Calculating the Average - PowerPoint Presentation

Slide1

Calculating the Average Atomic Mass Number

Where did that decimal come from?

Calculating Average Atomic Mass

I CAN

calculate the Average Atomic Mass Number of an element from its isotope data

.

The Case for a Decimal We learned earlier that

ATOMIC MASS NUMBER

is the

COMBINED NUMBER

of

P

+

and

N

o

in an atom.

Yet, the AMN given on the Periodic Table generally has a

DECIMAL

in it.

We discussed earlier that the AMN on the PT represents a

WEIGHTED AVERAGE

of all the

ISOTOPES

(atoms from the same element with varying numbers of N

o

) of an element.

Most elements have

2 OR MORE

isotopes.

Each different isotope always occurs in the

SAME RELATIVE AMOUNT

regardless of where the sample of the element is taken from.

For example: Lead has 4 isotopes:1.40 % of all lead atoms are

Pb -204

24.10%

of all lead atoms are

Pb-206

22.10%

of all lead atoms are

Pb-207

52.40%

of all lead atoms are

Pb-208

The

UNIT

for Atomic Mass is the

ATOMIC MASS UNIT

, abbreviated “

amu

” or simply “

u

”.

How would you determine the AVERAGE ATOMIC MASS NUMBER of lead?

First of all, why can’t we simply add all the AMNs of the four isotopes up and find the average by dividing by 4?

We can’t do this because there is

NOT AN EQUAL PERCENTAGE

of each isotope. It they were all

25%

each we could.

Since there is not an equal percentage of each, they do not contribute equally to the overall average.

Since we can’t do a simple average, we will have to calculate a

WEIGHTED AVERAGE

.

Calculating a Weighted AverageTo find a weighted average,

EACH VALUE

is

MULTIPLED

by its

PERCENTAGE

and the results are

ADDED

together.

For Average Atomic Mass, the equation looks like this:

Average AMN = Σ (Atomic Mass x

P

ercentage)

Σ =

sigma

=

“find the sum of”

Practice Problem

L

ead has 4 isotopes: 1.40 % of all lead atoms are Pb -204,

24.10% of all lead atoms are Pb-206, 22.10% of all lead atoms

are Pb-207, and 52.40% of all lead atoms are Pb-208. What is

the average AMN for lead?

STEPS

1. Multiple

EACH

mass by its percentage, making sure to

move the decimal in the percentage

TWO PLACES

to the

LEFT

before multiplying.

2. Add the results and

ROUND

to

SF

.

Pb-204 204 u x 0.0140 = 2.856 u

Pb-206 206 u x 0.2410 = 49.646 u

Pb-207 207 u x 0.2210 = 45.747 u

Pb-208 208 u x 0.5240 = 108.992 u

_________

≈ 207.241 u

MORE PRACTICEUranium has three common isotopes. If the abundance of

U-234

is 0.01%, the abundance of

U-235

is 0.71%, and the abundance of

U-238

is 99.28%, what is the average atomic mass of uranium?

U-234 U-234 u x 0.0001 = 0.0234 u

U

-235

U-235 u x 0.0071 = 1.6685 u

U

-238

U-238 u x 0.9928 =

236.2864 u

237.978

3

u

(There are only

3 SF

in 0.0234) ≈

237.978 u