Average Atomic MassAverage Atomic Mass

A A different different kind of average…kind of average…

What do these numbers mean?What do these numbers mean?

82

PbLead

207.2

Atomic #

Atomic Mass

the number of p+

The weighted average mass of the atoms in a naturally occurring sample of the element

How is atomic mass calculated?...

NOT mass number!

……as a as a weighted weighted averageaverageunlike a normal average unlike a normal average (or (or meanmean))

A weighted average takes into account the A weighted average takes into account the abundance of what is being averagedabundance of what is being averaged

for example, if 75% of coins in your pocket are pennies and 25% for example, if 75% of coins in your pocket are pennies and 25% are dimes, which has the greatest effect on the average value of are dimes, which has the greatest effect on the average value of the coins in our pocket? the coins in our pocket? The pennies, of course!The pennies, of course!

the the weighted averageweighted average value of the coins in your value of the coins in your pocket is:pocket is:

11¢ x .75¢ x .75 = .75¢= .75¢

10¢ x .2510¢ x .25 = 2.50¢= 2.50¢

3.25¢3.25¢

Because the pennies are more abundant, they have

the largest effect on the average

THAT’S WHY THE AVERAGE IS CLOSER TO THE VALUE OF A PENNY,

NOT A DIME

This is how it works…This is how it works… Here’s how you would normally calculate Here’s how you would normally calculate

the average value of 7 pennies and 3 the average value of 7 pennies and 3 quarters:quarters:

1+1+1+1+1+1+1+25+25+25= 821+1+1+1+1+1+1+25+25+25= 82

8.2 10

82

But it could have been calculated as a weighted average…

Total amount

Number of items added

Average value

Weighted averageWeighted average

7 pennies, 3 quarters = 10 total coins7 pennies, 3 quarters = 10 total coins Since 70% of the coins are pennies, 70 % of the average value Since 70% of the coins are pennies, 70 % of the average value

must be from the penniesmust be from the pennies Since 30% of the coins are quarters, 30% of the average value Since 30% of the coins are quarters, 30% of the average value

must be from the quartersmust be from the quarters

So…So…

Coin% abundance Value (¢)

Relative abundance (decimal equivalent) Subtotal

pennypenny 7070 11 xx .70.70 == .7.7

quarterquarter 3030 2525 xx .30.30 == 7.57.5

8.28.2Weighted average value is the sum of the subtotals

Average atomic mass calculation exampleAverage atomic mass calculation example

Given the following isotope data:

Isotope % abundance

Mass (amu)

Cu-63 69.2% 62.93

Cu-65 30.8% 64.93

Average atomic mass calculation exampleAverage atomic mass calculation example

Given the following isotope data:

Isotope % abundance

Mass (amu)

% decimal equivalent

Cu-63 69.2% 62.93

Cu-65 30.8% 64.93

Remember, this is just the % abundance with the decimal moved 2 places to the left

Average atomic mass calculation exampleAverage atomic mass calculation example

Given the following isotope data:

Isotope % abundance

Mass (amu)

% decimal equivalent

Cu-63 69.2% 62.93 .692

Cu-65 30.8% 64.93

Average atomic mass calculation exampleAverage atomic mass calculation example

Given the following isotope data:

Isotope % abundance

Mass (amu)

% decimal equivalent

Cu-63 69.2% 62.93 .692

Cu-65 30.8% 64.93 .308

Average atomic mass calculation exampleAverage atomic mass calculation example

Given the following isotope data:

Isotope % abundance

Mass (amu)

% decimal equivalent

Mass contribution

Cu-63 69.2% 62.93 x .692 =

Cu-65 30.8% 64.93 x .308 =

Average atomic mass calculation exampleAverage atomic mass calculation example

Given the following isotope data:

Isotope % abundance

Mass (amu)

% decimal equivalent

Mass contribution

Cu-63 69.2% 62.93 x .692 = 43.55

Cu-65 30.8% 64.93 x .308 =

( )

Average atomic mass calculation exampleAverage atomic mass calculation example

Given the following isotope data:

Isotope % abundance

Mass (amu)

% decimal equivalent

Mass contribution

Cu-63 69.2% 62.93 x .692 = 43.55

Cu-65 30.8% 64.93 x .308 = 20.00

( )( )

Average atomic mass calculation exampleAverage atomic mass calculation example

Given the following isotope data:

Isotope % abundance

Mass (amu)

% decimal equivalent

Mass contribution

Cu-63 69.2% 62.93 x .692 = 43.55

Cu-65 30.8% 64.93 x .308 = 20.00

Add the mass contributions up→Add the mass contributions up→ 63.55

The atomic mass of Cu is 63.55 amu

Example: Calculate the atomic mass for S using the Example: Calculate the atomic mass for S using the natural percent abundance data listed below:natural percent abundance data listed below:

IsotopeNatural % abundance Mass (AMU)

Relative abundance (decimal equivalent)

Mass contribution

S-32S-32 95.00295.002 31.97231.972 xx .95002.95002 == 30.37430.374

S-33S-33 0.760.76 32.97132.971 xx .0076.0076 == .2506.2506

S-34S-34 4.224.22 33.96733.967 xx .0422.0422 == 1.43341.4334

S-36S-36 0.0140.014 35.96735.967 xx .00014.00014 == .005035.00503532.0632.06The sum of the mass

contributions is the WEIGHTED AVERAGE

The atomic mass of S is 32.06 AMU