Isotopes and Average Atomic Mass

Isotopes and Average Atomic Mass

But first, a word from our sponsor . . .

How Your Final Mark in “Basketweaving 101”

is Determined

Assignments (ie making baskets) 60%History of Baskets 10%Basketweaving Theory 30%TOTAL 100 %

Now calculate your final grade . . .

Making baskets (@60%)—you got 76/80History (@10%)—you got 12/20Theory (@30%)—you got 20/40

Estimate your final mark in “Basketweaving 101”.

How do we do the calculation?

Why do we not simply take the average of the grade in baskets, history and theory—add them up and divide by 3?

No.Different weighting on each component.

Get busy.

Your final grade is . . .

Final = 0.60*(76/80) + 0.10*(12/20) + 0.30*(20/40) = 57 + 6 + 15 = 78%

We can also call “78” the weighted average of the three grades.

So what does this have to do with chemistry?

Li exists as two isotopes:

63Li; mass 6.015 amu (or u) @ 7.42%

(relative abundance)

73Li has mass 7.015 u @ 92.58%

Calculate the average atomic mass of lithium.

Average atomic mass of Li:

= 0.9258*(7.015 u) + 0.0742*(6.015 u)= 6.941 u which is the av. atomic mass of Li

Try this one:Boron has an average atomic mass of 10.81 u.

From where do we get this value?Periodic table.B exists as two isotopes:10

5B (10.01 u)11

5B (11.01 u)

Calculate the relative abundance of each isotope.

Solution . . . Let abundance of B-10 be x.Therefore, abundance of B-11 will be1 – x.Set up an equation; solve for x.10.81 = x(10.01) + (1 – x)(11.01)10.81 = 10.01x + 11.01 -11.01x

x = 0.2000Therefore, abundance of B-10 is 20.00%; B-11 will be 80.00% abundant.Does this make sense given ?

How are atomic masses determined?The Mass Spectrometer

Used to determine atomic mass . . . and the mass of molecules, too.

Invented in the early 20th century by F.W. Aston

F.W. Aston(1877 – 1945)

Won the Nobel Prize for Chemistry in 1922 for his development of the mass spectrograph (spectrometer)

Aside from science (!), Aston, a bachelor, was an avid sportsman and musician.

Basic Principle behind Mass Spec.

What will happen to an object traveling in a straight line if you subject it to a sideways force (perpendicular to its direction of travel)?

The path of the object will curve.

eg. If a cannonball is flying through the air in front of you and you spray it with a garden hose, will the path of the ball be deflected?

What if it were a table tennis ball?

The amount of deflection for a given sideways force depends on

the mass of the object.

This is the premise behind the Mass Spec.Ions can be deflected by a magnetic field—

neutral atoms are not.Therefore, the first thing that a Mass

Spectrometer does is ionize the sample.

Schematic of Mass Spectrometer

A few notes . . .

• Sample must be vapourized before ionization.

• Vacuum required inside mass spec so thations can travel unhindered.• Most ions formed will carry a +1 charge. Because it is much more difficult to remove

further electrons from a cation. (Why?)

Mass spectrum for MolybdenumWe get a stick chart like this:

How many isotopes of Mo are there?7Which is the most abundant?Mo-98

Homework

Sample problem on p18PP on p 19, do at least 4 of # 1 – 10.