Kaplan MCAT General Chemistry Review

Atomic Weights and Isotopes

Key Concept

• Atomic number (Z) = number of protons.

• Mass number (A) = number of protons + number of neutrons.

• Number of protons = number of electrons (in a neutral atom).

ATOMIC WEIGHT

As we’ve seen, the mass of one proton is defined as approximately one amu. The size of the atomic mass unit is defined as exactly the mass of the carbon-12 atom, approximately 1.66 × 10^-24 grams (g). Because the carbon-12 nucleus has six protons and six neutrons, an amu is really the average of the mass of a proton and a neutron. Because the difference in mass between the proton and the neutron is so small, the mass of the proton and the neutron are each about equal to 1 amu. Thus, the atomic mass of any atom is simply equal to the mass number (sum of protons and neutrons) of the atom. A more common convention used to define the mass of an atom is the atomic weight. The atomic weight is the mass in grams of one mole of atoms of a given element and is expressed as a ratio of grams per mole (g/mol). A mole is the number of “things” equal to Avogadro’s number: 6.022 × 10²³. For example, the atomic weight of carbon is 12 g/mol, which means that 6.022 × 10²³ carbon atoms (1 mole of carbon atoms) have a combined mass of 12 grams (see Chapter 4, Compounds and Stoichiometry). One gram is then equal to one mole of amu.

Mnemonic

Mole Day is celebrated at 6:02 on October 23 (6:02 on 10/23) because of Avogadro’s number (6.02 × 10²³). We will revisit this number in Chapter 4 when we discuss moles in more detail.

ISOTOPES

The term isotope comes from the Greek, meaning “the same place.” Isotopes are atoms of the same element (hence, occupying the same place on the periodic table of the elements) that have different numbers of neutrons (which means that these atoms of the same element have different mass numbers). Isotopes are referred to by the name of the element followed by the mass number (e.g., carbon-12 has six neutrons, carbon-13 has seven neutrons, etc.). Only the three isotopes of hydrogen are given unique names: protium (Greek protos; first) has one proton and an atomic mass of 1 amu; deuterium (Greek deuteros; second) has one proton and one neutron and an atomic mass of 2 amu; tritium (Greek tritos; third) has one proton and two neutrons and an atomic mass of 3 amu. Because isotopes have the same number of protons and electrons, they generally exhibit the same chemical properties.

In nature, almost all elements exist as two or more isotopes, and these isotopes are usually present in the same proportions in any sample of a naturally occurring element. The presence of these isotopes accounts for the fact that the accepted atomic weight for most elements is not a whole number. The masses listed in the periodic table are weighted averages that account for the relative abundance of various isotopes. See Figure 1.2 for the relative abundances in nature of the first several elements. Hydrogen, which is very abundant, has three isotopes.

Key Concept

Bromine is listed in the periodic table as having a mass of 79.9 amu. This is an average of the two naturally occurring isotopes, bromine-79 and bromine-81, which occur in almost equal proportions. There are no bromine atoms with an actual mass of 79.9 amu.

Figure 1.2

Example: Element Q consists of three different isotopes, A, B, and C. Isotope A has an atomic mass of 40 amu and accounts for 60 percent of naturally occurring Q. The atomic mass of isotope B is 44 amu and accounts for 25 percent of Q. Finally, isotope C has an atomic mass of 41 amu and a natural abundance of 15 percent. What is the atomic weight of element Q?

Solution: 0.60(40 amu) + 0.25(44 amu) + 0.15(41 amu) = 24.00 amu + 11.00 amu + 6.15 amu = 41.15 amu

The atomic weight of element Q is 41.15 g/mol.

Bohr’s Model of the Hydrogen Atom

We’ve come a long way from J. J. Thomson’s 1904 “plum pudding” model of the atom as negatively charged “corpuscles” (what we call electrons) surrounded by a density of positive charge that others (but not Thomson himself) likened to free-moving negatively charged “plums” suspended in a positively charged “pudding.” We kid you not; we couldn’t make this stuff up if we tried. In 1910, Ernest Rutherford provided experimental evidence that an atom has a dense, positively charged nucleus that accounts for only a small portion of the atom’s volume. Eleven years earlier, Max Planck developed the first quantum theory, proposing that energy emitted as electromagnetic radiation from matter comes in discrete bundles called quanta. The energy value of a quantum, he determined, is given by this equation:

E = hf