Essential Math of Chemistry

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Transcript Essential Math of Chemistry

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
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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)