## Molecular Formulas

Molecular formulas are a compact chemical notation that describe the type and number of atoms in a single molecule of a compound.

### Learning Objectives

Identify the molecular formula of a compound given either its name or structural formula.

### Key Takeaways

#### Key Points

• A molecular formula consists of the chemical symbols for the constituent elements followed by numeric subscripts describing the number of atoms of each element present in the molecule.
• The empirical formula represents the simplest whole-integer ratio of atoms in a compound. The molecular formula for a compound can be the same as or a multiple of the compound’s empirical formula.
• Molecular formulas are compact and easy to communicate; however, they lack the information about bonding and atomic arrangement that is provided in a structural formula.

#### Key Terms

• molecular formula: A formula that describes the exact number and type of atoms in a single molecule of a compound.
• empirical formula: A formula that indicates the simplest whole number ratio of all the atoms in a molecule.
• structural formula: A formula that indicates not only the number of atoms, but also their arrangement in space.

Molecular formulas describe the exact number and type of atoms in a single molecule of a compound. The constituent elements are represented by their chemical symbols, and the number of atoms of each element present in each molecule is shown as a subscript following that element’s symbol. The molecular formula expresses information about the proportions of atoms that constitute a particular chemical compound, using a single line of chemical element symbols and numbers. Sometimes it also includes other symbols, such as parentheses, dashes, brackets, and plus (+) and minus (–) signs.

For organic compounds, carbon and hydrogen are listed as the first elements in the molecular formula, and they are followed by the remaining elements in alphabetical order. For example, for butane, the molecular formula is C4H10. For ionic compounds, the cation precedes the anion in the molecular formula. For example, the molecular formula of sodium fluoride is NaF.

A molecular formula is not a chemical name, and it contains no words. Although a molecular formula may imply certain simple chemical structures, it is not the same as a full chemical structural formula. Molecular formulas are more limiting than chemical names and structural formulas.

### Empirical and Molecular Formulas

The simplest types of chemical formulas are called empirical formulas, which indicate the ratio of each element in the molecule. The empirical formula is the simplest whole number ratio of all the atoms in a molecule. For example:

• The molecular formula for glucose is C6H12O6. The molecular formula indicates the exact number of atoms in the molecule.
• The empirical formula expresses the smallest whole number ratio of the atoms in the element. In this case, the empirical formula of glucose is CH2O.

To convert between empirical and molecular formulas, the empirical formula can be multiplied by a whole number to reach the molecular formula. In this case, the empirical formula would be multiplied by 6 to get to the molecular formula.

### Examples of Empirical and Molecular Formulas

• The compound dichlorine hexoxide has an empirical formula ClO3 and the molecular formula Cl2O6
• The compound hydrogen peroxide has the empirical formula HO and the molecular formula H2O2

### Molecular Formulas and Structural Formulas

Molecular formulas contain no information about the arrangement of atoms. Because of this, one molecular formula can describe a number of different chemical structures. A structural formula is used to indicate not only the number of atoms, but also their arrangement in space. A structural formula is not as compact and easy to communicate, but it provides information that the molecular formula does not about the relative positioning of atoms and the bonding between atoms. Compounds that share a chemical formula but have different chemical structures are known as isomers, and they can have quite different physical properties.

Structural formula of butane: The chemical structure of butane indicates not only the number of atoms, but also their arrangement in space.

## Empirical Formulas

Empirical formulas describe the simplest whole-number ratio of the elements in a compound.

### Learning Objectives

Derive a molecule’s empirical formula given its mass composition

### Key Takeaways

#### Key Points

• Empirical formulas are the simplest form of notation.
• The molecular formula for a compound is equal to, or a whole-number multiple of, its empirical formula.
• Like molecular formulas, empirical formulas are not unique and can describe a number of different chemical structures or isomers.
• To determine an empirical formula, the mass composition of its elements can be used to mathematically determine their ratio.

#### Key Terms

• empirical formula: A notation indicating the ratios of the various elements present in a compound, without regard to the actual numbers.

Chemists use a variety of notations to describe and summarize the atomic constituents of compounds. These notations, which include empirical, molecular, and structural formulas, use the chemical symbols for the elements along with numeric values to describe atomic composition.

Empirical formulas are the simplest form of notation. They provide the lowest whole-number ratio between the elements in a compound. Unlike molecular formulas, they do not provide information about the absolute number of atoms in a single molecule of a compound. The molecular formula for a compound is equal to, or a whole-number multiple of, its empirical formula.

### Structural Formulas v. Empirical Formulas

An empirical formula (like a molecular formula) lacks any structural information about the positioning or bonding of atoms in a molecule. It can therefore describe a number of different structures, or isomers, with varying physical properties. For butane and isobutane, the empirical formula for both molecules is C2H5, and they share the same molecular formula, C4H10. However, one structural representation for butane is CH3CH2CH2CH3, while isobutane can be described using the structural formula (CH3)3CH.

Butane: The structural formula of butane.

Isobutane: The structural formula of isobutane.

### Determining Empirical Formulas

Empirical formulas can be determined using mass composition data. For example, combustion analysis can be used in the following manner:

• A CHN analyzer (an instrument that can determine the composition of a molecule) can be used to find the mass fractions of carbon, hydrogen, oxygen, and other atoms for a sample of an unknown organic compound.
• Once the relative mass contributions of elements are known, this information can be converted into moles.
• The empirical formula is the lowest possible whole-number ratio of the elements.

### Example 1

Suppose you are given a compound such as methyl acetate, a solvent commonly used in paints, inks, and adhesives. When methyl acetate was chemically analyzed, it was discovered to have 48.64% carbon (C), 8.16% hydrogen (H), and 43.20% oxygen (O). For the purposes of determining empirical formulas, we assume that we have 100 g of the compound. If this is the case, the percentages will be equal to the mass of each element in grams.

Step 1: Change each percentage to an expression of the mass of each element in grams. That is, 48.64% C becomes 48.64 g C, 8.16% H becomes 8.16 g H, and 43.20% O becomes 43.20 g O because we assume we have 100 g of the overall compound.

Step 2: Convert the amount of each element in grams to its amount in moles.

$\left(\frac{48.64 \mbox{ g C}}{1}\right)\left(\frac{1 \mbox{ mol }}{12.01 \mbox{ g C}}\right) = 4.049\ \text{mol}$

$\left(\frac{8.16 \mbox{ g H}}{1}\right)\left(\frac{1 \mbox{ mol }}{1.008 \mbox{ g H}}\right) = 8.095\ \text{mol}$

$\left(\frac{43.20 \mbox{ g O}}{1}\right)\left(\frac{1 \mbox{ mol }}{16.00 \mbox{ g O}}\right) = 2.7\ \text{mol}$

Step 3: Divide each of the mole values by the smallest of the mole values.

$\frac{4.049 \mbox{ mol }}{2.7 \mbox{ mol }} = 1.5$

$\frac{8.095 \mbox{ mol }}{2.7 \mbox{ mol }} = 3$

$\frac{2.7 \mbox{ mol }}{2.7 \mbox{ mol }} = 1$

Step 4: If necessary, multiply these numbers by integers in order to get whole numbers; if an operation is done to one of the numbers, it must be done to all of them.

$1.5 \times 2 = 3$

$3 \times 2 = 6$

$1 \times 2 = 2$

Thus, the empirical formula of methyl acetate is C3H6O2.

### Example 2

The empirical formula of decane is C5H11. Its molecular weight is 142.286 g/mol. What is the molecular formula of decane?

Step 1: Calculate the molecular weight of the empirical formula (the molecular weight of C = 12.011 g/mol and H = 1.008 g/mol)

5 (12.0111 g/mol) + 11 (1.008 g/mol) = C5H11

60.055 g/mol + 11.008 g/mol = 71.143 g/mol per C5H11

Step 2: Divide the molecular weight of the molecular formula by the the molecular weight of the empirical formula to find the ratio between the two.

$\frac{142.286 \ g/mol}{71.143 \ g/mol} = 2$

Since the weight of the molecular formula is twice the weight of the empirical formula, there must be twice as many atoms, but in the same ratio. Therefore, if the empirical formula of decane is C5H11, the molecular formula of decane is twice that, or C10H22.

From the Molecular Formula to the Empirical Formula – YouTube: This video shows how to go from the molecular formula of a compound to its corresponding empirical formula.

## Formulas of Ionic Compounds

An ionic formula must satisfy the octet rule for the constituent atoms and electric neutrality for the whole compound.

### Learning Objectives

Generate the empirical formula of an ionic compound given its molecular constituents.

### Key Takeaways

#### Key Points

• The overall ionic formula for a compound must be electrically neutral, meaning it has no charge.
• When writing the formula for the ionic compound, the cation comes first, followed by the anion, both with numeric subscripts to indicate the number of atoms of each.
• Polyatomic ions are a set of covalently bonded atoms that have an overall charge, making them an ion.
• Polyatomic ions form ionic bonds in the typical way, balancing so that the overall compound is electrically neutral.

#### Key Terms

• polyatomic ion: A set of covalently bonded atoms that have an overall charge, making them an ion.
• monatomic ion: An ion made of only one atom, for example Cl-.

Ionic bonds are formed by the transfer of one or more valence electrons between atoms, typically between metals and nonmetals. The transfer of electrons allows the atoms to effectively achieve the much more stable electron configuration of having eight electrons in the outermost valence shell ( octet rule ). When sodium donates a valence electron to fluorine to become sodium fluoride, that is an example of ionic bond formation.

Formation of sodium flouride: The transfer of electrons between two atoms to create two ions that attract each other because they are oppositely charged.

### Writing Ionic Formulas

Ionic compounds can be described using chemical formulas, which represent the ratios of interacting elements that are found in the ionic solid or salt. Ionic solids are typically represented by their empirical formulas. In formula notation, the elements are represented by their chemical symbols followed by numeric subscripts that indicate the relative ratios of the constituent atoms. The complete formula for an ionic compound can be determined by satisfying two conditions:

• First, the charge on the constituent ions can be determined based on the transfer of valence electrons necessary in order to satisfy the octet rule.
• Second, the cations and anions are combined in a way that produces a electrically neutral compound.

For example, in the reaction of calcium and chlorine, the compound is called calcium chloride. It is composed of Ca2+ cations and Cl anions; those ions are stable since they have filled valence shells. Its ionic formula is written as CaCl2, the neutral combination of these ions. Two chloride ions were needed in the final compound because calcium had a 2+ charge. To create a neutral compound, CaCl2, two 1- chloride ions were needed to balance out the 2+ charge from calcium.

### Polyatomic Ions

Polyatomic ions are a set of covalently bonded atoms that have an overall charge, making them an ion. For example, the hydroxide ion has the formula OH-1. Hydroxide is a compound made of oxygen and hydrogen that have been bound together. In the process of becoming a compound, hydroxide gained an extra electron from somewhere, making it OH-1. When creating ionic compounds with these polyatomic ions, treat them the same way as typical monatomic ions (only one atom).

For example, calcium hydroxide has the formula Ca(OH)2 because hydroxide has -1 charge and calcium has a 2+ charge. Two hydroxides were needed to balance off the +2 charge of calcium. The parentheses were used to indicate that OH was a polyatomic ion and came as a “package deal.” Two hydroxides couldn’t have been written O2H2 because that is a very different compound than (OH)2. Parentheses are always used when the compound contains multiples of the polyatomic ion.

Here is a list of common polyatomic ions:

• Ammonium, NH4+
• Carbonate, CO32-
• Bicarbonate, HCO3
• Cyanide, CN
• Phosphate, PO43-
• Hydroxide, OH
• Nitrate, NO3
• Permanganate, MnO4
• Sulfate, SO42-
• Thiocyanate, SCN
• Peroxide, O22-

Introduction To Ionic Compounds Video Series by Leah4sci – YouTube: This video explains the basics of ions.

Cation and Anion Formation – Ionic Compounds Part 2 – YouTube: This video shows you how monoatomic ions get their charge, and how to quickly find the charge of ions by looking at the periodic table.