Transcript Measurements

Ch. 1:
Measurements
Chem 20-1204
El Camino College
1
Units

Units of Length
meter (m), centimeter (cm), inch (in.)
 1 m = 100 cm
 1 m = 39.4 in.
 2.54 cm = 1 in.

Ex. Which is larger, a meter or a cm? a meter
Ex. Which is larger, an in. or a meter? a meter.
2
Units

Units of Volume
liter (L), milliliter (mL), quart (qt)
 1 L = 1000 mL
 1 L = 1.06 qt
 946 mL = 1 qt

Ex. Which is larger, a milliliter or a liter? a liter
Ex. Which is larger, a quart or a liter? a liter.
3
4
Units

Units of Mass
gram (g), kilogram (kg), pound (lb)
 1 kg = 1000 g
 1 kg = 2.20 lb
 454 g = 1 lb

Ex. Which is larger, a g or a kg?
Ex. Do you weigh a higher number of
pounds or kilograms?
a kg
lbs
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6
Units

Units of Temperature
Fahrenheit (oF), Celsius (oC), Kelvin (K)
 freezing pt of H2O is 32 oF, 0 oC, 273 K
 boiling pt of H2O is 212 oF, 100 oC, 373 K

Ex. What is being measured: length, volume,
mass, or temp?
temp
292 K
23 mL
volume
0.004 cm. length
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For Very Large or Small
Numbers
Scientific notation has a specific form
 a.bcd x 10e

a.bc (the number must be 1 to <10)
 10e (the e is the exponent)
x 101 = x 10
x 10-1 = x .1
x 102 = x 100
x 10-2 = x .01
x 103 = x1000
x 10-3 = x .001

11
Solved Examples
Write 53 in scientific notation
 Convert to a.bc form (between 1 and 10)
 5.3
 To go from the a.bc form to 53, the decimal
moves 1 place to the right
 5.3 x 101

12
Solved Examples
Write 8769 in scientific notation
 Convert to a.bc form (between 1 and 10)
 8.769
 To go from the a.bc form to 8769, the
decimal moves 3 places to the right
 8.769 x 103

13
Solved Examples
Write 100.30 in scientific notation
 Convert to a.bc form (between 1 and 10)
 1.0030
 To go from the a.bc form to 100.30, the
decimal moves 2 places to the right
 1.0030 x 102

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Solved Examples
Write 0.00367 in scientific notation
 Convert to a.bc form (between 1 and 10)
 3.67
 To go from the a.bc form to 0.00367, the
decimal moves 3 places to the left
 3.67 x 10-3

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Examples
Write these in scientific notation
 501 = 5.01 x 102
 3,256,000 = 3.256 x 106
 0.042 = 4.2 x 10-2
 0.0005395 = 5.395 x 10-4

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Solved Examples
Write 1.0389 x 102 in decimal form
 1.0389 x 102 means that the decimal moves
2 places to the right
 103.89
 Write 8.0 x 10-3 in decimal form
 8.0 x 10-3 means that the decimal moves 3
places to the left
 .0080

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Examples
Write these in decimal notation
 3 x 100 = 3
 6.022 x 104 = 60220
 5.33 x 10-3 = 0.00533
 9.99 x 101 = 99.9

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On Your Calculator
Don’t use the 10x key
 Don’t press “x 10”
 You must use the EE or EXP key
 5.62 x 10-3 is 5.62 exp 3 +/ Try this calculation. If you get a different
result, see me after class

5.62 x 10-3
-8
=
6.36
x
10
8.84 x 104
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Place Names
___ ___
___ . tenths
___
hundreds
tens ones
___ ___
thousandths
hundredths
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Dimensional Analysis
How many minutes are in 2.0 hrs?
 The 2.0 hrs is your given information
 The conversion (60 min/1 hr) is called a
conversion factor
 Always start with the given information
 Write the conversion factor so the units to
be cancelled are on the bottom.

2.0 hrs 60 min
1 hr
= 120 min
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Dimensional Analysis

How many minutes in 936.2 sec?
936.2 sec

1 min = 15.60 min
60 sec
How many hrs in 53 min?
53 min
1 hr
60 min
= 0.88 hr
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Dimensional Analysis
If you need two conversions, don’t stop in
the middle. Write one conversion after the
other.
 Hit the times (X) key between numerators
 Hit the divide (/) key between denominators


How many hours in 9365 sec?
9365 sec
1 min
60 sec
1 hour
60 min
= 2.601 hr
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Dimensional Analysis

How many hrs in 5,877 sec?
5,877 sec

1 min
60 sec
1 hour
60 min
= 1.633 hr
How many minutes in 0.052 days?
0.052 days 24 hrs
1 day
60 min
1 hr
= 75 min
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Metric Prefixes to Memorize
prefix
kilo
symbol
k
multiple
1000 g / 1 kg
centi
milli
micro
nano
c
m
m
n
1 m / 100 cm
1 L / 1000 mL
1 g / 1 x 106 mg
1 m / 1 x 109 nm
also useful is 1 cm = 10 mm
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Metric Conversion Factors
There are many ways to write conversion
factors
 Make sure you know which unit is bigger

Many small units = one big unit
 A fraction of a big unit = one small unit

1m
100 cm
100 cm
1m
1 x 102 cm
1m
1 cm
.01 m
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Examples: Use Dimensional
Analysis
Always put the number by itself before the
conversion factor
 How many cm in 4.6 m?

4.6 m
100 cm
1m
= 460 cm
How many kg in 54.8 g?
54.8 g
1 kg
= 0.0548 kg
1000 g
30
Examples
How many kL in 4,329,647 L?
1 kL
= 4329.647 kL
4,329,647 L
1000 L


How many mm in 0.33 m?
0.33 m 1 x 106 mm = 3.3 x 105 mm
1m
 How many kg in 828 mg?
828 mg
1g
1 kg
= 8.28 x 10-4 kg
1000 mg 1000 g
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English Units

These are the most common US units
mass: ounce, pound
 length: inch, foot, yard
 volume: cubic inch, fl. oz., gallon

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Metric-US Conversions: Don’t
Memorize
1 lb = 454 g
 1 oz = 28.3 g
 2.20 lb = 1 kg

1.06 qt = 1 L
 1 qt = 946 mL

1 in.  2.54 cm
 39.4 in. = 1 m
 0.621 mi = 1 km

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Examples
How many liters are in 2.98 quarts?
2.98 qt
1L
= 2.81 L
1.06 qt
 How many ounces are in 500.0 g?

500.0 g
1 oz
= 17.7 oz
28.3 g
 How many cm in 8.994 in.?
8.994 in. 2.54 cm = 22.84 cm
1 in.
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Place Names
___ ___
___ . tenths
___
hundreds
tens ones
___ ___
thousandths
hundredths
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Significant Figures
Sig figs apply to measured amounts
 Sig figs don’t apply to counted things

36
Significant Figures
For any apparatus, read 1 place past the
smallest mark
 The last significant digit is estimated (the
doubtful digit).

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Significant Figures
28 oC
50o
40o
30o
20o
10o
0 oC
The
smallest mark is in the tens place
One place past the smallest mark is the ones.
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Ex. Read These
3.6 oC
110 oC
4.7 oC
5.5 oC
meas-4
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Right on the Line?
Always read to one place past the smallest
mark
 Always read a piece of equipment to the
same place.


Note: Read the meniscus (the bottom of the
belly for water)
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Right on the Line?
3.0 mL
41
Conversion Factors in
Problems
Read the problem carefully, then write a
conversion factor
 When solving, write a number by itself first,
then write the conversion factor

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Example

A car is traveling 65.9 miles per hour. How
many miles will it go in 13.3 hrs?
65.9 miles
1 hour
The conversion factor is 1 hour or 65.9 miles
13.3 hrs 65.9 miles
1 hour
= 876 miles
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
A car is traveling 38.8 miles per hour. How
many hrs will it take to go 51.0 miles?
51.0 mi
1 hr
38.8 mi
=
1.31 hr
A pool empties at 4.2 gal per sec. How
many min will it take to empty 3200 gal?
3200 gal
1 sec
1 min
=
13 min
4.2 gal
60 sec

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Density

Density is mass/volume D = m
v
Find the density of 3.8 mL of liquid that has a
mass of 5.8 g.
5.8 g = 1.5 g/mL
3.8 mL

Note: 1 mL  1 cm3  1 cc
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
The density of gold is 19.3 g/cm3. Find the
mass of 87.3 cm3 of gold.
87.3 cm3 19.3 g
cm3

= 1685 g
Find the volume of 0.53 g of gold using the
density of 19.3 g/cm3.
0.53 g 1 cm3
19.3 g
= 0.027 cm3
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Density and Solids
The mass of a solid is measured on a balance or
scale
 The volume of a solid may be measured by
volume displacement

Measure the vol of water in a cylinder
 Add the solid
 Measure the vol of water again
 Vfinal - Vinitial = Vsolid

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A cylinder contains 11.3 mL water. A piece
of aluminum is added, and the water level
rises to 16.0 mL. What is the volume of the
aluminum?
 16.0 mL - 11.3 mL = 4.7 mL
 If the Al has a mass of 12.7 g, what is the
density of the Al?

12.7 g = 2.7 g/mL
4.7 mL
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Example
A cylinder contains 35.5 mL water. A piece
of zinc is added, and the water level rises to
45.0 mL. If the mass of the zinc is 68.60 g,
what is the density of the zinc?
 Volume 45.0 mL - 35.5 mL = 9.5 mL
 Density 68.60 g
= 7.2 g/mL
9.5 mL

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