ATOMIC MASS & AVERAGE ATOMIC MASS

Overview: This tutorial discusses isotopes and isotopic abundance. Nuclear binding

energy and mass defect are presented and the technique of mass spectrometry is introduced.

Every atom has its own unique atomic mass based on a standard comparison or relative scale e.g. It has been based on hydrogen H = 1 amu and oxygen O = 16 amu in the past.

The relative atomic mass scale is now based on an isotope of carbon, carbon-12, , which is given the value of 12.0000 amu. In other words the relative atomic mass of an element is now based on the arbitrary value of the carbon-12 isotope being assigned a mass of 12.0000 by international agreement! Examples are shown in the Periodic Table diagram above.

Note that because of the presence of neutrons in the nucleus, the relative atomic mass is usually at least double the atomic/proton number because there usually at the number of neutrons as protons in the nucleus (mass proton = 1, neutron = 1).

You should bear in mind that the letter A on its own usually means the mass number of a particular isotope and amu is the acronym shorthand for atomic mass units)

However there are complications due to isotopes and so very accurate atomic masses are not whole numbers.

Isotopes are atoms of the same element with different masses due to different numbers of neutrons. The very accurate atomic mass scale is based on a specific isotope of carbon, carbon-12, 12C = 12.0000 units exactly.

The current system of atomic masses was instituted in 1961 and is based on the mass of 12C (read carbon twelve). By definition the atomic mass of a single 12C atom is exactly 12 atomic mass units (denoted by the abbreviation amu or u). The masses of all other elements are based on this standard.

Subatomic Particle Masses mass of a proton, mp+ = 1.00728 u mass of a neutron, mn0 = 1.00867 u mass of an electron, me- = 5.5 x 10-4 u

Three processes that change the number of subatomic particles in an atom

Ion formation (Ionization): Changing the number of electrons in an atom.For example, starting with a neutral sodium atom: Na Na+ + e-. The cation, Na+, is generated by removal of an electron.The anion, I-, is formed by adding an electron to the neutral iodine atom: I + e- I-

Isotope Conversion: Changing the number of neutrons in the nucleus of an atom.As an example, 56Fe + n0 57Fe. 56Fe and 57Fe are two different isotopes of iron. They have different nuclear masses, but have the same nuclear charge (same number of protons) and essentially identical chemical reactivity.

Transmutation Changing the number of protons in the nucleus. This converts one element into another.55Mn + p+ 56Fe+

Note: These latter two processes only occur in nuclear reactions, not in normal chemical reactions. Chemical reactions are processes in which the number of electrons held or shared by an atom change. Nuclear reactions are processes that involve changing the number of neutrons or protons held in the nucleus of an atom.

How can we determine isotopic masses? It seems we should be able to add together the masses of the constituent subatomic particles to determine the isotopic mass. In the following example we will see how accurate this approach is.

Example: Estimate the atomic mass of 7Li based on the

masses of the constituent subatomic particles.7Li: Mass Number = 7 = (# of protons + # of neutrons)Atomic Number = 3 = # of protonsnumber of neutrons = 4number of electrons = 3 (this is a neutral atom).

(CONT.)

Atomic mass= (#p+)(mp+) + (#n0)(mn0) + (# e)(me-)

=(3)(1.00728 u) + (4)(1.00867 u) + (3)(5.5 x 10-4 u)

=7.05817 uThe experimentally determined value, measured by a

technique called mass spectrometry, is 7.016005 u.

The difference in mass is: Dmass = 7.05817 u - 7.016005 u = 0.042165 u.

Approximately 0.6% of the mass is missing. This raises the question, what happened to this mass?

Missing Mass and Nuclear Binding Energy

In atom: 4 n0, 3 p+, 3 e- Separate: 4n0 , 3p+, 3e-

mass = 7.016005 u mass = 7.05817 u

The missing mass is the difference between the experimental and calculated mass of an isotope. This missing mass (sometimes also called the "mass defect") has been converted into nuclear binding energy, which is the energy that holds the nuclear particles together. This is the energy that would be required to separate the nucleus into its constituent protons and neutrons.

The missing mass is < 1% of the nuclear mass for all cases, however successfully predicting the missing mass is difficult. Therefore the most accurate way to determine isotopic masses is experimentally.

The nuclear binding energy is related to the missing mass via Einstein's famous equation (from the Theory of Special Relativity).

E = m c2

E = Nuclear Binding Energy, m = mass (in this case it is the missing mass, Dm), c = speed of light = 2.9979 x 108 m/s

Continuing with the 7Li example, the nuclear binding energy is:

Therefore 3.79 x 109 kJ/mol is the amount of energy needed to break the nucleus apart. This is much larger than the energy involved in normal chemical reactions or processes. For instance, to remove an electron from an atom requires only 500 kJ/mol. Hence it takes ~107 (10,000,000) times more energy to break apart the 7Li nucleus. This is a massive amount of energy.

Elemental Atomic MassThe periodic table lists the atomic mass for each element. For instance, the entry for copper (Cu) in the periodic table indicates an atomic mass of 63.546 u, but what does this really mean? In nature, Cu exists in two different isotopic forms, 63Cu and 65Cu, and their natural abundances are 69% and 31%, respectively. We can use this data to solve for the elemental atomic mass.

i = an index identifying each isotope for the elementfi = fractional abundance of isotope imi = mass of isotope iThe elemental atomic mass is the atomic mass that appears in the periodic table. It is nothing more than a weighted average of the isotopic masses of all the naturally occurring isotopes.

We have been talking about isotopes for a while, but still have not formally defined them. Isotopes are atoms of the same element that differ in the number of neutrons in the nucleus and therefore they have different masses. Nevertheless isotopes have practically identical properties in terms of chemical reactivity.

Example:What is the elemental atomic mass of naturally occurring Silicon? The naturally occurring isotopes and their isotopic abundances are:

Silicon isotope natural abundance isotopic mass 28Si 92.21% 27.97693 u 29Si 4.70% 28.97649 u 30Si 3.09% 29.97379 u *Note that the natural abundances must add up to 100%!

Mass Spectrometry The atomic mass of a specific atom or molecule is determined by

using an experimental technique called mass spectrometry. This technique separates the different isotopes of atoms to allow determination of the percent abundance or isotopic composition of the element in the given sample.

Follow this link to learn the details of how a mass spectrometer works: http://www.chemguide.co.uk/analysis/masspec/howitworks.html.

Each isotope appears as a peak in the mass spectrum. The intensity (height) of each peak depends on the abundance of that isotope in the sample and the unique location of the peak on the x-axis indicates the mass-to-charge ratio (m/q) of the isotope.

Mass spectrometry is used in a diverse range of applications, such as accurate determinations of molecular masses, drug testing, determining the age of archaelogical artifacts (14C dating) and for studying the chemistry of DNA

Consider the mass spectrum of silicon, shown below. The abundances are the same as those in Example 2. As you can see, there are three isotopes. Each peak represents one of the isotopes. The most abundant isotope has the highest peak intensity and the least abundant isotope has the smallest intensity. Since the peak intensities (heights) are proportional to the isotopic abundances, analysis of the data allows for the determination of the relative abundances of each isotope in the sample.

Example #1: Carbon mass number exact weight percent abundance 12

12.000000 98.90 13 13.003355 1.10

To calculate the average atomic weight, each exact atomic weight is multiplied by its percent abundance (expressed as a decimal). Then, add the results together and round off to an appropriate number of significant figures.

This is the solution for carbon: (12.000000) (0.9890) + (13.003355)

(0.0110) = 12.011 amu

Example #2: Nitrogen

mass number exact weight percent abundance 1414.003074 99.63

15 15.000108 0.37

This is the solution for nitrogen: (14.003074) (0.9963) + (15.000108)

(0.0037) = 14.007 amu

Example #3: In a sample of 400 lithium atoms, it is found

that 30 atoms are lithium-6 (6.015 g/mol) and 370 atoms are lithium-7 (7.016 g/mol). Calculate the average atomic mass of lithium.

Solution: 1) Calculate the percent abundance for each

isotope: Li-6: 30/400 = 0.075 Li-7: 370/400 = 0.925 2)

2)Calculate the average atomic weight: x = (6.015) (0.075) + (7.016) (0.925) x = 6.94 g/mol

Example #4:

Copper occurs naturally as Cu-63 and Cu-65. Which isotope is more abundant?

Solution: Look up the atomic weight of copper:

63.546 amu Since our average value is closer to 63

than to 65, we conclude that Cu-63 is the more abundant isotope.

Your Assignment:

Sample #1: Chlorine   Sample #2: Silicon mass number exact weight percent abundance   mass number exact weight percent abundance 35 34.968852 75.77   28 27.976927 92.23 37 36.965903 24.23   29 28.976495 4.67     

30 29.973770 3.10

Calculate the Average mass for the following samples

More on the next page

mass number exact weight percent abundance

24 23.985042 78.99 25 24.985837 10.00 26 25.982593 11.01

Sample #3: magnesium

mass number exact weight percent abundance

92 91.906808 14.84 94 93.905085 9.25 95 94.905840 15.92 96 95.904678 16.68 97 96.906020 9.55 98 97.905406 24.13 100 99.907477 9.63

Sample #4: molybdenum

Sources used:

http://www.chemistry.wustl.edu/~coursedev/Online%20tutorials/Atomic%20Mass.htm

http://www.docbrown.info/page04/4_73calcs01ram.htm

http://www.chemteam.info/Mole/AverageAtomicWeight.html