# Measurement by gjjur4356

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Which liquid has the highest density?
least dense 1 < 3 < 5 < 2 < 4 most dense

1

3
2                                 5   4

Coussement, DeSchepper, et al. , Brain Strains Power Puzzles 2002, page 16
•   Density is an                               Density
INTENSIVE property
of matter.
- does NOT depend
on quantity of matter.      Styrofoam       Brick

-Examples:
color, melting point, boiling point, odor, density

•   DIFFERENT THAN
EXTENSIVE properties
- depends on
quantity of matter.
- mass, volume, length
Density
M
D =
V
M    ass
M = DxV
V = M
D
ensity    V     olume

D
Density of Some
Common Substance
Density of Some Common Substances

Substance                                          Density
(g / cm3)
Air                                               0.0013*
Lithium                                           0.53
Ice                                               0.917
Water                                             1.00
Aluminum                                          2.70
Iron                                              7.86
Gold                                             19.3
*at 0oC and 1 atm pressure
Consider Equal Masses
Equal masses…
…but unequal volumes.
The object with the
aluminum                              larger volume
(aluminum cube) has
the smaller density.       gold

Christopherson Scales

Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition, 1990, page 71
Comparing Densities (g/cm3)

cork
0.25
0.9       ice

water 1.0
aluminum
2.7

Jaffe, New World of Chemistry, 1955, page 66
Density Practice Problems
1. What is the density of carbon
dioxide gas if 0.196 g occupies a
volume of 100. mL?

M
D =
V
0.196 g
1.96 x 10-3 g/mL
100. mL
Density Practice Problems
2. An irregularly shaped stone has a
volume of 5.0 mL. The density of
the stone is 1.75 g/mL. What is
the mass of this stone?

M = DxV

1.75 g/mL x 5.0 mL     8.8 g
Density Practice Problems
3. A sample of iron has a mass of
94 g and a density of 7.8 g/cm3.
What is the volume of the iron?

V = M
D
94 g
12 cm3
7.8 g/cm3
Prefix   Symbol   Meaning           Exponential Notation
mega     M                  1,000,000
kilo     k                      1,000
hecto    h                        100
deka     da                         10
---      ---                          1
deci     d                            0.1
centi    c                            0.01
milli    m                            0.001
micro    µ                            0.000001
nano     n                            0.000000001

Also know…
1 mL = 1 cm3
Practice Measuring

0    1   2   3   4   5   4.5 cm
cm

0    1   2   3   4   5   4.54 cm
cm

0    1   2   3   4   5   3.0 cm
cm

Timberlake, Chemistry 7th Edition, page 7
20

15.0 mL

15 mL ?

10
Practice Recording Temperature
60oC                     (Celcius)

100oC
25oC
50oC

80oC
20oC
40oC

60oC
15oC
30oC

40oC
10oC
20oC

20oC
5oC
10oC

0oC
0oC
0oC                                  E
C   18.0oC                   60.oC
A   30.0oC
Scientific Notation
 Calculating with scientific notation

(5.44 × 107 g) ÷ (8.1 × 104 mol) =

5.44    EE    7                  ÷                  8.1                  EE             4   =

= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Scientific Notation

65,000 kg  6.5 × 104 kg
 Converting into scientific notation:
 Move decimal until there’s 1 digit to
its left. Places moved = exponent.
 Large # (>1)  positive exponent
Small # (<1)  negative exponent
 Only include sig. figs.
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Scientific Notation
Practice Problems
2,400,000 g                                                 2.4                  10 6   g
0.00256 kg                                                   2.56                  10 -3   kg
7  10-5 km                                                  0.00007 km
6.2  104 mm                                                 62,000 mm
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Percent Error

 Indicates accuracy of a measurement

experimental  accepted
% error                                                                                100
accepted

real value
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Percent Error
 A student determines the density of a
substance to be 1.40 g/mL. Find the %
error if the accepted value of the density
is 1.36 g/mL.
1.40 g/mL  1.36 g/mL
% error                                                                               100
1.36 g/mL

% error = 2.94 %
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Significant Figures
 Counting Sig Figs

 All digits are significant EXCEPT…
 Trailing zeros without
a decimal point -- 2,500

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Significant Figures
 Calculating with Sig Figs (con’t)
 Exact Numbers do not limit the # of sig
 Counting            numbers: 12 students
 Exact   conversions: 1 m = 100 cm

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Significant Figures
 Calculating with Sig Figs
 Multiply/Divide - The # with the fewest
sig figs determines the # of sig figs in
(13.91g/cm3)(23.3cm3) = 324.103g
4 SF                            3 SF
3 SF

324 g
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Significant Figures
Practice Problems
(15.30 g) ÷ (6.4 mL)
4 SF                                      2 SF

= 2.390625 g/mL  2.4 g/mL
2 SF
18.9 g
- 0.84 g
18.06 g  18.1 g
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Significant figures: Rules for zeros
Leading zero     0.421 – three significant figures

Captive zeros are significant.
Captive zero     4012 – four significant figures

Trailing zeros are significant.
Trailing zero    114.20 – five significant figures
Rules for Counting Significant Figures

1. Nonzero integers always count as significant figures.
2. Zeros: There are three classes of zeroes.
a.       Leading zeroes precede all the nonzero digits and DO NOT count as
2
significant figures. Example: 0.0025 has ____ significant figures.

b.       Captive zeroes are zeroes between nonzero numbers. These always
4
count as significant figures. Example: 1.008 has ____ significant figures.

c.       Trailing zeroes are zeroes at the right end of the number.

Trailing zeroes are only significant if the number contains a decimal point.
3
Example: 1.00 x 102 has ____ significant figures.

Trailing zeroes are not significant if the number does not contain a decimal
1
point. Example: 100 has ____ significant figure.

3.       Exact numbers, which can arise from counting or definitions such as 1 m
= 100 cm, never limit the number of significant figures in a calculation.

Ohn-Sabatello, Morlan, Knoespel, Fast Track to a 5 Preparing for the AP Chemistry Examination 2006, page 53

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