Calculating Average Atomic Mass
-
This is how chemists found the atomic mass to report on the periodic table.
Takes into account the mass and abundance of an element’s isotopes.
This is also how teachers calculate the quarter and semester grades (now you’ll be able to use it too)
Part I: Solving for the average mass
Steps:
1. divide each abundance by 100 (to get rid of percent)
2. multiply each answer from step 1 by the mass of that isotope (either given as decimal or mass numbernote: use decimal number if given)
3. repeat steps 1 and 2 until this has been done for all isotopes
4. add the answers together
Note: the formula below summarizes the first 4 steps
5. round your answer to three decimal places… wacky sig fig rules…
6. check to see if your answer is close to the atomic mass on the Periodic Table. If not, check your work
Formula:
avg
atomic
mass
=
% abundance
of isotope 1 Mass of
isotope 1 +
100
% abundance
of isotope 2
100
Mass of
isotope 2
+
.
Atomic mass example problems:
Use the problems below as part of your notes for this topic. The answers are after the question, in parentheses.
Sample Problem:
Based on the table below, what is the atomic mass for boron? (10.811u)
isotope
%abundance
atomic mass of isotope
boron-10
19.78 %
10.013 u
boron-11
80.22 %
11.009 u
Answer:
x = 19.78/100 (10.013u) + 80.22/100 (11.009u)
x = 10.811u
You try: Based on the table below, what is the atomic mass for lead? (207.2u)
isotope
lead 204
lead-206
lead-207
lead-208
%abundance
1.4 %
24.1 %
22.1 %
52.4 %
Part II: Solving for the mass of a specific isotope
Steps:
1.
2.
3.
4.
5.
6.
7.
8.
9.
divide each abundance by 100 (to get rid of percent)
multiply each answer from step 1 by the mass of that isotope. One of your masses will be x this time.
repeat steps 1 and 2 until this has been done for all isotopes
place this into the formula given previously as you go
place the atomic mass of the element, from the periodic table, on the left side of the equals
solve for x
round your answer to three decimal places, if possible
check to see if your answer makes sense (think of the penny lab)
state a final answer: the mass of isotope-x is so many u
Sample Problem:
By looking at the atomic mass of carbon on the Periodic Table (12.011u) it is obvious that the majority of
carbon is carbon-12. In actuality, 98.90% of carbon has a mass of 12.00u. The other 1.10% is accounted for in
another carbon isotope. What is the mass and name of this other isotope? (13.003u, carbon-13)
Answer:
12.011u = 98.90/100 (12.00u) + 1.10/100 (x)
12.011 = 11.868 + 0.0110x
0.143 = 0.0110x
x = 13
the mass of carbon-13 is 13.00u (note: don’t put 13.003 because our calculations didn’t show it)
You try: What is the name and mass of the second most common copper isotope based on the following table.
(copper-65, 64.928u) Hint: look on the Periodic Table for the average mass.
isotope
copper-63
copper-?
%abundance
69.17 %
30.83 %
atomic mass of isotope
62.939 u
?