Atomic Theory

The calculation of Average Atomic Weight

Let’s Review

• Elements exist as atoms – the smallest part of an element that is still that element.

• You can think of atoms as “nature’s basic building blocks”

• Atoms have two regions that we care about – the nucleus and the electron cloud.

Particles in the Atom

• We have learned that the nucleus contains two particles.– Protons that have a

positive charge– Neutrons that do not

have a charge – they are neutral.

• As a result – the nucleus has a positive charge.

• The electron cloud is mostly empty space and contains the electrons.– Remember that the

electrons have a negative charge

– Remember too that the number of protons equals the number of electrons.

• As a result, the atom is neutral – it has no net charge.

Review of Vocabulary

• Atomic Number– Remember that the

atomic number is defined as the number of protons.

– It also gives you the number of electrons

– It is found on the periodic chart above the atomic symbol

• Mass Number– This is defined as the

sum of the protons and neutron in an atom’s nucleus.

– It is NOT found on the periodic chart – you have to be given information to calculate this number (or it is simply given to you)

Isotopes

• These are atoms of a single element that have different mass numbers.

• They will have the same number of protons and the same number of electrons.

• But, they will have different numbers of neutrons – this is why they have different mass numbers !!

Now for some new stuff…

• You already know that atoms are really really really small.

• Because they are so tiny, science has created a special unit for describing their weight – its called the “atomic mass unit” or

“amu” .

Here is how the “amu” connects.

• Each proton in the nucleus has a mass of 1 amu.

• Each neutron in the nucleus has a mass of 1 amu.

• But – the electron is sooooo small that science ignores its weight – we say that it weighs zero.

Connecting to the Isotopes

• Consider an atom that has 12 protons and 14 neutrons (this was on the worksheet on isotopes).

• Since each of the protons weighs 1 amu, the protons weigh (all together) 12 amu’s.

• Since each of the neutrons weighs 1 amu, the 14 of them all together weigh 14 amu.

• Therefore – the complete nucleus weighs

12 + 14 = 26 amu

Continuing….

• So, we can now say that the mass of any atom is simply the total of the protons and neutrons in the nucleus.

• Question for you – what do we call the sum of the protons and neutrons ????

• This means that we can say that the mass of the carbon – 14 isotope is simply 14 amu.

• Or we could say that the mass of the uranium – 238 isotope is 238 amu.

• Do you see how this works??

Changing directions a bit.

Mg12

24.305

Here is one of the elements from the periodic chart.

You know that it represents magnesium from the symbol.

You also know that the “12” at the top is the Atomic Number that tells you the umber of protons and the number of electrons.

But what about the number at the bottom?

Mg12

24.305

What does that number

represent?

It is the Atomic Weight

• This value is actually an average of the mass numbers of the different isotopes of the element.

• But, calculating this value is a bit more involved than a typical average…

Mg12

24.305

Let’s see if we can work through this:

90 80

Suppose that we have two test papers. One of the tests is scored as a “90” and the other is scored as a an “80” . What would the average score be reported for the two tests?

Correct !

• You would get the average as “85” by adding the two scores and then dividing by “2” because there are 2 test papers.

• But now consider the scenario on the next slide.

This time there are 8 papers:

90 90

90 90

90

80

80

90

What is the average test score here?

Strategy:

• The answer to that question is “87.5” .

• You could get that by adding up all 8 scores and then dividing by “8”

(90+90+90+90+90+90+80+80) / 8 = 87.5

• Or… you could solve it this way:

[(90 x 6) + (80 x 2)] / 8=

87.5

There is still another way to do this calculation:

• Remember that there are 8 scores.

• 6 of them are a “90”• 2 of them are an “80”• Just for a minute, let’s

focus on the number of times we see each score.

• 6 of the eight scores is actually 75% of those scores.

• 2 of the eight scores is 25% of the scores.

• So we can say that 75% of the scores are a “90” and 25% are an “80”.

Here is how we use the percentages in the calculation:

Average Score = (90 x 75%) + (80 x 25%)

= (90 x 0.75) + (80 x 0.25)

= 67.5 + 20

= 87.5

This type of calculation is called the determination of a weighted average.

Weighted Average and Atomic Weights

We use this strategy to determine an average atomic weight because the atoms are so small that it is not possible to count them like we could test scores..

Instead, we look at the mass numbers of the isotopes of an element and the percentages of each of those isotopes.

Let’s look at the element magnesium as an example of this strategy.

Mg exists as three common isotopes

• There is Mg – 24 which occurs 78.99 % of the time.

• There is Mg – 25 which occurs 10.00 % of the time.

• There is Mg – 26 which occurs 11.01 % of the time.

• Notice how the percentages add up to 100% - all of the element.

• The next slide will show how we can use the weighted average strategy to calculate the average atomic weight of an element.

Here is what the calculation will look like.

Ave At Wt = (24 x 78.99%) + (25 x 10.00%) + (26 x 11.01%)

= (24 x 0.7899) + (25 x 0.1000) + (26 x 0.1101)

= 18.9576 + 2.500 + 2.8626

= 24.3202

The units are amu’s so the answer is actually 24.3202 amu