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The Mathematics of Chemistry

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Title: The Mathematics of Chemistry

1
The Mathematics of Chemistry

Mole Concept

Kenneth E. Schnobrich
2
Counting Things

It is relatively easy to count the number of
things in
A pair of soxs
A dozen oranges
A gross of paper clips
Atoms, molecules, and ions are extremely small
units of matter and visually it would be
impossible to count them in any sample we are
given.
Experimentally, we can determine the number of
atoms in a given sample indirectly

3
Avogadros Number

It has been determined that the number of atoms
contained in a mass equivalent to the atomic mass
of an element, expressed in grams 6.02 x 1023
atoms of that element.
The term used for 6.02 x 1023 things is a MOLE
(or MOL). It is also referred to as Avogadros
Number (it is unitless).

4
An Example

There are 1 x 1028 atoms in the average sized
person (an Octillion)
If the atom were the size of a pea, an Octillion
peas would cover the complete surface of 250,000
planets, each the size of Earth, to a depth of 4
feet
The atom is an incredibly small unit of matter.

5
Some Mole Relationships
AMOUNT OF MOLES
7 grams of Li 1 mole of Li
28 grams of Fe 0.5 moles of Fe
8 grams of Mg 0.25 moles of Mg
1.204 x 1024 Na atoms 2 moles of Na
3.01 x 1023 S atoms 0.5 moles of S
6
Doing the Conversion

Always start with what you are given

7
Using Table T
On Table T a formula is given for calculating the
number of moles - lets use it for a
calculation of moles (n) given mass/gram
formula mass of moles (n) given mass/gram
atomic mass Gram formula mass - mass of the
compound in grams Gram atomic mass - mass of
the element in grams
Given 8.0 grams of Mg how many moles do you
have? moles(n) 8.0 grams/24.0 grams moles(n)
0.25
NYS Reference Tables for Chemistry
8
Determining Formula Mass
Element Atomic Mass atoms Total Mass
Na 23 1 23
H 1 1 1
S 32 1 32
O4 16 4 64
NaHSO4 Total Mass (1 mole) 120
9
Determining Formula Mass
Element Atomic Mass atoms Total Mass
C 12 6 72
H 1 12 12
O 16 6 96

C6H12O6 Total Mass (1 mole) 180
10
Using Formula Mass
Given 90. grams of C6H12O6 how many moles in the
sample?
moles (n) given mass/ gram formula mass
moles (n) 90. grams/ 180 grams/mole 0.50
moles
11
Mixing It Up A Bit
Substance Mass (g) moles
CaCO3 300.
(NH4)2SO4 0.50
Cr(NO3)3 150.
CuSO45H2O 2.0
Sr(OH)2 50.
12
Mols and Gases
At STP one mol of any gas occupies a volume of
22.4 L
So, if we had 2 mols of H2 gas at STP it would
occupy 44.8 Liters
PROBLEM If a sample of N2 gas at STP occupies
a volume of 67.2 Liters, how many moles of the
gas do you have in the sample?
mols volume given/volume of one mol at STP
mols 67.2 Liters/22.4 Liters/mol 3 mols
PROBLEM How many grams of N2 gas are there in
the sample? g mols x g/one mol g 3 mol
(28 g/mol) 84 grams
13
Percent Composition

These problems are worked like any percentage -
if you miss 25 out of 50 questions you have a
50.
(mass of part/mass of whole) x 100
This equation can be found on Table T
If I wanted to know the percent by mass of
hydrogen in water
H (2.00 g H/18.0 g H2O) x 100 11.2

NYS Reference Tables for Chemistry
14
Composition Examples
Compound C H O
C6H12O6
CH4 No Oxygen
C2H5OH
CH3COOH
15
H2O in a Hydrate
Certain substances have water molecules
associated with their structure. Many salts
fall into this category and we refer to them as
hydrated salts. Different salts have different
numbers of of water molecules - BaCl22H2O
CuSO45H2O.
PROBLEM Calculate the by mass of water in one
mole of BaCl22H2O
H2O (mass of H2O in one Mol/mass of
BaCl22H2O) x 100 H2O (36 grams/243 grams) x
100 14.8 H2O
16
Empirical MolecularFormulas

Empirical formulas represent the smallest whole
number ratio of atoms in a compound (cannot be
reduced any further)
Molecular (or True) formula represents the actual
whole number ratio of atoms in a compound (it
will be a small whole number multiple of the
Empirical formula)

17
Empirical MolecularFormulas

CH2O would be the empirical formula of a typical
monosaccharide
C6H12O6 would represent the molecular or true
formula of the monosaccharide
6 x (CH2O) - each of the subscripts would be
multiplied by 6

18
Simple EF/MF Problems

Vitamin C has an empirical formula of C3H4O3 and
a molecular mass of 176 amu. What is the
molecular formula?
First determine the mass of the empirical
formula (3 x 12) (4 x 1) (3 x 16) 88
Now divide the molecular mass by the empirical
mass 176/88 2
Now multiply each of the subscripts in the
empirical formula by 2 C6H8O6

19
Some Problems
Empirical Formula Molecular Mass (amu) Molecular Formula
CH2 70
CH 78
CH2 28
CH3 30
20
Moles in Equations

In chemical reactions it is important that
equations be balanced and the mole ratio taken
into account.
For this unit we will provide the balanced
equation
2C2H6 7O2 -gt 4CO2 6H2O
The coefficients represent the of moles of
each substance.

21
Moles in Equations

Regardless of the number of moles of any reactant
or product, the ratio must always remain -
2746 for this reaction
2C2H6 7O2 -gt 4CO2 6H2O
Problem Starting with 1 mole of C2H6 how many
moles of H2O will be produced?
Divide the coefficients by 2
The new ratio is - 17/223
Therefore we will produce 3 moles of H2O starting
with 1 mole of C2H6

22
Other Mole Relationships

Lets use another reaction and take a slightly
different approach
2KClO3 2KCl 3O2
Problem 3.5 moles of KClO3 will produce how many
moles of O2?
Place the given of moles over the substance
Place an X over the substance in question
Below the substance given indicate the of moles
from the balanced equation
Below the substance you are looking for place the
number of moles from the balanced equation

23
Mole Relationships(cont.)
3.5 moles
X