average atomic mass a different kind of average…
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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