Carbon average atomic mass

Carbon-12 is the basis for the average atomic mass units (amu) that is used to determine the atomic weights of the elements. Carbon is one of the few elements that can form covalent bonds with itself as well as with many metals and nonmetals. 

These three isotopes are why you see carbon s atomic mass on the periodic table written as 12.01. If you do a quick bit of deductive reasoning, you can probably determine that carbon-12 is far and away the most common of the three isotopes due to the average atomic mass being closest to 12. 

Certain elements, such as chlorine, occur in several very common isotopes, so their average atomic mass isn t close to a whole number. Other elements, such as carbon, occur in one very common isotope and several very rare ones, resulting in an average atomic mass that s very close to the whole-number mass of the most common isotope. 

The identity of an element depends on the number of protons in the nucleus of the atom. Atoms and ions of a given element that differ in number of neutrons and have a different mass are called isotopes. A nucleus with a specified number of protons and neutrons is called a nuclide, and a nuclear particle, either a proton or neutron, may be called a nucleon. The total number of nucleons is called the mass number and this number is a whole number and is calculated by rounding up the average atomic mass value, for hydrogen, the atomic mass is 1.008 amu (atomic mass units) and is rounded up and the mass number of hydrogen is 1. 1 amu is equivalent to 1 /12th of the atomic mass of carbon. 

It is important to interpret averages carefully. For example, in 1996, the average size of a Canadian family was 3.1. Of course, no one family actually has 3.1 people. In the same way, while the average atomic mass of carbon is 12.01 u, no one atom of carbon has a mass of 12.01 u. 

The average atomic mass for carbon is computed as follows. Chemists know that natural carbon is composed of 98.89% 12C atoms and 1.11% 13C atoms. The amount of l4C is negligibly small at this level of precision. Using the masses of 12C (exactly 12 amu) and 13C (13.003355 amu), the average atomic mass for natural carbon can be calculated. 

The average atomic mass for carbon to five significant digits is 12.011. 

For example, carbon has two stable isotopes found in nature, carbon-12 and carbon-13. The average atomic mass of carbon takes into account the masses of both isotopes and their relative abundance. So, while the atomic mass of a carbon-12 atom is exactly 12 amu, any carbon sample will include enough carbon-13 atoms that the average mass of a carbon atom is 12.0107 amu. 

Like carbon, most elements are a mixture of isotopes. In most cases, the fraction of each isotope is the same no matter where the sample comes from. Most average atomic masses can be determined to several decimal places. However, some elements have different percentages of isotopes depending on the source of the sample. This is true of native lead, or lead that occurs naturally on Earth. The average atomic mass of lead is given to only one decimal place because its composition varies so much from one sample to another. 

You know from Chapter 2 that average atomic masses of the elements are given on the periodic table. For example, the average mass of one iron atom is 55.8 u, where u means atomic mass units. The atomic mass unit is defined so that the atomic mass of an atom of the most common carbon isotope is exactly 12 u, and the mass of 1 mol of the most common isotope of carbon atoms is exactly 12 g. The mass of 1 mol of a pure substance is called its molar mass. For example, the molar mass of iron is 55.847 g, and the molar mass of platinum is 195.08 g. Relative masses of elements are demonstrated in Figure 12.4. The molar mass is the mass in grams of the average atomic mass. 

This value is carbon s atomic mass. Because an element s atomic mass is often described without units, carbon s atomic mass is usually described as 12.011 instead of 12.011 u. The atomic mass of any element is the weighted average of the masses of the naturally occurring isotopes of the element. (It is very common to call this property atomic weight, but because it describes the masses of the atoms, not their weights, this text will use the term atomic mass.) Scientists have calculated the atomic masses of all elements that have stable isotopes, and they can be found on any standard periodic table, including the table in this book. 

When you look up the atomic mass of carbon in a table such as the one on the inside front cover of this book, you will find that its value is not 12.(X) amu but 12.01 amu. The reason for the difference is that most naturally occurring elements (including carbon) have more than one isotope. This means that when we measure the atomic mass of an element, we must generally settle for the average mass of the naturally occurring mixture of isotopes. For example, the natural abundances of carbon-12 and carbon-13 are 98.90 percent and 1.10 percent, respectively. The atomic mass of carbon-13 has been determined to be 13.00335 amu. Thus the average atomic mass of carbon can be calculated as follows ... 

A more accurate determination gives the atomic mass of carbon as 12.01 amu. Note that in calculations involving percentages, we need to convert percentages to fractions. For example, 98.90 percent becomes 98.90/100, or 0.9890. Because there are many more carbon-12 atoms than carbon-13 atoms in naturally occurring carbon, the average atomic mass is much closer to 12 amu than to 13 amu. 

The average atomic mass for carbon atoms is 12.01 amu. This means that any sample of carbon from nature can be treated as though it were composed of identical carbon atoms, each with a mass of 12.01 amu. 

It is important to understand that when we say that the atomic mass of carbon is 12.01 amu, we are referring to the average value. If carbon atoms could be examined individually, we would find either an atom of atomic mass 12.00000 amu or one of 13.00335 amu, but never one of 12.01 amu. Example 3.1 shows how to calculate the average atomic mass of an element. 

A table of atomic masses is given on the inside front cover of this book. Hydrogen atoms, with a mass of about 1/12 that of a carbon atom, have an average atomic mass of 1.00797 amu on this relative scale. Magnesium atoms, which are about twice as heavy as carbon, have an average mass of 24.305 amu. The average atomic mass of oxygen is 15.9994 amu. 

The mass number, A, of an isotope of a given element is defined by the sum of the number of protons, Z, and neutrons, N, in its nucleus. Elements have more than one isotope with varying numbers of neutrons. For example, there are two common isotopes of carbon, and C, which have six and seven neutrons, respectively. The atomic mass is primarily determined by the number of protons and neutrons in the nucleus. The average atomic mass of an element is called atomic weight, see Sect. 3.2. 

Before 1961, two definitions of the atomic mass unit were used. In physics, the atomic mass unit was defined as one-sixteenth the mass of one 0 atom. In chemistry, the atomic mass unit was defined as one-sixteenth the average atomic mass of oxygen. These units were slightly smaller than the current carbon-12 based unit. 

How do we use the mole in chanical calculations Recall that Avogadro s number is defined as the number of atoms in exactly 12 g of C. This means that 12 g of contains 6.022 X 10 atoms. It also means that a 12.01-g sample of natural carbon contains 6.022 X 10 atoms (a mixture of C, C, and atoms, with an average atomic mass of 12.01). Since the ratio of the masses of the samples (12 g/12.01 g) is the same as the ratio of the masses of the individual components (12 n/12.01 u), the two samples contain the same number of atoms (6.022 x 10 ). 

Natural carbon, which has an atomic weight of 12.011 amu, consists of carbon-12 and carbon-13 isotopes. Given that the mass of carbon-13 is 13.00335 amu, what would be the average atomic mass (in amu) of a carbon sample prepared by mixing equal numbers of carbon atoms from a sample of natural carbon and a sample of pure carbon-13 ... 

The absolute mass of an isotope can be computed by summing the individual masses of the subatomic particles (see Table 2.1) and reporting the total number of grams that an isotope must weigh however, it is more convenient to quote masses in relative terms using the atomic mass unit (amu). By definition, the most abundant isotope of carbon is exactly 12.000 amu. All other isotope masses are reported relative to carbon-12. Appendix 1 lists the average atomic mass (i.e, the average of the abundances of the stable isotopes) of each element in atomic mass units. 

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