# Molecular Weight

Molecular weight is the sum of the atomic weights of the atoms in a molecule. A molecule can be viewed as an entity of one or more different atoms bound together by some kinds of mutual interactions. As an example, the molecular weight of water, H2O, is calculated as (2 × 1.00797) + (1 × 15.9994) = 18.0153, where 1.00797 and 15.9994 are the atomic weights of hydrogen (H) and oxygen (O) atoms, respectively. In general, molecular weight can be determined by either chemical methods or mass spectrometry.

To know more about "molecular weights," one must first become familiar with the concept of "atomic weights." Because an element (e.g., carbon, oxygen, sulfur, etc.) often exists as a mixture of two or more (stable and unstable forms) natural isotopes that have the same number of protons but differ in the number of neutrons, atomic masses of these isotopes are slightly different from each other. In this case, atomic masses are averaged and the ratio of the resultant value to some standard is defined as the "atomic weight" of the element.

In 1961, the 12C isotope of carbon was adopted as the atomic weight standard with a value of 12.00000 d, where d is dalton, the unit of mass for nuclides, named after the English chemist and physicist John Dalton (1766-1844). The dalton is, therefore, defined as exactly 1/12 of the mass of the neutral carbon (C) atom. According to this, the atomic weight of oxygen is 15.9994 ± 0.0001, and ± 0.0001 is due to natural variations in the isotopic composition of the oxygen element. For an oxygen molecule, O2, the molecular weight is then given by 2 × 15.9994 = 31.9988, or 32 for all practical purposes. Strictly speaking, molecular weights are dimensionless, but in many cases, people do not distinguish them from molecular masses and use "gram/mole" as the unit.

Because molecules range in size from monatomic, diatomic, triatomic, to polyatomic, molecular weights can be as small as 4.0026 for gaseous helium (He), 2.0159 for hydrogen (H2), and 44.01 for carbon dioxide (CO2), or as large as several hundred thousand in proteins. For many macromolecules formed by polyreactions, for instance, a solution of polystyrene in benzene, the masses of the individual polymer molecules are distributed over a range of values. Thus, we have to use an average value to describe their molecular weight, and the easiest way to do that is simply to take the number average, i.e., Waverage = Nniwi/ni, where we add the products of each molecular weight (wi) and the number of molecules (ni) having that wi, divide it by the total number of molecules in the solution and finally multiply it by the Avogadro number N.

Depression of the melting point of a pure substance by adding a second compound and elevation of the boiling point of a liquid due to dissolving nonvolatile substances can be used to determine the molecular weight of the added compound or the dissolved substances. In the latter case, for instance, we have the temperature elevation ΔT = bm, where m is the total molality (e.g., moles of solute per 1,000-gram solvent) of solutes and b is a constant characteristic of the solvent (e.g., 0.51 for H2O and 2.6 for C6H6). As long as the weight ratio of solute to solvent is known, we can determine the molecular weight of the solute.

If we would like to obtain molecular weights directly and accurately, mass spectrometry is a good approach. Its principle can be explained in the following way: molecules of interest are bombarded by energetic electrons, ionized, and broken up into many fragments of particular values of the charge-to-mass ratio, q/m. By applying an electrical potential and/or a magnetic field, ions are deflected according to their individual m/q values and either displayed on a photographic plate at different positions (an old method, also known as "mass spectrograph") or detected electronically. In other words, ions are differentiated because of the difference in their individual energy and angular spread as they travel. Of two ions either with the same charge or with the same mass, the lighter one or the one with greater charge will be deflected by the larger amount. By analyzing recorded mass spectra, information on the exact molecular weight and the structural units of the investigated molecules can be further derived.

## Resources

### Books

Loudon,G. Mark. Organic Chemistry. Oxford: Oxford University Press, 2002.

Pauling, L. General Chemistry. New York: Dover Publications, Inc., 1970.

White, F.A., and G.M. Wood. Mass Spectrometryl-Applications in Science and Engineering. New York: Wiley, 1986.

Pang-Jen Kung

## KEY TERMS

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—The number of molecules present in one mole of whatever the compound is always equal to 6.0229 × 1023. It was named for the Italian physicist Amedeo Avogadro.

Isotopes

—Two molecules in which the number of atoms and the types of atoms are identical, but their arrangement in space is different, resulting in different chemical and physical properties.

Mass number A

—It is equal to the sum of the number of protons (i.e., the atomic number, given the symbol Z) and the number of neutrons in atoms.

Nuclides

—It is used to describe the kind of matter involving nuclei with given values of mass number A and atomic number Z.