Atomic and Molecular Weights

Atomic and molecular masses are the building blocks of chemistry. Therefore, it is important to know as much as possible about them. For this topic, one should know at least the first \(30\) elements of the periodic table in order.

Atomic weight is a common name for relative atomic mass, which is defined as the ratio of the average mass of one atom of an element to \(\frac{1}{12}\) of the mass of an atom of carbon-12.

The relative atomic mass (atomic weight) scale has traditionally been one without an explicit unit, with the first relative atomic mass basis suggested by John Dalton in 1803 as \(\ce{_{ 1 }^{ 1 }{ H }}\). Despite the initial mass of \(\ce{_{ 1 }^{ 1 }{ H }}\) being used as the natural unit for relative atomic mass, it was suggested by Wilhelm Ostwald that relative atomic mass would be best expressed in terms of units of \(\frac{1}{16}\) mass of oxygen. This evaluation was made prior to the discovery of the existence of elemental isotopes, which occurred in 1912.

The discovery of isotopic oxygen in 1929 led to a divergence in relative atomic mass representation, with isotopically weighted oxygen (i.e., naturally occurring oxygen relative atomic mass) given a value of exactly 16 atomic mass units (amu) in chemistry, while pure \(\ce{_{ 8 }^{ 16 }{ O }}\) was given the mass value of exactly 16 amu in physics.

The divergence of these values resulted in errors in computations, and was unwieldy. The chemistry amu, based on the relative atomic mass (atomic weight) of natural oxygen (including the heavy naturally-occurring isotopes \(\ce{_{ 8 }^{ 17 }{ O }}\) and \(\ce{_{ 8 }^{ 16 }{ O }}\)), was about 1.000282 as massive as the physics amu, based on pure isotopic \(\ce{_{ 8 }^{ 16 }{ O }}\).

For these and other reasons, the reference standard for both physics and chemistry was changed to carbon-12 in 1961.

Inside the atom, there are many sub-atomic particles, but the ones most prominent are the protons, the neutrons and the electrons. The protons are positively charged, while the electrons are negatively charged. Thus, there are an equal number of protons and electrons in an atom to make the atom neutral as a whole. The neutrons are chargeless or neutral. Their abundance may or may not be equal to the number of protons.

The atomic number of a chemical element (also known as its proton number) is the number of protons found in the nucleus of an atom of that element. Thus, the atomic number of \(\ce{H}\) is \(1\), of \(\ce{O}\) is \(8\), and of \(\ce{F}\) is \(9\). It is denoted by \(\text{Z}\). The number of neutrons is denoted by \(N\). Atoms of the same element having different atomic masses are called isotopes. Isotopes have the same number of protons but differ in the number of neutrons. They have similar chemical properties, but different physical properties.

The atomic mass of an atom is the sum of the masses of the protons and neutrons of this atom. The mass of a proton is \(1.672621 \times {10}^{-27} \text{ kg}\) while that of a neutron is \(1.674927 \times {10}^{-27} \text{ kg}\). They are almost the same, and we can say that relatively they have a mass of \(1\) unit. This unit was originally termed as the atomic mass unit or \(\text{amu}\). Now, the IUPAC has changed the \(\text{amu}\) to \(\text{u}\), which is short for unified mass. Thus, the mass of a proton is \(1\text{ u}\) and that of a neutron is also \(1\text{ u}\). The electron, on the other hand, has a mass of \(9.109382 \times {10}^{-31} \text{ kg}\), which is negligible. Hence, the mass of an electron is \(0\text{ u}\). The atomic mass is denoted by \(\text{A}\).

Hence \[\text{Z}+\text{N}=\text{A}.\]

Atoms of different elements having the same mass number but different atomic number are called isobars. Examples include tritium and helium-3.

Atomic mass

The atomic mass of an isotope of O is \(\text{A}=17\text{ u}\), while the atomic number is \(\text{Z}=8\text{ u}\). Find the number of neutrons in this isotope.

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We know that \[\text{Z}+\text{N}=\text{A}.\] Hence, \[\begin{align} \text{A}-\text{Z} &=\text{N} \\ &=17-8\\ &=9.\ _\square \end{align}\]

An atom of an element \(\text{E}\) is denoted as

\[_{ Z }^{ A }\ce{ E }.\]

For example, the notations of carbon-12, oxygen-16, and neon-20 are

\[_{ 6 }^{ 12 }\ce{C},~ _{ 8 }^{ 16 }\ce{O},~ _{ 10 }^{ 20 }\ce{Ne},\]

respectively.

The molecular weight is the total number of protons and neutrons in a compound. In other words, it is the sum of the atomic masses of the individual atoms in a compound.

Find the molecular weights of the following compounds:

\[\begin{array} &\ce{HF}, &\ce{H_2SO_4}, &\ce{C_6H_{12}O_6}. \end{array} \]

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We have

\[\begin{align} (\text{molecular weight of } \ce{HF}) &= (\text{molecular weight of } \ce{H}) + (\text{molecular weight of } \ce{F}) \\ &=1+19 \\ &= 20\\\\ (\text{molecular weight of } \ce{H_2SO_4}) &= 2(1)+32+4(16) \\ &= 98\\\\ (\text{molecular weight of } \ce{C_6H_{12}O_6}) &= 6(12)+12(1)+6(16) \\ &= 180.\ _\square \end{align}\]

Find the molecular weight of the amino acid cysteine.

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You should have memorized all structural formulas of amino acids. If you know them, you would know that cysteine has the formula \(\ce{C_{3}H_{7}NO_{2}S}.\) Either you can add the sums of protons and neutrons, or you can go by the given molecular weights on the periodic table:

• Carbon: \(12 \times 3\)
• Hydrogen: \(1 \times 7\)
• Nitrogen: \(14 \times 1\)
• Oxygen: \(16 \times 2\)
• Sulfur: \(32 \times 1\),

the sum of which will give a molecular weight of about \( 121 \). \(_\square\)