Empirical and Molecular Formulas

A. Romero 2009

Empirical and Molecular Formulas CHEM 1A

Empirical Formula: The lowest whole number ratio between the elements in a compound (not necessarily the actual formula of the compound).

Molecular Formula: The actual formula of a molecular compound (the fixed ratio between the elements in the molecule). Example: glucose molecular formula C6H12O6  

empirical formula CH2O

The empirical formula is useful because it can be determined experimentally from the percent composition by mass or from the combustion products (see following pages). The molecular formula can be found from the empirical formula using the scaling factor if the molar mass of the compound is known (the molar mass can also be determined experimentally).

Scaling Factor =

molar mass of compound molar mass of empirical formula

Example: The molar mass of a compound with the empirical formula CH2O is 180.156 g/mol. What is the molecular formula of the compound?

Scaling Factor =

mass compound mass CH2O

=

180.156 g/mol 30.026 g/mol

= 6

CH2O = 1(12.01 g/mol) + 2(1.008 g/mol) + 1(16.00 g/mol)

CH2O x6 C6H12O6

 empirical formula  multiply subscripts by scaling factor  molecular formula

Molecular formula = C6H12O6

Calculating the empirical and molecular formulas from the percent composition by mass and the molar mass of the compound: Steps:  Assume that you have a 100.0 gram sample of the compound. The percent by mass would then be the mass (in grams) you have of each element.  Convert grams of each element to moles using the molar mass.  Divide all moles by the least number of moles.  If any resulting number is not a whole number, multiply through by the smallest number that would make the fractions whole numbers.  These whole numbers are the subscripts in the empirical formula.  Use the molar mass of the compound to determine the scaling factor, and scale the empirical formula up to the molecular formula.

Example: A compound is 43.7% P, and 56.3% O by mass, and has a molar mass of 283.88 g/mol. What are the empirical and molecular formulas?

Assume a 100.0 g sample of the compound:

P

43.7 g P

1 mol P

= 1.41 mol P

= 1.00

= 2

30.97 g P ×2

÷ 1.41 moles O

56.3 g O

1 mol O

= 3.52 mol O

= 2.50

16.00 g O

= 5

Empirical formula = P2O5

Scaling Factor =

mass compound mass P2O5

=

283.88 g/mol 141.94 g/mol

= 2

P2O5 = 2(30.97 g/mol) + 5(16.00 g/mol) P2O5 x2 P4O10

 empirical formula  multiply subscripts by scaling factor  molecular formula

Molecular formula = P4O10

(tetraphosphorus decoxide)

Determining the empirical & molecular formulas from combustion products and the molar mass of the compound:    

All the Carbon is converted to CO2 CxHyOz + O2 All the Hydrogen is converted to H2O If there is a third element present it is the balance of the mass Combustion Problem Flow Chart:

 CO2 + H2O

g CO2

mol CO2

mol C

gC

g H2O

mol H2O

mol H

gH

need for emp. formula gO

subtract from mass of compound to get g O

mol O

Example: A sample contains only C, H, & O. Combustion of 10.68 mg of sample yields 16.01 mg CO2 and 4.37 mg H2O. The molar mass of the compound is 176.1 g/mol. What are the empirical and molecular formulas? 176.1 g/mol

CxHyOz + O2  CO2 + H2O 10.68 mg

16.01 mg

g mol

16.01 mg CO2

4.37 mg H2O

1 mmol CO2

1 mmol C

44.01 mg CO2

1 mmol CO2

1 mmol H2O

2 mmol H

18.016 mg H2O

1 mmol H2O

4.37 mg

mg =

mmol

= 0.36378 mmol C

= 0.48512 mmol H

10.68 mg total – 4.369 mg C – 0.489 mg H = 5.822 mg O

12.01 mg C 1 mmol C

1.008 mg H 1 mmol H

= 4.369 mg C

= 0.489 mg H

0.36378 mmol C

= 1.000

=3

From previous steps 0.48512 mmol H

5.822 mg O

1 mmol O 16.00 mg O

= 1.33

÷ 0.36378 mmol

= 0.36387 mmol O

= 1.00

×3

=4

=3

Empirical formula = C3H4O3

Scaling Factor =

mass compound mass C3H4O3

=

176.1 g/mol 88.062 g/mol

= 2

C3H4O3 = 3(12.01 g/mol) + 4(1.008 g/mol) + 3(16.00 g/mol) = 88.062 g/mol C3H4O3 x2 C6H8O6

 empirical formula  multiply subscripts by scaling factor  molecular formula

Molecular formula = C6H8O6