Calculating Average Atomic Mass

The atomic mass of an element is a weighted average of the different isotopes of a naturally occurring sample of the element.

WEIGHTED AVERAGE: Grades are often computed using a weighted average. Suppose that homework counts 10%, labs 20%, and tests 70%. If Pat has a homework grade of 92, a lab grade of 68, and a test grade of 81, what is his grade?

(0.10)(92) + (0.20)(68) + (0.70)(81) = 79.5

We can do this for isotopes!

Average Atomic Mass

Fractional abundance of

isotope 1{= x Mass of isotope 1} Fractional

abundance of isotope 2{+ x Mass of

isotope 2}

Quiz Lab Test

29

CuCopper

63.54

Average Atomic Mass

To calculate the atomic mass of an element, multiply the mass of each isotope by its natural % abundance, expressed as a decimal, and then add the products.

If you had 100 Atoms of Carbon

12C

13C

12C 12C 12C 12C 12C 12C 12C 12C 12C

12C 12C 12C 12C 12C 12C 12C 12C 12C 12C

12C 12C 12C 12C 12C 12C 12C 12C 12C 12C

12C 12C 12C 12C 12C 12C 12C 12C 12C 12C

12C 12C 12C 12C 12C 12C 12C 12C 12C 12C

12C 12C 12C 12C 12C 12C 12C 12C 12C 12C

12C 12C 12C 12C 12C 12C 12C 12C 12C 12C

12C 12C 12C 12C 12C 12C 12C 12C 12C 12C

12C 12C 12C 12C 12C 12C 12C 12C 12C 12C

12C 12C 12C 12C 12C 12C 12C 12C 12C

6

CCarbon

12.011

Carbon has an average atomic mass very close to that of Carbon-12 because close to 99% of naturally occurring carbon on earth is carbon-12 and only 1% is carbon-13.

Carbon-12 Carbon-13

Carbon has two stable isotopes, Carbon-12 and Carbon-13. Calculate the average atomic mass of carbon

using the data below.

12C 13C

Mass number/Isotope Exact weight (amu) Percent Abundance

Carbon-12 12.000000 98.90

Carbon-13 13.003355 1.10

Average Atomic Mass

Fractional abundance of

isotope 1{= x Mass of isotope 1} Fractional

abundance of isotope 2{+ x Mass of

isotope 2}

(0.9890 x 12.000000) + (0.0110 x 13.003355) = 12.011amuCarbon-12 Carbon-13

Fractional abundance is the percent abundance divided by 100!

Nitrogen has two stable isotopes, Nitrogen-14 and Nitrogen-15.

Calculate the average atomic mass of nitrogen using the data below.

14N 15N

Mass number/Isotope Exact weight (amu) Percent Abundance

Nitrogen-14 14.003074 99.63

Nitrogen-15 15.000108 0.37

Average Atomic Mass

Fractional abundance of

isotope 1{= x Mass of isotope 1} Fractional

abundance of isotope 2{+ x Mass of

isotope 2}

(0.9962 x 14.003074) + (0.0037 x 15.000108) = 14.007amuNitrogen-14 Nitrogen-15

Mass number vs. exact weight/atomic mass?

% Abundanceamu

Average Atomic Mass of Magnesium?

What is the Fractional Abundance of Carbon-12 (12.00000 amu) and Carbon-13 (13.003355 amu) granted that the average atomic

mass of Carbon is 12.011?

(12 amu * x ) + (13.003355 amu * y) = 12.011

But x + y must = 1 (must have 100%)

So writing y in terms of x yields

(12 amu * x ) + (13.003355 amu *(1- x)) = 12.011

Quirky Quantum Chemistry• If a small marble has a mass of 3 grams and a large

marble has a mass of 5 grams how much will three small marbles and two big marbles weigh in total?

• Well, atoms don’t follow these simple rules. Helium has two protons and two neutrons but the mass of a helium atom is actually less than the combined mass of two protons and two neutrons. AN ATOM WEIGHS LESS THAN THE SUM OF ITS PARTS!

• This is called a mass defect and its related to Einstein’s equation E =mc2.

• Crudely: Some of the mass is converted into binding energy used to hold the nucleons together.

1. What is the difference between the mass number and the exact atomic mass?2. An atom cannot have a fraction of a neutron or a proton. Why is the exact mass of various elements not a

whole number? Hint, I am not asking about the weighted average on the periodic table?3. The sum of its parts does not equal the whole. What does that mean in regards to an atom?4. Boron has an atomic mass of 10.81 amu according to the periodic table. However, no single atom of boron

has a mass of 10.81 amu. How do you explain this?5. The average atomic mass of Copper is 63.546amu. Which of copper’s two naturally occuring isotopes is more

common, Copper-63 or Copper-65?6. Boron has two isotopes, Boron-10 and Boron-11. Which is more abundant given that the atomic mass of

Boron is 10.81.7. Calculate the atomic mass of bromine. The two isotopes of bromine have atomic masses and relative

abundances of 78.92 amu (50.69%) and 80.92 amu (49.31%).8. What is the % Abundance of Lithium-6 ( 6.015122 amu) and Lithium 7 (7.016004 amu) if the average atomic

mass of lithium is 6.94.

% Abundanceamu

9. Calculate the average atomic mass of Calcium.