Learning Objective: To learn about the average atomic mass and how to calculate it from its isotopic mass and natural abundance.
Skill Level – Intermediate
Prerequisites:
The arithmetic average (also known as the arithmetic mean) is calculated by summing all the numbers in a set and then dividing by the total number of values in that set.)
Periodic Table (check the display of atomic weight and atomic number)
Related –
Chapter: Structure of an Atom
Author's Note: In the previous section, we studied mass number, which counts the protons and the neutrons for each isotope separately. In reality, 20 naturally occurring elements exist in only one form and have no natural isotopes. Other elements occur as a mixture of two or more isotopes. Some elements, like Tin, have 10 natural isotopes. In such situations, it becomes important to calculate the atomic weight of an element by taking into consideration its isotopic mass and its natural abundance. Only then do we arrive at a value of atomic mass for an element as a whole, the one you would normally see on the Periodic Table. An important factor that leads to this value is giving a weightage to an element's isotopic abundance. Therefore, a weighted average calculation is used instead of an arithmetic average. This section would cover the basics of average atomic weight and its calculations.
Average Atomic Mass (How to Calculate)
Only 20 naturally occurring elements exist in only one form and have no natural isotopes. Other elements occur as a mixture of two or more isotopes.
An isotopic mass can provide the mass of a single atom of a specific isotope; however, this value can prove insufficient. For example, Tin has 10 natural isotopes with isotopic mass numbers 112, 114, 115, 116, 117, 118, 119, 120, 122, and 124. Therefore, to determine the atomic mass accurately for the element as a whole, the average atomic mass is used. The average atomic mass is the value you normally find on the periodic table for the element as a whole.
Such an average atomic mass is obtained by taking the weighted average of all the isotopes of the element.
Therefore, by definition,
‘The Average Atomic mass of an element is the weighted average mass of all its naturally occurring isotopes.’
Preference of the weighted average over the arithmetic average
The weighted average gives a more accurate value than the normal average by considering all isotopic forms of an element. The accuracy is determined by the ‘weight’ or ‘values’ given to a specific variable; in the case of the isotopes, it is their percentage of natural abundance.
A few examples of elements, their isotopes, and corresponding natural abundance on earth are:
Element | Isotope | % Natural abundance | Isotopic mass (amu) |
|---|---|---|---|
Hydrogen | 11H | 99.985 | 1.0078 |
21H | 0.015 | 2.0141 | |
31H | negligible | 3.0160 | |
Carbon | 126C | 98.89 | 12.000 |
136C | 1.11 | 13.003 | |
146C | trace | 14.003 | |
Oxygen | 168O | 99.759 | 15.995 |
178O | 0.037 | 16.995 | |
188O | 0.204 | 17.999 | |
Chlorine | 3517Cl | 75.77 | 34.969 |
3717Cl | 24.23 | 36.966 | |
Copper | 6329Cu | 69.17 | 62.930 |
6529Cu | 30.83 | 64.928 |
For example, the arithmetic average of three isotopes of Hydrogen would give the atomic mass as 2.
(1.0078 + 2.0141 + 3.0160)/3= 2
The weighted average accurately predicts the atomic mass of Hydrogen as 1.0080 by giving weightage to its most abundant form (11H).
Calculating Average Atomic Mass
Oxygen has three isotopic forms- 168O, 178O, and 188O, and their percentage abundance is 99.759 %, 0.037 %, and 0.204 %. The 168O isotope predominates the other forms in natural abundance and is given the highest weight or value, followed by 188O and 178O.
Once established, the weights are multiplied by the atomic mass. The atomic mass of the isotopes is- 168O (15.995), 178O (16.995), and 188O (17.999).
Element | Isotope | % natural abundance | Isotopic mass (amu) |
|---|---|---|---|
Oxygen | 168O | 99.759 | 15.995 |
178O | 0.037 | 16.995 | |
188O | 0.204 | 17.999 |
The result of the two steps is added to give the Average Atomic mass.
Therefore, the weighted Average Atomic Mass of Oxygen
= 99.759/100 x 15.999 + 0.037/100 x 16.995 + 0.204/100 x 17.999
= 15.960 + 0.00628815 + 0.03671796
= 16.0030061
The average atomic mass is also called the atomic weight or atomic mass, expressed in the atomic mass unit (amu).
Therefore, the atomic mass of the Oxygen atom is 16 amu, obtained by calculating the average atomic masses of its three isotopes.
The average atomic mass of other elements is-
Element | Isotope | % Natural abundance | Isotopic mass (amu) | Average Atomic Mass (amu) |
|---|---|---|---|---|
Hydrogen | 11H | 99.985 | 1.0078 |
1.0080 |
21H | 0.015 | 2.0141 | ||
31H | negligible | 3.0160 | ||
Carbon | 126C | 98.89 | 12.000 |
12.011 |
136C | 1.11 | 13.003 | ||
146C | trace | 14.003 | ||
Oxygen | 168O | 99.759 | 15.995 |
15.999 |
178O | 0.037 | 16.995 | ||
188O | 0.204 | 17.999 | ||
Chlorine | 3517Cl | 75.77 | 34.969 |
35.453 |
3717Cl | 24.23 | 36.966 | ||
Copper | 6329Cu | 69.17 | 62.930 |
63.546 |
6529Cu | 30.83 | 64.928 |
The atomic mass of the isotopes is usually close to the mass number, a sum of protons and neutrons. Therefore, the mass number of each isotope gives an estimate of the isotope's atomic mass (isotopic mass) measured in amu unit (μ). Isotopic mass is usually within 0.1 μ of the mass number.
For example, the mass number of 168O is 16, and the isotopic mass is 15.995 amu. The mass number of isotopes 178O and 188O is 17 and 18, having isotopic masses of 16.995 and 17.999. The difference between mass number and isotopic masses of Oxygen is 0.1 μ.
This excerpt is from the chapter Atom part of CurlyArrows' Organic Chemistry Fundamentals Course. Preview the Book. Subscribe to learn about the average atomic mass and other basic concepts important to understand the structure and functioning of an atom.
Related Numerical Problem : Chlorine has two isotopes, 35Cl and 37Cl; 75.77 % of chlorine is 35Cl, and 24.23% is 37Cl. The atomic mass of 35Cl is 34.969 amu, and the atomic mass of 37Cl is 36.966 amu. What is the atomic weight of Chlorine?
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