Diphosphorus Pentoxide: Formula And Molar Mass

Diphosphorus Pentoxide is a covalent compound that has an empirical formula of P₂O₅ and a chemical formula of  P₄O₁₀. The molar mass of diphosphorus pentoxide is the sum total of the molar mass of each of the atoms in its chemical formula. The molar masses of phosphorus (P) and oxygen (O) are:

M(P) = 30.973762 g/mol

M(O) = 15.999 g/mol

Thus, the molar mass of diphosphorus pentoxide is M(P₄O₁₀) = 30.973762(4) + 15.999(10) = 283.886 g/mol. Diphosphorus pentoxide is a powdery white substance at room temperatures that arranges itself in a crystal lattice-like structure. Diphosphorus pentoxide is extremely hygroscopic and readily absorbs moisture and water vapor. As such, it is often used a desiccant to keep places dry and free from moisture.

“Moreover, the abundance of chemical compounds and their importance in daily life hindered the chemist from investigating the question, in what does the individuality of the atoms of different elements consist.” — Johannes Stark

Molecular And Empirical Formula

The chemical formula of a compound is a representation of the kind and number of constituent atoms of that compound. In short, a chemical formula is a string of symbols that each represents a kind of atom, with subscripts to represent the number of each atom in a molecule of the compound.  A chemical formula is used to determine the general atomic makeup of a compound and the ratios of its constituent elements. The general form of a chemical formula is

AₓBᵧ

where A and B are chemical elements and x and y are integer values that specify the amount of As and Bs in a single molecule.

There are two kinds of chemical formulas: molecular formulas and empirical formulas.

The molecular formula of a compound tells us the amount and kind of atoms found in a single unit molecule. For instance, water has a molecular formula of:

H₂O

This formula tells us that a single molecule of water is composed of 2 hydrogen atoms and one oxygen atom. The molecular formula of a substance does not give explicit information regarding its structure, but it can be used to make guess about its organization.

In contrast to a full molecular formula, an empirical formula is a condensed chemical formula that represents the simplest integer ratio of atoms in the compound. For example, glucose has molecular formula of C₆H₁₂O₆ but its empirical formula is CH₂O as it has twice as many hydrogen atoms as carbon and oxygen atoms. Compounds with different molecular formulas can have the same empirical formula. Acetic acid, for example, has the same empirical formula as glucose (CH₂O) and CH₂O is the actual molecular formula for formaldehyde. In some cases, the common name of a compound will come from its empirical formula, not its molecular formula. This is the case with diphosphorus pentoxide. It has a molecular formula of P₄O₁₀, however, its name diphosphorus pentoxide comes from its empirical formula P₂O₅ (“di-“=2, “pent-“=5). Speaking of naming chemical compounds…

Rules For Naming Molecular Compounds

There is a set of rules you can follow to generate scientific nomenclature for a molecular compound based on its chemical formula. For any given chemical formula, one can generate a name by:

1. The element that is most to the left on the periodic table is the first part of the name. If the two elements are in the same group, the lower one goes first.
2. Remove the ending of the second element, and ad the suffix “-ide” (e.g. oxygen → oxide).
3. Add prefixes to each element name to indicate the number of atoms of each element.

The prefixes used to name chemical compounds stem from Greek and indicate the number of atoms of the element they are attached to. The prefixes are:

1. “mono-“
2. “di-“
3. “tri-“
4. “tetra-“
5. “penta-“
6. “hexa-“
7. “hepta-“
8. “octa-“

There are prefixes for atoms that have more than 8 of one kind of atom, but they are rarely used. In cases where there is only a single atom of the leftmost element, you are not required to attach the “mono-“prefix. Hence, why CO is “carbon monoxide,” not monocarbon monoxide.

“Success is little more than a chemical compound of man with moment.” — Philip Guedalla

Take the formula N₂O₄. How would we go about deriving this compound’s name? First, we identify the leftmost element on the periodic table. Nitrogen is to the left of oxygen, so it goes first. Next, we take the rightmost element oxygen and turn it into an “-ide” ending, so “oxide.” By looking at the subscripts, we know how many atoms of each element there are. Nitrogen has a 2, so it gets the prefix “di-” and oxygen has 4, so it gets the prefix “tetra-“. So, the entire chemical name is “dinitrogen tetroxide”

Let’s look at some more examples. What are the names of the following chemical compounds?:

1. SF₆
2. BrCl₃
3. N₂O₅

Answers

1.  Sulfur is more to the left on the periodic table that fluorine, so it goes first. SF₆ has one sulfur atom and 6 fluorine atoms, so sulfur gets no prefix and fluorine gets a “hexa-” prefix. The whole name is sulfur hexafluoride
2. Bromine and chlorine are in the same group (group 7 halogens). But, bromine is below chlorine, so it goes first. In BrCl₃ there is one bromine atom and three chlorine atoms, so bromine does not get a prefix and chlorine gets a “tri-” prefix. Therefore, the whole name is bromine trichloride.
3. Nitrogen is to the left of oxygen, so its name goes first. N₂O₅ has 2 nitrogen atoms and 5 oxygen atoms, so nitrogen gets a “di-” prefix and oxygen a “penta-” prefix. So, the whole name is dinitrogen pentoxide.

Many compounds have a common name that they go by instead of their prefix nomenclature. According to the naming convention, CH₄ would be called “carbon tetrahydride,” but most of the time it is just called methane. Likewise, H₂O is just called water, instead of the ominous-sounding “dihydrogen monoxide.”

How To Find Molar Mass

The molar mass of an element is the total mass present in one mole of that element. The molar mass of an element can be determined by multiplying the element’s standard atomic weight by the molar mass constant:

M = 1 g/mol

The molar mass constant is required for the correct dimensional analysis. Standard atomic weights are dimensionless quantities (pure numbers) so they must be multiplied by some dimensional quantity to give the correct units.

The standard atomic weight of an element can be found on the elements tile in the periodic table. The standard atomic weight is just the number under the symbol. In the above picture, the standard atomic weight of tungsten is 183.84. Multiplying this value by the molar mass constant will give the molar mass of tungsten, e.g.

183.84 x 1 g/mol = 183.84 g/mol

The molar mass of tungsten is 183.84 g/mol. In other words, if we had one mole of tungsten, it would have a mass of 183.84 grams.

In order to find the molar mass of a compound, all one has to do is find the sum total of the molar masses of each element in the compound, taking into account how many of each element is present in the molecule. In the case of H₂O, hydrogen and oxygen have standard atomic weights of 1.007825 and 15.999 respectively. Multiplying by the molar mass constant gives us the molar masses of both hydrogen and oxygen:

M(1.007825) = 1.007825 g/mol

M(15.99) = 15.99 g/mol

Since a water molecule has two hydrogen atoms for every oxygen atom, a mole of water molecules will have two moles of hydrogen for every mole of oxygen. By multiplying the molar mass of each element by the proportion of the composition of the compound and summing the values, we can determine the molar mass of the whole molecule:

M(H₂O) = 1.007825(2) + 15.99(1) = 18.0565 g/mol

A single mole of water molecules has a mass of 18.0565 grams.

“Chemical compounds of carbon can exist in an infinite variety of compositions, forms and sizes. The naturally occurring organic substances are the basis of all life on Earth, and their science at the molecular level defines a fundamental language of that life.” — Elias James Corey

Let’s try some more. What are the molar masses of the following compounds?

1. SF₆
2. BrCl₃
3. N₂O₅

Answers

1. Sulfur and fluorine have atomic weights of 32.065 and 18.99803 respectively. Multiplying by the molar mass constant for each yields M(S) = 32.065g/mol and M(F) = 18.99803g/mol. Lastly, multiplying each term by the frequency it occurs in a compound gives us M(SF₆) = 32.065(1) + 18.99803(6) = 146.05318 g/mol.
2. Bromine and chlorine have atomic weights of 79.904 and 35.453 respectively. Thus, the molar mass of each is M(Br) = 79.904g/mol and M(Cl) = 35.453g/mol. Multiplying by the number of moles of each element and summing the values gives us: M(BrCl₃) = 79.904(1) + 35.453(3) = 186.263 g/mol.
3. Nitrogen and fluorine has standard atomic weights of 14.0067 and 15.999. The molar mass of each is M(N) = 14.0067g/mol and M(O) = 15.999g/mol. Once again, multiplying by the proportion of each element gives us M(N₂O₅) = 14.0067(2) + 15.999(5) = 108.0084 g/mol.

In summation, the chemical formula of a substance is a representation of the kinds and proportions of elemental constituents in a given compound. A chemical formula tells you what kind of atoms a compound is made of, and how many of each atom there are. The scientific nomenclature of compounds can be derived from its chemical formula by changing the ending of the more electronegative element and adding prefixes to indicate the proportions of each element.

The chemical formula can also be used to determine a compounds molar mass. In order to find the molar mass of a compound, first one must find the molar mass of each constituent element. Then, one must multiply those molar mass values by the frequency that they occur in the compound. Summing those values will give you the molar mass of the compound.