Transcript Math of Chemistry

The Mole &
Stoichiometry
-
Quantitative study of
substances and their
relationship to each
other in chemical
reactions.
-
The “Math” of Chemistry
The Mole

Similar to how a dozen = 12 things

One mole = 602 billion trillion things
602,000,000,000,000,000,000,000

6.02 X 1023 (in scientific notation)

6.02 X 1023 is called
Avogadro’s number.

Amedeo Avogadro


(1776 – 1856)
Mole is abbreviated mol

(gee, that’s a lot quicker to
write, huh?)
Just How Big is a Mole?

Enough soft drink cans to cover the
surface of the earth to a depth of
over 200 miles.

If you had Avogadro's number of
unpopped popcorn kernels, and
spread them across the United
States of America, the country would
be covered in popcorn to a depth of
over 9 miles.

If we were able to count atoms at the
rate of 10 million per second, it
would take about 2 billion years to
count the atoms in one mole.
Mole Concept
A mole is equal to 3 things:

1 mole = gram formula mass (molar mass)

1 mole = 6.02 X 1023 particles

1mole = 22.4 liters of a gas at STP
Mole Conversions
The Mole

1 mole Al = 6.02 X 1023 “atoms”

1 mole H2O = 6.02 x 1023 “molecules”

Note:
the NUMBER of particles is always the same, but
the MASS of each mole will be very different!
 This is because atoms have different atomic
masses.

Molar Mass

Molar Mass =
Mass of 1 mole of
particles (in grams)

Use average atomic mass rounded to the
nearest whole number
1 mole of C atoms
=
12 g
1 mole of Mg atoms
=
24g
1 mole of Cu atoms
=
63.5 g
Learning Check!
Find the molar mass
1 mole of Br atoms
=
1 mole of Sn atoms
=
________ g/mole
________ g/mole
Molar Mass of Molecules and
Compounds
Called “gram formula mass” or “molecular mass”
Add up atomic masses of atoms in the formula
1 mole of CaCl2
1 mole Ca x 40 g/mol
+ 2 moles Cl x 35.5 g/mol
= 111 g/mol
Learning Check!
A.
Molar Mass of K2O = ________
B. Molar Mass of Al(OH)3 = ________
Learning Check

Prozac, C17H18F3NO, is a widely used
antidepressant that inhibits uptake of
serotonin by the brain. Find molar mass.
C:
 H:
 F:
 N:
 O:

12 g/mol x 17 =
1 g/mol x 18 =
19 g/mol x 3 =
14 g/mol x 1 =
16 g/mol x 1 =
Total =
g/mol
Calculations with Molar Mass
# moles = given mass (grams)
gram-formula mass
Converting Moles and Grams
Aluminum is often used for the structure of
light-weight bicycle frames. How many
grams of Al are in 3.00 moles of Al?
3.00 moles Al
? g Al
On Ref Tables find molar mass of Al
1 mole Al = 27 g Al
3.00 moles Al
=
Answer
x grams
27 g/mol
= 81 g Al
Mole/Gram Conversion Practice

If you have 30 grams of CO2 how many
moles do you have?

If you have 6 moles of MgBr2 how many
grams do you have?
Learning Check!
The artificial sweetener aspartame
(Nutra-Sweet) formula C14H18N2O5 is
used to sweeten diet foods, coffee and
soft drinks. How many moles of
aspartame are present in 225 g of
aspartame?
Add up the formula mass
 C:
12 g/mol x
14 =
 H:
1 g/mol x
18 =
 N:
14 g/mol x
2=
 O:
16 g/mol x
5=
Total =
# moles = ____grams
g/mol
=
g/mol
______ mol
Particles and Moles

1 mole = 6.02 x 1023 particles
# Moles =
# particles
6.02 x 1023 particles
A Mole of Particles
Contains 6.02 x 1023 particles
1 mole C
= 6.02 x 1023 C atoms
1 mole H2O = 6.02 x 1023 H2O molecules
1 mole NaCl = 6.02 x 1023 NaCl “formula units”
(technically, ionics are compounds not molecules
so they are called formula units)
A Mole of Gas

1 mole = 22.4 Liters of any gas at STP
# Moles =
# liters of gas (at STP)
22.4 Liters
Chemical Quantities
Percent Composition
and
Empirical Formulas
Copyright © 2008 by Pearson Education, Inc.
Publishing as Benjamin Cummings
Percent Composition

Formula on Ref. Tables
% Comp. by Mass = Mass of Part
x 100
Mass of Whole
Percent Composition
Is the percent by mass of each element in a formula.
Ex: Calculate the percent composition of CO2.
CO2 = 1 (12g) + 2 (16 g) = 44 g/mol)
12. g C
44g CO2
x 100
32 g O
x 100
44 g CO2
=
27.27 % C
=
72.72 % O
Learning Check
What is the percent composition of lactic acid,
C3H6O3, a compound that appears in the blood
after vigorous activity?
Solution
STEP 1
3 (12) + 6 (1) + 3 (16) = 90 g/mol
STEP 2
%C = 36 g C x 100
90 g
= 40% C
%H = 6 g H x 100
90 g
= 6.7% H
%O = 48 g O x 100
90 g
= 53.3% O
Percent Composition
What is the percent carbon in C5H8NO4 (the
glutamic acid used to make MSG
monosodium glutamate), a compound used
to flavor foods and tenderize meats?
a) 8.22 %C
b) 24.3 %C
c) 41.1 %C
Solution
64.58 %C
Molar mass C7H14O2 =
7(12) + 14(1) + 2(16) = 130g/mol
% C = 84g C x 100 = 64.6 % C
130g
You Try
The chemical isoamyl
acetate C7H14O2 gives the
odor of pears. What is the
percent carbon in isoamyl
acetate?
1) 7.102 %C
2) 35.51 %C
3) 64.58 %C
Percent of Water in a Hydrate

Hydrate: an ionic
compound with water
molecules loosely
attached.
Ex: BaCl2 ∙ 2H2O

Anhydrous Salt: the
hydrate with the water
driven off by heating in a
crucible

Finding % from Formula
Ex: BaCl2 ∙ 2H2O

Finding % from Experimental Data

Ex: If 11 grams of an unknown hydrate is
heated in a crucible to a constant mass of
9.5 grams calculate the % of water that
was in the hydrate.
Chemical Formulas and Moles


Formulas can tell us:

Relative number of atoms of each element in compound
Ex: NO2 2 atoms of O for every 1 atom of N

Mole ratio of each element in a formula unit
Ex: 1 mole of NO2 contains 2 moles of O atoms
to every 1 mole of N atoms
Thus if we know or can determine the relative number of
moles of each element in a compound, we can determine a
formula for the compound.
Types of Formulas

Empirical Formula: expresses smallest
whole number ratio of the atoms present.
Ex: ______________
(Note: Ionic formulas are always empirical)

Molecular Formula: states actual number of
each kind of atom found in one molecule of
the compound.
Ex: ______________
Writing Empirical Formulas
• The simplest whole number ratio of the atoms.
• Some molecular formulas can be reduced to their
empirical form
• Calculated by dividing the subscripts in the actual
(molecular) formula by a whole number to give the
lowest ratio.
C5H10O5  5
actual (molecular)
formula
= C1H2O1 = CH2O
empirical
formula
Molecular and Empirical Formulas
• The molecular formula is the same or a
multiple of the empirical.
Learning Check
A. What is the empirical formula for C4H8?
1) C2H4
2) CH2
3) CH
B. What is the empirical formula for C8H14?
1) C4H7
2) C6H12 3) C8H14
C. Which is a possible molecular formula for CH2O?
1) C4H4O4 2) C2H4O2 3) C3H6O3
Find Empirical Formula Given Grams
1. Determine the mass in grams of each element
present, if necessary.
2. Calculate number of moles of each element.
3.
Divide each by the smallest number of moles to
obtain the simplest whole number ratio.
Note:
If whole numbers are not obtained* multiply through by the
smallest number that will give all whole numbers
Find Empirical Formula Given Grams
A compound contains 7.31 g Ni and 20.0 g Br.
Calculate its empirical (simplest) formula.
Solution
Convert 7.31 g Ni and 20.0 g Br to moles.
Moles of Ni = 7.31 g Ni = 0.124 mol Ni
59 g Ni
Moles of Br = 20.0 g Br = 0.250 mol Br
80 g Br
Divide by smallest # moles to get ratio
0.124 mol Ni = 1 Ni
0.250 mol Br = 2 Br
0.124
0.124
Write ratio as subscripts: NiBr2
Converting Decimals to Whole
Numbers
When number of moles for an element is a decimal, all the
moles are multiplied by a small integer to obtain whole number.
A sample of a brown gas, a major air pollutant, is
found to contain 2.34 g N and 5.34g O.
Determine empirical formula:
You need mole ratios so convert grams to moles
moles of N = 2.34g of N =
14 g/mole
moles of O = 5.34 g =
16 g/mole
N0.167 O0.334
_______moles of N
_________moles of O
N 0.167 O 0.334  NO 2
0.167
Formula: _______________
0.167
Empirical Formula from
% Composition
A substance has the following composition
by mass:
60.80 % Na ; 28.60 % B ; 10.60 % H
What is the empirical formula of the
substance?
Consider a sample size of 100 grams
60.80 grams of Na
28.60 grams of B
10.60 grams H
Determine the number of moles of each
Determine the simplest whole number ratio
Empirical Formula from
% Composition
Aspirin is 60.0% C, 4.5 % H and 35.5 % O.
Calculate its empirical (simplest) formula.
Solution
Calculate moles of each element in 100 g.
100 g aspirin contains 60.0% C or 60.0 g C,
4.5% H or 4.5 g H, and 35.5% O or 35.5 g O.
60.0 g C =
12 g C
5.00 mol C
4.5 g H
1gH
4.5 mol H
=
35.5 g O =
16 g O
2.22 mol O
Solution (continued)
Divide by the smallest number of mol.
5.00 mol C
2.22
=
2.25 mol C (decimal)
4.5 mol H
2.22
=
2.0 mol H
2.22 mol O
2.22
=
1.00 mole O
Solution (continued)
Use the lowest whole number ratio as subscripts
When the moles are not whole numbers, multiply by a factor
to give whole numbers, in this case x 4
.
C: 2.25 mol C
x 4 = 9 mol C
H: 2.0 mol H
x 4 = 8 mol H
O: 1.00 mol O
x 4 = 4 mol O
Using these whole numbers as subscripts the simplest
formula is
C9H8O4
Finding the Molecular Formula

Molecular Mass (GFM) of a compound is
either equal to or some whole number
multiple of the empirical formula’s mass.
Molecular Mass
Empirical Mass
=
“Magic Number”
Distribute this number through the Empirical
formula to determine the Molecular formula
Finding the Molecular
Formula
A compound has an empirical formula of
NO2. The colorless liquid, used in rocket
engines has a molar mass of 92.0 g/mole.
What is the molecular formula of this
substance?
Finding the Molecular
Formula
A compound has an empirical formula of
CH2O. The white crystal, has a molar mass
of 180.0 g/mole. What is the molecular
formula of this substance?