Measurement &
Calculations
Honors Chemistry
Chapter 2
Scientific Notation
Shorthand way of expressing
very large or very small numbers
Consists of two factors:



Coefficient - a number between 1 and 10 (only 1
digit to the LEFT of the decimal point)
Base - a power of 10  “power of 10” shows the
number of 10’s that are to be multiplied together
Examples on the number line:
1x102
4x101
1x100
1x10-10 1x10-1
Place numbers on the line:
4x101 1x10-10 1x100 1x102 1x10-1
0
Uncertainty in Measurement
– due to instrument flaw and estimation

Measurements are uncertain because



Instruments are not free from ERROR.
Measuring always involves some
ESTIMATION.
Estimating with a scale

Estimate ONE digit more than the
instrument measures.
Length - Rulers
3
4
5
3
4
5
3
4
5
How to use a
graduated cylinder
Read the
meniscus
How to use a graduated cylinder
Triple Beam Balance
0
100
200
0
10
20
30
40
50
60
70
80
90
100
0
1
2
3
4
5
6
7
8
9
10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
How to read a triple beam balance
Temperature
Uncertainty
A.
Precision – represents agreement between
several measurements of the same quantity
•
B.
Accuracy – represents agreement between a
measurement & the true value (within the
limits of the instrument); enhanced with
calibration
•
C.
Precise data vs. Imprecise data
Accurate data vs. Inaccurate data
% Error =
measured value –accepted value x 100%
accepted value
Accuracy vs. Precision
Exact numbers – numbers with no
uncertainty
E. Significant Digits – certain digits plus 1
uncertain digit in a measurement;
indicative of precision
D.
Nonzero Digits
 Every
nonzero digit is
assumed significant.
 24.7 m
 0.743 g
 714 m
Captive Zeros
 Zeros
appearing between
nonzero digits are significant.
 7003 m
 40.79 g
 1.503 m
Leading Zeros

Leftmost zeros appearing in front
of nonzero digits are NOT
significant. They are placeholders.
 0.0071m = 7.1 x 10-3m
 0.42m = 4.2 x 10-1m
 0.000099m = 9.9 x 10-5m
Trailing Zeros

Zeros at the END of a number AND
to the RIGHT of a decimal point
are always significant.
 43.00 m
 1.010 m
 9.000 m
Trailing Zeros


Zeros at the rightmost end of a
measurement that lie to the left of
an understood decimal point are
NOT significant if they serve as
placeholders to show the magnitude
of the number.
 300 m
7000 m 27,210 m
Use decimal point at end to signify
that the last 0(s) are significant.
 300. m or 3.00 x 102 m
Significant Digits
Use Atlantic-Pacific Rule – imagine a US map
decimal
decimal
point
point
Pacific
Atlantic
1100
1100.
11.010000
0.025
0.00035000
1,000,100
Decimal
Present
Start
counting
with the 1st
nonzero
digit and
count all
the rest.
Decimal
Absent
Start
counting
with the 1st
nonzero
digit and
count all
the rest.
Calculations
Multiplication and Division (fewest sig digits)
1) 2.20cm x 0.96cm x 3.21cm =
2) 3.6g ÷ 4.20mL =
Addition and Subtraction (least number of
decimal places)
1) 28.751g – 7.2g =
2) 125.7mL + 1.88mL + 676mL =
3) 1600m + 1.50m =
4) 100.cm + 3.82cm =
Using a Manometer
a device used to measure pressure



When a gas is produced during the reaction, the
gas can be pumped into the bulb of the manometer
and the pressure of the gas can be determined.
There are 2 types of manometers – closed & open.
Closed: the difference in the height of the Hg
columns is the pressure of the gas in the bulb.
Gas has no
pressure
140mm
20mm
Using a Manometer


Open: To use an open manometer, you must also
have a barometer to determine the atmospheric
pressure. In an open manometer, the gas pressure
is working against atmospheric pressure.
Assume the atmospheric pressure is 760 mm Hg.
140 mm
70mm
20mm
20mm
Measurements:
basic to all sciences & all are
comparisons to a standard



English – still used in US
Metric – devised in the late 1700’s in
France
SI – Le Système Internationale d’Unités



Modern metric system (1960)
Based on 7 base units
Base units are modified by prefixes
SI Base Units
1.
Length
2.
Mass (SI standard unit) kilogram (kg)
3.
Time
second (s)
4.
Temperature
Kelvin (K)
5.
Amount of a substance mole (mol)
6.
Electric current
ampere (A)
7.
Luminous intensity
candela (cd)
meter (m)
Metric Conversion
Derived Units

Area: 2-D


Volume: 3-D



Solid –
Liquid or irregular shaped object –
Density

The Liter
=




The liter is 1000 mL
10cm x 10cm x 10cm
1 liter = 1000 cm3 = 1 dm3
1 milliliter = 1 cm3 = 1 cc = 20 drops
megakilo-
1,000,000
1,000
hectodeka-
100
10
Scientific
Notation
1 x 106
1 x 103
1 x 102
1 x 101
1
100
0.1
1 x 10-1
centimillimicro-
0.01
0.001
0.000 001
1 x 10-2
1 x 10-3
1 x 10-6
nano-
0.000 000 001
1 x 10-9
pico-
0.000 000 000 001
1 x 10-12
Prefix
BASE UNIT
(g, m, L)
deci-
Abbreviation
--------------
Meaning
Length Relationships
Conversions between units

Factor-label method or dimensional
analysis – based on using unit equalities
1000 m
1 km = _____
_____
1 km
1000 m
OR
1000 m
1 km
60 s = 1 min
60 s
OR
1 min
1 min
60 s
V. Tools for Analysis
A.
Organize data into tables

B.
Ascending values for independent variable
Present data in a graph



Independent variable is graphed on the x-axis
Dependent variable is graphed on the y-axis
Best-fit line or curve

C.
Used to see a relationship
Develop a relationship from the graph



Direct
Indirect or inverse
Develop an equation to relate the variables



The characteristic plot for a Direct
Relationship is a straight line graph.
Indirect Relationship
The characteristic plot for an Inverse
Relationship is a curve of the type
illustrated here. As one of the
variables increases, the other
decreases. Note: It is not a straight
line sloping downward.
Examples
A. Determine the density of aluminum from the analysis of data
from 5 samples.
54.0-g
14.0-g
3) 41.0-g
4) 27.0-g
5) 19.0-g
1)
2)
sample
sample
sample
sample
sample
has
has
has
has
has
a
a
a
a
a
volume
volume
volume
volume
volume
of
of
of
of
of
20.0 mL
5.0 mL
15.0 mL
10.0 mL
7.0 mL
HINT: Graph the data with volume as the independent variable.
Find the slope of the line!
B. Convert the density of benzene, 0.8787 g/cm3, to kg/m3.
C. Calculate the density of mercury if 1.00 x 102 g occupies a
volume of 7.36 cm3.
Density Graph
Density of Aluminum
60
Mass (g)
50
y = 2.7134x
40
30
20
10
0
0
5
10
Volume (mL)
BACK
15
20
Specific Heat

Amount of energy required to raise the
temperature of 1 g of substance by 1°C or 1K.
q = mCT
q – heat (J)
m – mass of substance (g)
C – specific heat capacity constant (J/g·°C)
- different for every substance
T – change in temp (Tf – Ti) (°C)
Specific heat capacities of substances
in reference packet.