen as the new standard. And so, the definition changed to- the number of atoms in 12.00g of carbon-12.

The definition changed yet again and in the year 2017, the BIPM (Bureau International des Poids et Mesures) defined Avogadro’s constant as the exact value of 6.02214076×1023. It is expressed with N or NA. The value can be rounded up to 6.0226×1023.

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This value is insanely larger than it looks. Let’s write it without using the scientific form.

602,214,076,000,000,000,000,000- That’s 602 sextillion or two times billion.

There is no analogy that you can easily imagine and understand. Suppose, the earth was completely made up of softballs. The seas, mountains, buildings, everything. The number of softballs you would need is Avogadro’s number.

Or suppose, you stacked 1 mole of papers. Paper sheets are very thin. So how high will the stack be? Any guess? If your answer is up to space then you are not right. The stack will reach space and beyond. It is so high that it will go up to the moon and back 80 billion times. How big is that!!

Now imagine 6.02214076×1023 water molecules. How much would that be? Hold tight, it’s about the amount you drink in a sip.  That is 18 mL of water. No need to worry, atoms are that small. It’s a perfect contrast.

It would take 20 drops of water to form a milliliter. Just think, for each drop of water people waste, 1.67 x 10^21 molecules of water are wasted.

Never waste even a drop of water.

The Mole

As said earlier, it is not the furry earth animal, it is a unit. Specifically, a counting unit.

It is defined as the amount of substance that contains 6.02214076×1023 number of atoms, molecules, ions, particles, or any entities is called a mole of that substance. It is expressed with n. It can also be abbreviated to mol.

But 6.02214076×1023 is Avogadro’s constant. So, do you get it now? A mole is any amount that contains Avogadro’s number of particles.

The mole is similar to the dozen. Let’s see,

1 dozen apples= 12 apples

1 dozen eggs= 12 eggs

So,

1 mole apples= 6.02214076×1023 apples

1 mole eggs= 6.02214076×1023 eggs.

It is as simple as it looks.

Now let’s see how the mole relates to the mass of a substance. As you’ve already seen, the mole is defined in a way so that the mass of a mole of any substance is the same as the relative mass expressed in gram. So,

1 mole of carbon= 12g carbon

1 mole of aluminum= 27g aluminum

And this mass of 1 mole of any substance is called the molar mass of that substance which has the unit gmol-1.

Thus, you can say,

number of moles (mol), n=mass of substance in grams gmolar mass g mol–1

or n= mM

You must have thought many times by now, “Why is mole so important?” It’s because most of the measurements in chemistry are done in terms of moles. The mole can at the same time relate both the mass of the substance and the number of atoms or molecules. Also, chemical substances react in terms of numbers and the mole represents a whole number. So, the mole is also used in expressing reactions and plays a great role in quantitative chemistry.

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It’s common knowledge that 2 atoms of hydrogen react with one atom of oxygen to produce 1 molecule of water. Now, this can be also said in terms of mole.

2 mol hydrogen + 1 mol oxygen= 1 mol water.

H2 + 12 O2 = H2O  [Hydrogen and oxygen are diatomic gases]

You don’t get much information using only numbers of atoms. But from this mole equation, we can immediately know,

2g hydrogen+ 16g oxygen= 18g water

The benefits of using the mole unit are way more than this.

Let’s do some mathematical problems involving the mole now.

How to calculate the mole numbers of a given amount of substance

The equation that relates the mole and mass of the substance is,

number of moles (mol), n=mass of substance in grams g, mmolar mass g mol–1, M

Note that the mass of the substance has to be in grams. And you already know that the molar mass is basically the relative mass expressed in grams or in this case, gmol-1.

Problem 1: Use these Ar (relative atomic mass) values (Fe = 55.8, N = 14.0, O = 16.0, S = 32.1) to calculate the amount of substance in moles of 10.7 g of sulfur atoms

Solution: 

Molar mass of sulfur atoms= 32.1 gmol-1

Mass of given sulfur atoms= 10.7 g

So, number of moles= 10.7 g32.1 gmol-1

= 0.33 mol

Suppose, what’s given is the number of moles and you are told to determine the amount of substance, how would you do that? Have you already figured it out? Yes, you just need to rearrange the above equation. After rearranging we have,

Mass of substance in grams (g)= number of moles (mol)×molar mass (gmol-1)

Problem 2: Calculate the mass of 0.050 moles of sodium carbonate, Na2CO3 (Ar values: C = 12.0, O = 16.0, Na = 23.0).

Solution: Molar mass of Na2CO3 = (23×2) + 12 + (16×3) gmol-1

= 106 gmol-1

Number of moles= 0.050 mol

Thus, mass of 0.050 moles of Na2CO3= 106 gmol-1 × 0.050 mol

=5.3 g

Pretty easy, right?

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Have a good day!!

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