Transcript Rules for Significant Figures in calculations

Chemical
Foundations
Chapter 1
The Scientific Method
Observation
Hypothesis
Experiment
Summary of
observed
(measurable)
behavior
Ex: law of
conservation of
mass
Theory
(model)
Theory
Modified
As
needed
Prediction
Experiment
A Theory (model)
attempts to explain
why it happens
The Scientific Method
Qualitative
Quantitative
Overview:
• Deals with descriptions
• Data can be observed but not
measured
• Colors, textures, smells etc.
•Qualitative -----Quality
Overview:
• Deals with numbers
• Data which can be measured
• Length, Height, volume, weight,
speed, time, temp
• Quantitative-----Quantity
Example: Oil Painting
• Blue & green paint
• Gold frame
• Masterful brush strokes
Example: Oil Painting
• 10” x 14”
• surface area 140 in2
• Weight: 8.5 pounds
Units of Measurement (1.3)
SI System: based on the metric system and
units derived from the metric system.
Physical Quantity
Name of Unit
Abbreviation
Mass
Kilogram
kg
Length
Meter
m
Time
Second
s
Temperature
Kelvin
k
Electric Current
Ampere
A
Amount of substance
Mole
mol
Luminous intensity
Candela
cd
Units of Measurement (1.3)
Symbol
Prefix
Factor
G
giga
109
M
mega
106
k
kilo
103
h
hecto
102
da
deka
101
BASE
d
deci
10-1
c
centi
10-2
m
milli
10-3
μ
micro
10-6
n
nano
10-9
Units of Measurement (1.3)
Volume: is not
a fundamental
SI unit but is
extremely
important in
chemistry.
Volume can be
derived from
length.
Units of Measurement (1.3)
Mass vs. Weight
Remember MASS IS NOT THE SAME AS WEIGHT!
Mass is a measure of the resistance of an
object to a change in its motion.
Weight is the response of mass to the
force of gravity.
Uncertainty in Measurement (1.4)
Uncertainty: the
uncertainty of measurement
depends on the precision of
the measuring device.
Report any observed measurements
by recording all the certain digits plus
the first uncertain digit.
20.15 ml
20.1 is certain 0.05 is uncertain
Precision and Accuracy (1.4)
Accuracy: agreement of a particular value with the
accepted value.
Precision: agreement among several measurements of
the same quantity (reproducibility).
Precision and Accuracy (1.4)
Random Error: equal probability of being high or low.
Systematic Error: error that occurs in the same
direction each time.
Significant Figures &
Calculations (1.5)
Scientific Notation
98,500,000 = ?
64,100,000,000 = ?
0.0000000279 = ?
4,200,000 = ?
9.85 x 107
6.41 x 1010
2.79 x 10-8
4.2 x 106
Significant Figures &
Calculations (1.5)
Rules for counting Significant Figures:
1. Nonzero integers always count!
2. Zeroes (3 classes):
a. Leading zeroes do not count (place holders)
b. Captive zeroes do count
c. Trailing zeroes are if there is a decimal point
3. Exact numbers (counting or from
definitions)
Significant Figures &
Calculations (1.5)
Rules for Significant Figures in calculations:
1. For multiplication or division: the resultant is the same
as the LEAST precise number in the calculation.
2. For addition or subtraction: the resultant is the same
number of decimal places as the least precise
measurement in the calculation.
3. Rounding: DO NOT round until all calculations are
completed. Use only the first number to the right of the
last significant figure.
Significant Figures &
Calculations (1.5)
Example:
12.11
18.0
+ 1.013
31.123
31.1
Dimensional Analysis (1.6)
Unit Factor Method/Dimensional Analysis: converting
a given result from one system of units to another.
Rules for Dimensional Analysis:
•
•
•
•
•
Start with what value is known, proceed to the unknown.
Draw the dimensional lines.
Insert the unit relationships.
Cancel the units.
Do the math, include units in answer.
Temperature (1.7)
Boiling point of
water
Freezing point
of water
Fahrenheit
Celsius
Kelvin
212 ˚F
100 ˚C
373 K
180˚F
100˚C
32 ˚F
0 ˚C
Notice that 1 kelvin = 1 degree Celsius
100 K
273 K
Temperature (1.7)
Tf = Tc x 9oF/5oC + 32o F
Tc = 5oC/9oF(Tf – 32o F)
Tk = Tc + 273.15
Density (1.7)
Recall that you can measure either the volume
or the mass of an object. Density is a property
that describes the relationship between these
two measurements.
Density (1.7)
Compound
Density in g/cm3 at 20o C
Chloroform
1.492
Diethyl ether
0.714
Ethanol
0.789
Isopropyl alcohol
0.785
Toluene
0.867
A chemist has an unknown solution that he
wants to identify. He measured out exactly
25.00 ml (cm3) of the substance and found that
it has a mass of 19.735 g at 20 C.
Density = 19.735 g/25.00 cm3 = 0.794 g/cm3
Classifying Matter
Mixtures (a variable composition)
A homogeneous mixture is the same
throughout with visibly
indistinguishable parts. (Solutions)
A heterogeneous mixture is one
that has visibly distinguishable
parts.
Classifying Matter
Substances, on the other hand, cannot be
separated into different kinds of matter
by physical means such as sorting, filtering,
heating, or cooling. (ex: Table salt)
Some substances, like silver, contain only
one kind of matter. These substances are
called elements.
Classifying Matter
Matter
Heterogeneous
Physical Means
Homogenous
Pure Substances
Compounds
Chemical Means
Elements