Moles & Avogadro's Constant

Basics

We will need to know the basic definitions that exams ask

Relative atomic mass - A_r

The average mass of a natural occurring atom of an element on a scale where a carbon atom has exactly 12 units

You can use this definition or the below one

The average mass of a natural occurring atom of an element compared to 1/12 th of a mass of a carbon - 12 atom

A good point to remember is that the mass of 1/12 of C - 12 atom is 1

MCQ's can give it in different ways such as the examples below

R.A.M = Average mass of an atom / ((1/12) * 12)

Same as:

R.A.M = Average mass of an atom *12 / 12

You will need to know how to calculate the relative atomic mass of an atom using different values of Isotopic masses. First let us see what is Isoptopic mass

Isotopes

Isotopes are atoms of the same element which has the same number of protons but different number of neutrons

For example the carbon element has 3 isotopes which are C-12 , C-13 and C-14. These all have the same number of protons because the proton number is used to uniquely identify each element

However, they all have different neutron numbers which results in different mass numbers also ( As mass/nucleon number is the total number of protons and neutrons in the nucleus of an atom)

More of isotopes will be discussed later

Isotopic mass

The mass of an atom of that particular isotope of an element

So you may see that different isotopes have different mass number. The mass number of each atom is called the isotopic mass and it is different for each isotope

Relative Molecular Mass - M_r

It is the mass of a molecule of a substance on a scale where carbon - 12 atom has exactly 12 units

You can also use the other definition if you want

This is found by adding the individual relative atomic masses of atoms in a molecule. For example HCl - 38.5

Relative Formula Mass - M_r

The mass of a formula of a substance on a scale where carbon - 12 atom has exactly 12 units

This is very similar to RMM however we use it in a different situation. We use it only for compounds and giant ionic structures

For example the relative formular mass of NaCl is 58.5

Also remember this is not molar mass but they both have the same values - this is because molar mass has units but RFM has no units

Also the relative formula mass is calculated depending on the formula given - keep in this mind as when the formula simplifies (empirical) it has a different value

Moles

1 mole of any substance has 6.02 * 10²³ atoms , molecules or formula units. This is also known as Avogadro's constant

This is how you must be defined

The reason why we use molecules , atoms or formula units is that this depends on the type of structure of the substance.

We will see 3 examples below

Let us take 1 mole of NaCl. This should contain 6 * 10²³ of what?

If it was a ionic compound like NaCl then it will give 6 * 10²³ formula units or groups of NaCl.

So this means there are 6 * 10²³ Na⁺ ions and also 6 * 10²³ Cl^- ions

Let's take a different example. Let's see 1 mole of Magnesium

This means that there are 6 * 10²³ Mg⁺ ions in the sample but because it is neutral we can say that it has 6 * 10²³ Mg atoms

Lastly, let's see 1 mole of Hydrogen gas

You need to know hydrogen exists as a diatomic moleculeof H₂

So 1 mole of H₂ will give us 6 * 10²³ molecules of hydrogen gas

To find the total number of atoms we just need to multiply by 2 as each molecule has 2 hydrogen atom

Important Equations

Now you need to know the most important equations in this chapter

• Finding the number of moles

To find the number of moles just divide the mass of the sample by its molar mass(relative formula mass)

Moles = Mass/Molar Mass

n = m / M

The reason we use molar mass is because it has units of g/mol. So this gives us the correct units for moles

Also remember we use grams as the units for mass



• Finding the concentration

Just divide moles by the number of by the volume of the solution

C = n / V

The units of the concentration is moldm^-3

This definition of concentration is very important especialy when talking about how rate is affected by the concentration




Mass Spectrometry



The mass spectrometer is a machine which used to calculate the relative atomic masses of fragments and atoms of different isotopes

We will see how we can use the mass spectrometer to calculate the relative atomic masses by finding the average of the isotopic masses

Before that, we need to know the parts of a mass spectrometer:

• Ioniser and Vaporiser

This part vaporises the elements to form gaseous atoms which are then bombarded with fast moving electrons. This causes the gaseous atoms to become ionised.

• Accelerator or an Electric field

This contains an electric field which accelerates the ions so they will all have the same kinetic energy

The masses will be different so it will result in different speeds

Remember that the work done by an electric field is irrespective of the mass. See more

• Deflector

This is a Tube which contains a magnetic field. This is used to deflect the ions depending on their mass to charge ratio

The Deflection depends on a quantity called mass-charge ratio

If the mass-charge ratio is greater then the deflection is less

Deflection ∝ 1/(mass/charge)

How do you calculate the mass to charge ratio of an ion!

We take the Nucleon number of the ion and divide it by the charge. For example, if I have a Na+ ion which has a nucleon number of 23 then the mass to charge ratio is also 23

23 = 23/1

For most examples and questions, we assume that the charge is +1 only and not greater. This means that the mass to charge ratio is equal to the nucleon number or the isoptic mass of an atom

To summarise, Deflection increases with charge and decreases with mass.

• Detector

The position of the ions and particles is detected by the detector and is recorded. This depends on the deflection of the ion(mass-charge ratio) but, we assume the charge is always +1

So usually on the detector, ions of the same mass will hit in the same place where as ions of different masses hits in a different place

Usually in exams, they will give an intensity graph where the intensity of each isotopic mass ( same as the mass of the ion ) is given



When the intensity is higher and at a greater peak then the relative abudance of the isotope of the element is greater, This means that there is a higher percentage of finding this particular isotope of an element

Here is the equation:

RAM = (Isotopic mass₁ * Intensity₁ + Isotopic mass₂ * Intensity₂ +...) / Total Intensity

There maybe many isoptopes for the same element and all will be different

This is gives the average mass of all the isotopes of an element depending on their relative abudance or percentage

The same could be achieved using percentages

We will use an example for this

There are two isoptopes of Sodium. Na - 23 has a relative abudance of 98% whereas Na- 24 has an abundance of 2%. Find the relative atomic mass of Sodium

RAM = (23 * 98 + 24 * 2 ) / 100

RAM = 23.02

Focus on where 98 and 2 adds up to 100. This is divided by 100

You can do it this way also which is basically the same thing

RAM = 23 * 98% + 24 * 2%

In the next chapter, we will discuss what is empirical and molecular formula and how we calculate them




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