Molecular Weight

Resources

Molecular weight (MW) is the sum of the atomic weights of the atoms in a molecule. (Although molecular weight is often used, the more accurate terminology is molecular mass.) 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.

The first direct approach to determining molecular weight was proposed by two French scientists in 1819, Pierre Louis Dulong (1785–1838) and Alexis-The´rèse Petit (1791–1820). They suggested that the amount of heat required to raise the temperature of an atom of a solid material by a given amount should be independent of the type of atom, with the result that the gram atomic weight should be inversely proportional to the material’s specific heat. Although the law of Dulong and Petit proved a fair approximation for many elements, it was far from exact for many others, and it was not at all helpful in determining the atomic weights of gaseous elements.

In 1811, the Italian physicist Lorenzo Romano Amadeo Carlo Avogadro di Quaregua e di Cerreto (1776–1856), known to posterity as Avogadro, concluded that equal volumes of all gases at the same temperature and pressure contain the same number of molecules. Unfortunately, Avogadro’s ideas had little influence on the work of his contemporaries, and it was not until 1860 that another Italian scientist, Stanislao Cannizzaro (1826–1910), pointed out that Avogadro’s hypothesis could be used as a basis for determining atomic and molecular weights.

The classical method of determining the molecular weight of a gas is to use density data. Experimentally, a few milliliters of a volatile liquid are placed in a stoppered flask containing a small orifice. The flask is then heated to a temperature above the boiling point of the liquid. As the liquid evaporates, its vapor replaces the air in the flask. The flask is then allowed to cool, and the vapor condenses as air re-enters the flask. The mass of the vapor is then calculated, and used in conjunction with the ideal gas law to determine the molecular weight of the liquid. This method works quite well for many gases and volatile liquids, but it cannot be used for substances that decompose on heating, such as urea.

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, the¹²C 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 English chemist and physicist John Dalton (1766–1844). The dalton is, therefore, defined as exactly one-twelfth (1/12th) 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 poly-reactions, for instance, a solution of polystyrene in benzene, the masses of the individual polymer molecules are distributed over a range of values. Thus, scientists have to use an average value to describe their molecular weight. The easiest way to do that is simply to take the number average, i.e., W_average = N (n_i + w_i/n_i), where one add the products of each molecular weight (w_i) and the number of molecules (n_i) having that w_i, 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, one has 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, scientists can determine the molecular weight of the solute.

If scientists 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

KEY TERMS

Avogadro’s number N— The number of molecules present in one mole of whatever the compound is always equal to 6.0221415 × 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.

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

Bloch, Daniel R., ed. Organic Chemistry Demystified. New York: McGraw-Hill, 2006.

Carey, Francis A. Organic Chemistry. Dubuque, IA: McGraw-Hill, 2006.

Hoffman, Robert V. Organic Chemistry: An Intermediate Text. Hoboken, NJ: Wiley-Interscience, 2004.

Loudon,G. Mark. Organic Chemistry. Oxford: Oxford

University Press, 2002.

Pang-Jen Kung

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

Avogadro's number N

—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.

relative molecular mass (formerly molecular weight) Mass of a molecule, the sum of the relative atomic masses of all its atoms. It is the ratio of the average mass per molecule of an element or compound to one twelfth of the mass of an atom of carbon-12. The molecular masses of reactants (elements or compounds) must be known in order to make calculations about yields in a chemical reaction.

relative molecular mass (molecular weight) Symbol M_r. The ratio of the average mass per molecule of the naturally occurring form of an element or compound to 1/12 of the mass of a carbon–12 atom. It is equal to the sum of the relative atomic masses of all the atoms that comprise a molecule.

molecular weight See relative molecular mass