Essential Math of Chemistry
“No human endeavor can be called science
if it can not be demonstrated mathematically.”
Leonardo da Vinci (1452-1519)
The Importance of Units
Units must be carried into the
answer, unless they cancel.
5.2 kg (2.9 m) = 0.64 kg-m
(18 s)(1.3 s)
s2
4.8 kg (23 s)
(5.2 s)(37 s)
= 0.57 kg
s
Basic Algebra
Solve the following for x.
x+y=z
x and y are connected by
addition. Separate them
using subtraction. In general,
use opposing functions to
separate things.
x+y=z
–y –y
The +y and –y cancel on
the left,
leaving us with…
x=z–y
Basic Algebra
Solve for x.
x and 24 are connected by
subtraction. Separate
them using the opposite
function: addition.
x – 24 = 13
x – 24 = 13
+24 +24
The –24 and +24 cancel
on the left,
leaving us with…
x = 37
Basic Algebra
Solve for x.
x and k are connected by
multiplication. Separate
them using the opposite
function: division.
The two k’s cancel on
the left,
leaving us with…
F=kx
()
()
__
1
__
1
F=kx
k
k
(or)
F=kx
k k
__
F
x=
k
Basic Algebra
Solve for x.
x and 7 are connected by
multiplication. Separate
them using the opposite
function: division.
The two 7’s cancel on
the right,
leaving us with…
8=7x
()
()
__
1
__
1
8=7x
7
7
(or)
8=7x
7 7
__
8
x=
7
Basic Algebra
Solve for x.
One way to solve this
is to cross-multiply.
Then, divide both
sides by TR.
The answer is…
___
BA = ___
TR
x
H
BAH = xTR
( )
( )
___
1 BAH = xTR ___
1
TR
TR
BAH
x = ___
TR
Solve for T2, where…
P
1V1
____
=
P1 = 1.08 atm
T1
P2 = 0.86 atm
____
1 PVT =
V1 = 3.22 L
1 1 2
P
V
1
1
V2 = 1.43 L
P2V2T1
T1 = 373 K
( )
P
2V 2
____
T2
( )
____
1
P1V1
P2V2T1
______
T2 =
P1V1
(0.85
atm)(1.43 L)(373 K)
_____________________
T2 =
= 130 K
(1.08 atm)(3.22 L)
A General Procedure for Solving
Problems
• Read the problem carefully and make a list of
the “knowns” and the ‘unknowns”
• Look up all needed information
– Your lecture notes will have much, if not all, of the
needed information
• Work out a plan and, following your plan, obtain
an answer by carrying out the required math.
• Check over your work
– This is best done by estimating your answer
– Ask yourself: “Does the answer seem reasonable?”
How to Succeed in Chemistry
•
•
•
•
•
Learn the language
Use the illustrations
Review your notes frequently
Work as many problems as possible
Do NOT cram for exams.
Hollow Penny
Data Table
Post-1982
Pre-1982
Post-1982
Initial mass
3.086 g
2.354 g
2.329 g
Final mass
3.067 g
2.304 g
0.130 g
with scratches
Score side of penny
in 3 locations
Place penny in HCl
acid overnight
Percent Composition
What metal disappeared from the penny...copper or zinc?
www.usmint.gov
THE END
This PowerPoint has been
made possible through
LOTS of my free time!
Resources - Intro. to Chemistry
Worksheet - vocabulary
Worksheet - material safety data sheet (acetone)
Activity - checkbook activity
Worksheet - graphing
Worksheet - real life chemistry
General Chemistry PP
Worksheet - conversion factors
Worksheet - scientific notation
Worksheet - metric article (questions)
Episode 1 - The World of Chemistry
Worksheet - significant digits
Episode 3 – Measurement:
The Foundation of Chemistry
Worksheet - math review
Episode 4 - Modeling The Unseen
Worksheet - math of chemistry
Worksheet - article on the metric system
Textbook - questions
Lab – introduction to qualitative analysis
Outline (general)