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Empirical & Molecular Formulas. Chapter 3. Mathematical Methods. STEP 1 Obtain in the laboratory, the number of grams OR the weight percentage of each element in the compound. This can be found by: breaking down the existing compound into its elements

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mathematical methods
Mathematical Methods

STEP 1

Obtain in the laboratory, the number of grams OR the weight percentage of each element in the compound. This can be found by:

  • breaking down the existing compound into its elements
  • building the compound from the elements
slide3
STEP 2
  • Determine the number of moles of each element in the compound.
  • Use dimensional analysis with the atomic mass of the element.
slide4
STEP 3
  • Find the simplest whole number ratio of the moles of each element. Since each mole contains the same number of atoms, the simplest whole number ratio of the moles is also the simplest whole number ratio of the atoms of each element.
  • To do this, take all the mole values and divide them by the SMALLEST one
  • The answers are the subscripts in the empirical formula
05 rule
.05 Rule
  • After step #3, if the value is within .05 of a whole number (+ 0.05 or - 0.05), then the value may be rounded to that whole number.
  • The values used in these problems are obtained by experimentation. The 0.05 rule allows for experimental error.
slide6
IF the application of the .05 Rule does not produce whole numbers, then ALL of the results of step 3 must be multiplied by the same smallest integer that WILL produce values that can be rounded to whole numbers by the .05 Rule.
slide7
EXAMPLE: A compound is found to contain 72.3% Fe and 27.7% O by weight. Calculate the empirical formula.

STEP 1 In 100 g of compound there would be 72.3 g Fe and 27.7 g O

slide8

1 mole Fe

X ——————

55.8 g Fe

72.3g Fe

= 1.296 mole Fe

1.296 mole

1.296 mole

X 3 = 3.00 = 3

= 1.000

Fe3O4

1 mole O

X ——————

16.0 g O

27.7g O

= 1.731 mole O

1.731 mole

1.296 mole

=1.336

X 3 = 4.01 = 4

slide9
Example of a hydrated compound

CaSO4 7 H2O

  • Compounds with molecules of water held in their crystal structure
  • Very common in nature
  • Water can be removed by heating, leaving behind what is called the anhydrous compound (CaSO4 for the above example)
slide10
Naming -- the following is tacked on the name obtained from the ions

H2O monohydrate 2 H2O dihydrate

3 H2O trihydrate 4 H2O tetrahydrate

5 H2O pentahydrate 6 H2O hexahydrate

7 H2O heptahydrate 8 H2O octahydrate

9 H2O nonahydrate 10 H2O dekahydrate

CaSO4 7 H2O -- named as

calcium sulfate heptahydrate

finding the empirical formula of a hydrate
Finding the empirical formula of a hydrate
  • Find the empirical formula of a hydrate of CaSO4 hydrate that is 28.5% H2O
  • To solve this problem, find the simplest mole ratio between the anhydrous part of the compound (CaSO4)and the water (H2O)
  • H2O =28.5 % CaSO4 =71.5 %

(100% - 28.5%)

slide12
1 mole CaSO4

71.5 g CaSO4 X ------------------- = .5250 mole CaSO4

136.2 g CaSO4

. (molar mass of CaSO4)

1 mole H2O

28.5 g H2O X ----------------- = 1.583 mole H2O

18.0 g H2O

.5250

------- = 1.00 = 1

.5250

  • When you are finding formulas of hydrates they ALWAYS come out even!

1.583

------- = 3.01 = 3

.5250

CaSO4 3 H2O

molecular formula
Molecular Formula
  • A molecular formula tells the actual number of atoms of each element in a molecule.
  • It is a multiple of the empirical formula.
molecular formula problem
Molecular Formula Problem:

The compound with a molar mass of 171.0 g/mole that contains 14.0% carbon, 41.5% chlorine, and 44.4% fluorine is a chlorofluorocarbon (CFC) that was once used as a refrigerant, but is now on the list of chemicals known to be ozone depleting. What is the molecular formula of this compound?

slide15

Empirical formula =CClF2

Molar Mass of Empirical Formula:

C: 1(12.0) = 12.0

Cl: 1(35.5) = 35.5

F: 2(19.0) = 38.0

85.5

(CClF2)2=C2Cl2F4

combustion analysis
Combustion Analysis

A 3.489g sample of a compound containing C, H, and O yields 7.832 g of CO2, and 1.922g of water upon combustion. What is the simplest formula of the compound?

slide17

Since it’s combustion, you know

CxHyOz + O2 CO2 + H2O

All the C goes into the CO2

All the H goes into the H2O

(our job is to find x, y, and z!)

slide18

First find the amounts of C, H, and O

Using the MM of CO2:

Using the MM of H2O:

x=1.137 g O

slide19

=2.520

X 2 ≈ 5

=3.024

X 2 ≈ 6

=1.000

X 2 = 2

C5H6O2