Empirical and Molecular Formulas, Combustion Analysis, and Polyatomic Ions

Empirical and Molecular Formulas

Definitions and Key Concepts

Understanding the difference between empirical and molecular formulas is fundamental in general chemistry. These formulas describe the composition of chemical compounds in terms of the elements present and their ratios.

• Empirical Formula: The simplest whole-number ratio of atoms of each element in a compound. It is often determined from mass percentages using the mole concept.

• Molecular Formula: The actual number of atoms of each element in a molecule. It is a whole-number multiple of the empirical formula.

• Relationship: The molecular formula is always an integer multiple (n-factor) of the empirical formula.

Example: For glucose, the empirical formula is CH2O, while the molecular formula is C6H12O6.

Calculating the Empirical Formula

The empirical formula can be calculated from the mass percentages or masses of elements within a compound.

1. Write down the mass (or percentage) of each element.

2. Convert the masses to moles by dividing by the atomic mass of each element.

3. Divide each mole value by the smallest number of moles to obtain whole-number ratios.

4. If necessary, multiply by a factor to obtain whole numbers.

Example: A compound is 57.47% sodium, 40.01% oxygen, and 2.52% hydrogen. Calculate the empirical formula by converting percentages to grams (assuming 100 g sample), then to moles, and finally to the simplest ratio.

Calculating the Molecular Formula

Once the empirical formula is known, the molecular formula can be determined if the molar mass is also known.

1. Calculate the molar mass of the empirical formula.

2. Divide the compound's molar mass by the empirical formula mass to get the n-factor.

3. Multiply the subscripts in the empirical formula by the n-factor to obtain the molecular formula.

Example: Ibuprofen (M = 206.3 g/mol) has a percent composition of 75.70% C, 8.80% H, and 15.50% O. Find the empirical formula, then use the molar mass to determine the molecular formula.

Combustion Analysis

Concept and Procedure

Combustion analysis is a technique used to determine the empirical formula of a compound, especially those containing carbon, hydrogen, and oxygen. The compound is combusted in oxygen, and the masses of CO2 and H2O produced are measured.

• Combustion of hydrocarbons produces CO2 and H2O.

• For compounds containing other elements (e.g., N, Cl), additional steps are needed to account for these elements.

Steps:

1. Convert the grams of CO2 to grams of C.

2. Convert the grams of H2O to grams of H.

3. If necessary, subtract the masses of C and H from the original sample mass to find the mass of the third element (e.g., O).

4. Convert all masses to moles.

5. Divide by the smallest number of moles to get the simplest ratio.

Example: Combustion of 12.01 g of 2,3-dihydroxybutanedioic acid produces 14.08 g CO2 and 4.32 g H2O. Calculate the empirical formula.

Combustion Apparatus

A combustion apparatus is used to vaporize the sample and convert it to gaseous products for analysis. The apparatus typically includes chambers for vaporization, conversion of hydrogen to water, and absorption of CO2 and H2O.

• Chamber A: Sample vaporization

• Chamber B: Hydrogen conversion to H2O

• Chamber C: Water absorption

• Chamber D: Gas trapping

Example: The combustion of a jet fuel sample produces changes in the mass of CO2 and H2O absorbers. Use these changes to determine the empirical formula.

Polyatomic Ions

Definitions and Classification

Polyatomic ions are groups of covalently bonded atoms that carry an overall charge. They are important in naming and understanding ionic compounds.

• Polyatomic Oxyanions: Negatively charged ions containing oxygen.

• Trioxides: Ions with three oxygens (e.g., CO32-, NO3-).

• Tetraoxides: Ions with four oxygens (e.g., SO42-, PO43-).

Deriving Oxyanion Names

Oxyanion names change based on the number of oxygens:

• Decrease the number of oxygens by one: change the ending from -ate to -ite.

• Prefix hypo- and per- are used for ions with fewer or more oxygens, respectively.

Example: PO43- is phosphate; PO33- is phosphite.

Halogen Oxyanions

Halogen oxyanions are named based on the halogen present and the number of oxygens.

Halogen	Base Name
Fluorine (F)	fluor-
Chlorine (Cl)	chlor-
Bromine (Br)	brom-
Iodine (I)	iod-

# of Oxygens	Base Name
1	hypo-...ite
2	...ite
3	...ate
4	per-...ate

Polyatomic Cations

• NH4+: Ammonium ion (only major polyatomic cation with +1 charge).

• Hg22+: Mercury(I) ion (composed of two mercury atoms bonded together).

Other Polyatomic Ions

The Other Tetraoxides
Permanaganate
Chromate
Oxalate

The Other Polyatomic Ions
Cyanide
Hydroxide
Peroxide
Thiocyanate
Acetate

Examples and Applications

• Example: The formula for the thiosulfate ion is derived by replacing one oxygen in sulfate (SO42-) with a sulfur atom, resulting in S2O32-.

• Example: The silicate ion is the silicon analog of the carbonate ion, with the structure SiO32-.

Summary Table: Common Polyatomic Ions

Ion Name	Formula	Charge
Ammonium	NH4+	+1
Nitrate	NO3-	-1
Sulfate	SO42-	-2
Phosphate	PO43-	-3
Carbonate	CO32-	-2
Acetate	CH3COO-	-1
Hydroxide	OH-	-1
Permanganate	MnO4-	-1
Chromate	CrO42-	-2
Thiosulfate	S2O32-	-2

Key Equations

• Empirical Formula Calculation:

$\text{Moles of element} = \frac{\text{mass of element (g)}}{\text{atomic mass (g/mol)}}$

• Molecular Formula Calculation:

$n = \frac{\text{Molar mass of compound}}{\text{Empirical formula mass}}$

$\text{Molecular formula} = n \times \text{Empirical formula}$

• Combustion Analysis:

$\text{Mass of C} = \text{mass of CO}_2 \times \frac{12.01}{44.01}$ $\text{Mass of H} = \text{mass of H}_2\text{O} \times \frac{2.016}{18.02}$

Additional info:

• Practice problems throughout the notes reinforce the calculation of empirical and molecular formulas, combustion analysis, and polyatomic ion nomenclature.

• Tables and diagrams are used to clarify the classification and naming of polyatomic ions.