Scientific & Chemical
Fundamentals
Measurement, Conversions &
Calculations
Dr. Ron Rusay
Fall 2007
© Copyright 2003-2007 R.J. Rusay
Measurement & Units
SI units & common units in General Chemistry
(Lab Manual pp. 139-142)
1
• Quantitative vs. Qualitative
• MASS (Chem: gram; SI: kg)
• LENGTH (Chem: cm & others; SI: m)
• TEMPERATURE (Celsius & Kelvin; SI: K)
• VOLUME (Chem: mL; SI: Liter)
• CHEMICAL AMOUNT: Mole (mol)
© Copyright 1998-2007 R.J. Rusay
Units of Measure
Units
U.S.
SI
Chemistry
Mass (weight)
Pound (lb)
Kilogram (kg)
Volume
Gallon (gal)
u
Liter (L)
Temperature
Fahrenheit
(oF)
Mile (mi),
Feet(ft), Inches
(in)
Kelvin (K)
“ Gram”
(g, mg)
“ Liter”
(mL, L)
K & Celsius (oC)
Length
Time
Meter (m)
“ Meter”
(cm, mm, nm)
Second (s)
Second (s)
Mole (mol)
Mass and Volume Measurements:
Refer to pp. 5-8
Mass Determination
(Weighing Devices: Balances)
Volumes of regular shapes
V=s3
h
V=lxwxh
01_05
1m3
Volume
1dm3= 1 L
1cm3= 1 mL
1 cm
1 cm
Liquid Measurement Tools
Numbers & Measurement
The Importance of Units

Measurement - quantitative observation
consisting of 2 parts
• Part 1 - number
• Part 2 - unit

Examples:
• 20 grams
• 6.63   joules / second
Scale: Size & Comparison
 Macroscopic
vs. Microscopic
 IBM financed Video:
http://www.wordwizz.com/imagendx.htm
How would you compare your lifespan?.. to that
of a dog? ….to the age of the earth?…How
about the age of mankind to that of all life?..
..the age of industrialized mankind to the age
of mankind?
Graphic Comparisons
Powers of Ten:
Scale
Language describes scale (prefixes)
Shorthand Prefixes
How many zeroes does yotta yotta yotta have?
Commonly used prefixes in
Chemistry
These should be known from memory.
Commonly used prefixes in Chemistry
Attosecond spectroscopy = 10 -15 x 10 -3 seconds
Science, 317, 765-775, (2007)
“The Electron Stopwatch”
QUESTION
Conveniently, a U.S. nickel has a mass of approximately 5 grams.
If you had one dollar’s worth of nickels what would be the mass
of the nickels in milligrams?
1.
2.
3.
4.
100 milligrams
50 milligrams
1,000 milligrams
100,000 milligrams
1000 milligrams (mg) = 1 gram (g)
Scientific Notation &
Significant Digits
Scientific Notation: A single digit followed by a
decimal and a power of ten.
Examples: 2,345 mL and 0.002340 g
2,345 mL = 2.345 x 10 3mL 0.002340 g = 2.340 x 10 -3 g
Numbers
1
• Expressing a number correctly is determined
by the method used in the measurement!
• How many numbers should I include?
Significant Digits (Figures)
Consider: the exactness of the measured value
• Short Hand expression translates the
number: Scientific Notation
© Copyright 1998-2007 R.J. Rusay
What is the length of the rod?
Different measurement tools give different numbers:
Which ruler is better?
? cm
4.2 - 4.3cm
? cm
4.24 - 4.25cm
What is the diameter of a circle?
All measuring devices are not the same, and the values
(numbers) that come from them indicate their
limitations.
Is there a better instrument to use other than a ruler?
Buret
08
mL
0
10
22.2 mL
20
30
40
50
What does each line represent?
1 mL
What can be estimated?
O.1 mL
Measurement Assignment
http://chemconnections.llnl.gov/General/Chem120/volume1.htm
Temperature Scales
Relative to Water
“Normal” Body Temperature
QUESTION
Dr. R. walks into class and claims, “It is very cold in here today. It
feels like 242 K.” If that were the temperature, would you agree
that you would feel cold? What would that be in Celsius degrees?
1.
2.
3.
4.
I agree, that would be 31°C.
I agree, that would be – 31°C.
I do not agree, that would be 31°C.
I agree, that would be –31.15°C.
Temperature
Reporting Numbers
Rules for Significant Digits (Figures)

Nonzero integers always count
as significant figures.
 3456
g has how many sig figs?
 4 sig figs.
• Expressed in scientific notation?
3.456 x 10 3 g
Reporting Numbers
Rules for Significant (Digits) Figures

Exact numbers (unit, conversion
or scale factors) can have an infinite
number of significant figures.
1
liter = 1,000. ml, exactly
1
inch = 2.54 cm, exactly
Zeros

Leading zeros do not count as
significant figures.

0.0486 mL has how many sig figs?
 3 sig figs.
• Number expressed in scientific
notation?
4.86 x 10 -2 mL
Zeros



Captive zeros always count as
significant figures.
16.07 cm has how many sig figs?
 4 sig figs.
Number expressed in scientific
1.607 x 10 1 cm
notation?
Zeros


Trailing zeros are significant only if
the number contains a decimal
point.
9.300 kg has how many sig figs?
 4 sig figs.
• Number expressed in scientific
9.300 kg
notation?
QUESTION
Which one of the following does NOT represent a result with four
significant digits?
1.
2.
3.
4.
0.07100
0.7100
0.7010
0.0710
Mathematics & Arithmetic
1
• Relative to method(s) of measurement
• Short Hand expression: Scientific Notation
• Numbers : How many to include?
Quantitative vs. Qualitative
• Addition/Subtraction......
• Multiplication/Division.....
• What is “significant”?.....Rounding Off
• http:dbhs.wvusd.k12.ca.us/SigFigsFable.html
© Copyright 1998-2007 R.J. Rusay
Systematic Problem Solving
Dimensional/Unit Analysis: Conversions
Workshop pp. 145-149
How many mL of milk are in a1/2 gallon carton?
0.50 gal
1 gal = 4 qt
? mL
1 qt = 946 mL
0.50 gal | 1 qt | 946 mL = ? mL
| 4 gal | 1 qt
Complete the following
Units & Conversions
Number
13,000,000,000 yrs.
Scientific Notation
10 yrs
1.3
x
10
________________
546
___________
mL
5.46 X 10 2 mL
______________
0.845
____________
kg __8.45 x 10 -1 kg___
Named unit
__? gigayears
13 Gyrs
0.546 Liters
0.546 L
_? grams__
845 g
Computational Rules
1
• Addition/Subtraction: Answer expressed
•
to the least number of decimal places of
the figures in the process
Multiplication/Division: Answer
expressed to the least number of
significant figures
© Copyright 1998-2007 R.J. Rusay
Addition
 Four
students were each asked to
measure a piece of wire and provide a
total length for the four pieces.
 Report the result correctly:
0.05 cm
12.01 cm
1.9 cm
+
2.386 cm
_______
16.346 cm
QUESTION
If you were unloading a 23.50 kg box of books from your car and
a “friend” added two more 482 gram chemistry books, how much
in kg and using the rules for significant digits, would you be
lifting?
1.
2.
3.
4.
23.98 kg
24.464 kg
24.46 kg
24.5 kg
Mathematical Processes:

Provide correct answers assuming each value (unit
omitted) is written with the correct number of sig figs:
12.01
x
1.90
_______ ______________
= 9.56370
2.386
12.01
x
1.90
_______ ______________
+ 0.05 = 9.61370
2.386
QUESTION
The average mass of a certain brand of vitamin C tablets is 253 mg.
What is the mass of three such tablets rounded to the proper
number of significant digits?
1.
2.
3.
4.
0.760 grams
0.759 grams
0.7590 grams
0.253 grams
Conversion Factor Method
(Dimensional Analysis)
1
• Qualitative Descriptions vs. Quantitative
• Use exact numbers / “scale factor” UNITS
• A Bookkeeping Method: Example Short”
5 ft___in
5
___
--------> ? m
• (1 ft = 12 in; 2.54 cm = 1 in; 100 cm = 1 m)
5
5
• ___ft
x 12 in/ft + ___in
= 65
___in
1.651
65
• ___in
x 2.54 cm/in x 1 m/100cm = ___m
© Copyright 1998-2007 R.J. Rusay