GIA 5-6: Determining Empirical and Molecular Formulas

Unit 5: Chemical Quantities and Calculations                                                                            Chapter 10

Goals:

• to determine the empirical formula of a compound from percent composition information.
• to determine the molecular formula of a compound from empirical formula and molecular mass information.
• to determine the empirical formula of a compound from experimental mass data.

Overview:  One can calculate the percent composition of the elements in the compound from an empirical formula and the reverse is also true.  In this GIA you will learn how to calculate the empirical formula from percent composition data (and also from experimental data.)

Instructions: Working on your own or with a partner carefully follow the steps listed below.  Then use these same steps in the problems given.

Question: What is the empirical formula of a compound that is 27.3% C and 72.7% O?

Step 1: Change the % sign into grams.  (This assumes you have 100 grams of the compound.)

                                    27.3 % C à  27.3 g C

                                    72.7 % O à 72.7 g O

Step 2: Calculate how many moles of each element you have.

                                    27.3 g C x 1 mol C     =  2.27 mol C
                                                      12.0 g C

                                    72.7 g O x  1 mol O   =  4.54 mol O
                                                       16.0 g O

Step 3: Find the lowest whole number ratio of moles of elements in the compound.

                        4.54 mol O  =  2 mol O  =  2 O

                        2.27 mol C      1 mol C       1 C

Step 4: Use the whole numbers from your ratio in step 3 to write the empirical formula.

                        CO₂

Notes:  If there is more than two elements, you will need to set up more than one ratio each with the element with the lowest number of moles on the bottom.  If the mole ratio does not give you a whole number ratio, you will need to find the whole number ratio equal to the ratio you calculated.  (i.e. If your ratio is 1.5 mol O : 1.0 mol Fe, your whole number ratio becomes 3 mol O : 2 mol Fe and your formula would be Fe₂O₃.)

Practice:

1. What is the empirical formula of a compound that is 85.7% C and 14.3% H?

Answer: CH₂

2. Determine the empirical formula of a compound that contains 17.6% sodium, 39.7% chromium and 42.7% oxygen.              Answer: Na₂Cr₂O₇

Determining empirical formula from experimental data:  If the information is given in grams, you can skip Step 1 and start with Step 2.

3. Determine the empirical formula of the compound which was found to contain 5.82 g Na, 8.10 g S, and 6.08 g O.  Answer: Na₂S₂O₃

Determining molecular formula from empirical formula and molecular mass:  Since a molecular formula has a whole number multiple of elements in the empirical formula, the molecular formula’s mass will be a whole number times greater than the empirical formula.  Therefore, to determine the molecular formula from an empirical formula divide the molecular formula’s mass by the empirical formula’s mass and use that whole number as a multiple for the empirical formula’s subscripts.

1. A compound has the empirical formula C₂H₅ and a gram molecular mass of 58.1g.  What is its molecular formula?               Answer: C₄H₁₀

2. A given compound has an empirical formula of C₃H₅O₂ and a gram molecular mass of 146.14 g.  What is the molecular formula of this compound?
               Answer: C₆H₁₀O₄

3. A compound consisting of phosphorus and oxygen, and has an empirical formula of P₂O₃ a gram molecular mass of 219.9 g/mol.  Determine its molecular formula.

Answer: P₄O₆

Putting them all together:

The gram formula mass of a compound is 166.3 g.  The compound contains 47.1% potassium, 14.5% carbon, and 38.4% oxygen.  What is the molecular formula for the compound?  (Hint, first determine the empirical formula.)

                        Answer: K₂C₂O₄