Transcript Measurement - Clayton State University

SURVEY OF CHEMISTRY I
CHEM 1151
CHAPTER 1
DR. AUGUSTINE OFORI AGYEMAN
Assistant professor of chemistry
Department of natural sciences
Clayton state university
CHAPTER 1
MEASUREMENT
MEASUREMENT
- Is the determination of the dimensions, capacity, quantity,
or extent of something
- Is a quantitative observation and consists of
two parts: a number and a scale (called a unit)
- Is the tool chemists use most
Examples
mass, volume, temperature, pressure, length, height, time
SIGNIFICANT FIGURES
Precision
- Provides information on how closely individual
(repeated) measurements agree with one another
Accuracy
- Refers to how closely individual measurements
agree with the true value (correct value)
Precise measurements may NOT be accurate
SIGNIFICANT FIGURES
Exact Numbers
- Values with no uncertainties
- There are no uncertainties when counting objects or people
(24 students, 4 chairs, 10 pencils)
- There are no uncertainties in simple fractions
(1/4, 1/7, 4/7, 4/5)
Inexact Numbers
- Associated with uncertainties
- Measurement has uncertainties (errors) associated with it
- It is impossible to make exact measurements
SIGNIFICANT FIGURES
Measurements contain 2 types of information
- Magnitude of the measurement
- Uncertainty of the measurement
Only one uncertain or estimated digit should be reported
Significant Figures
digits known with certainty + one uncertain digit
RULES FOR SIGNIFICANT FIGURES
1. Nonzero integers are always significant
4732 (4 sig. figs.)
875 (3 sig. figs.)
2. Leading zeros are not significant
0.0045 (2 sig. figs.)
0.00007895 (4 sig. figs.)
The zeros simply indicate the position of the decimal point
3. Captive zeros (between nonzero digits) are always significant
1.0025 (5 sig figs.)
12000587 (8 sig figs)
RULES FOR SIGNIFICANT FIGURES
4. Trailing zeros (at the right end of a number) are significant
only if the number contains a decimal point
2.3400 (5 sig figs)
23400 (3 sig figs)
5. Exact numbers (not obtained from measurements) are assumed
to have infinite number of significant figures
RULES FOR SIGNIFICANT FIGURES
How many significant figures are present in each of the following?
What is the uncertainty in each case?
1.24 g
0.0024 L
0.39200 mL
3.0026 kg
significant figures
3
2
5
5
uncertainty
± 0.01 g
± 0.0001 L
± 0.00001 mL
± 0.0001 kg
RULES FOR SIGNIFICANT FIGURES
Rounding off Numbers
1. In a series of calculations, carry the extra digits through
to the final result before rounding off to the required
significant figures
2. If the first digit to be removed is less than 5, the
preceding digit remains the same (round down)
Round to two significant figures
2.53 rounds to 2.5 and 1.24 rounds to 1.2
RULES FOR SIGNIFICANT FIGURES
Rounding off Numbers
3. If the first digit to be removed is greater than 5, the
preceding digit increases by 1 (round up)
(2.56 rounds to 2.6 and 1.27 rounds to 1.3)
4. If the digit to be removed is exactly 5 (round even)
- The preceding number is increased by 1 if that
results in an even number
(2.55 rounds to 2.6 and 1.35000 rounds to 1.4)
- The preceding number remains the same if that
results in an odd number
(2.45 rounds to 2.4 and 1.25000 rounds to 1.2)
RULES FOR SIGNIFICANT FIGURES
- The certainty of the calculated quantity is limited by the least
certain measurement, which determines the final number of
significant figures
Multiplication and Division
- The result contains the same number of significant figures as the
measurement with the least number of significant figures
2.0456 x 4.02 = 8.223312 = 8.22
3.20014 ÷ 1.2 = 2.6667833 = 2.7
RULES FOR SIGNIFICANT FIGURES
- The certainty of the calculated quantity is limited by the least
certain measurement, which determines the final number of
significant figures
Addition and Subtraction
- The result contains the same number of decimal places as the
measurement with the least number of decimal places
2.045
3.2
 0.234
5.479 = 5.5
7.548
 3.52
4.028 = 4.03
9.47
 3.47
6.00 = 6.00 (not 6)
SCIENTIFIC NOTATION
- Used to express too large or too small numbers (with many zeros)
in compact form
- The product of a decimal number between 1 and 10 (the coefficient)
and 10 raised to a power (exponential term)
24,000,000,000,000 = 2.4 x 1013
coefficient
exponent (power)
exponential term
0.000000458 = 4.58 x 10-7
SCIENTIFIC NOTATION
- Provides a convenient way of writing the required
number of significant figures
6300000 to 4 significant figures = 6.300 x 106
2400 to 3 significant figures = 2.40 x 103
0.0003 to 2 significant figures = 3.0 x 10-4
SCIENTIFIC NOTATION
- Add exponents when multiplying exponential terms
(5.4 x 104) x (1.23 x 102)
= (5.4 x 1.23) x 10 4+2
= 6.6 x 106
- Subtract exponents when dividing exponential terms
(5.4 x 104)/(1.23 x 102)
= (5.4/1.23) x 10 4-2
= 4.4 x 102
MEASUREMENT SYSTEMS
Two measurement systems:
English System of Units (commercial measurements):
pound, quart, inch, foot, gallon
Metric System of Units (scientific measurements)
SI units (Systeme International d’Unites)
liter, meter, gram
More convenient to use
FUNDAMENTAL (BASE) UNITS
Physical Quantity
Name of Unit
Abbreviation
Mass
Length
Time
Temperature
Amount of substance
Electric current
Luminous intensity
Kilogram
Meter
Second
Kelvin
Mole
Ampere
Candela
kg
m
s (sec)
K
mol
A
cd
DERIVED UNITS
Area = length x length = m x m = m2
Volume = m x m x m = m3
Volume may also be expressed in LITERS (L)
1L = 1000 mL = 1000 cm3 or cubic centimeters (c.c.)
Implies 1mL = 1c.c.
mL is usually used for volumes of liquids and gases
c.c. is usually used for volumes of solids
Density = kg/ m3
DERIVED UNITS
Physical Quantity
Name of Unit
Abbreviation
Force
Pressure
Energy
Power
Frequency
Newton
Pascal
Joule
Watt
Hertz
N (m-kg/s2)
Pa (N/m2; kg/(m-s2)
J (N-m; m2-kg/s2)
W (J/s; m2-kg/s3)
Hz (1/s)
UNIT CONVERSIONS
Prefix
Abbreviation
Notation
Giga
Mega
Kilo
Deci
Centi
Milli
Micro
Nano
Pico
Femto
G
M
k
d
c
m
µ
n
p
f
109
106
103
10-1
10-2
10-3
10-6
10-9
10-12
10-15
UNIT CONVERSIONS
1 gigameter (Gm)
= 109 meters
1 megameter (Mm)
= 106 meters
1 kilometer (km)
= 103 meters
1 decimeter (dm)
= 10-1 meter
1 centimeter (cm)
= 10-2 meter
1 millimeter (mm)
= 10-3 meter
1 micrometer (µm)
= 10-6 meter
1 nanometer (nm)
= 10-9 meter
1 picometer (pm)
= 10-12 meter
1 femtometer (fm)
= 10-15 meter
UNIT CONVERSIONS
Length/Distance
Time
Volume
Mass
2.54 cm = 1.00 in.
12 in. = 1 ft
1 yd = 3 ft
1 m = 39.4 in.
1 m = 1.09 yd
1 km = 0.621 mile
1 km = 1000 m
1 min = 60 sec
1 hour = 60 min
24 hours = 1 day
7 days = 1 week
1 gal = 4 qt
1 qt = 0.946 L
1 L = 1.06 qt
1 L = 0.265 gal
1 mL = 0.034 fl. oz.
1 Ib = 454 g
1 Ib = 16 oz
1 kg = 2.20 lb
1 oz = 28.3 g
UNIT CONVERSIONS
Conversion Factors
1 km = 1000 m
»
1 km
1000 m
or
1000 m
1 km
1 L = 1000 mL
»
1L
1000 mL
or
1000 mL
1L
24 hours = 1 day
»
24 hours
1 day
or
1 day
24 hours
1 kg = 2.20 lb
»
1 kg
2.20 lb
or
2.20 lb
1 kg
UNIT CONVERSIONS
given number · unit new unit
= new number · new unit
unit to be converted
quantity to be
expressed in
new units
conversion factor
quantity now
expressed in
new units
given data desired unit
= answer in desired unit
unit of given data
UNIT CONVERSIONS
Convert 34.5 mg to g
1g
34.5 mg x
 0.0345 g or 3.45 x 102 g
1000 mg
How many gallons of juice are there in 20.0 liters of the juice?
0.265 gallon
20.0 liters x
 5.30 gallon
1 liter
Convert 4.0 gallons to quarts
1 liter
1 quart
4.0 gallons x
x
 15.9559 quarts  16 quarts
0.265 gallons 0.946 liter
UNIT CONVERSIONS
Convert 2.64 μg to kg
10-6 g 1 kg
2.64 μg x
x 3  2.64 x 10 9 kg
1μg 10 g
Convert 3.912 m2 to km2
2
(1
km)
6
2
3.912 m 2 x

3.912
x
10
km
(103 m) 2
Convert 4.0 cm3 to μm3
(1μm) 3
12
4.0 cm x

4.0
x
10
μm
(10 -4 cm) 3
3
DENSITY
- The amount of mass in a unit volume of a substance
Density = Ratio of mass to volume =
mass
volume
Units
Solids: grams per cubic centimeter (g/cm3)
Liquids: grams per milliliter (g/mL)
Gases: grams per liter (g/L)
- Density of 2.3 g/mL implies 2.3 grams per 1 mL
- Density usually changes with change in temperature
DENSITY
For a given liquid:
- Objects with density less than that of the liquid will float
- Objects with density greater than that of the liquid will sink
- Objects with density equal to that of the liquid will remain
stationary (neither float nor sink)
DENSITY
The liquid level in a graduated cylinder reads 12.20 mL.
The level rises to 18.90 mL when 129.31 g of piece of
gold is added to the cylinder. What is the density of gold?
Volume of the piece of gold = 18.90 mL – 12.20 mL = 6.70 mL
Mass of the piece of gold = 129.31 g
Density = mass/volume
= 129.31 g/6.70 mL = 19.3 g/mL or 19.3 g/cm3
TEMPERATURE
- The degree of hotness or coldness of a body or environment
3 common temperature scales
Metric system: Celsius and Kelvin
English system: Fahrenheit
Celsius Scale (oC): Reference points are the boiling and freezing
points of water (0oC and 100oC) - 100 degree interval
Kelvin Scale (K): Is the SI unit of temperature (no degree sign)
The lowest attainable temperature on the Kelvin scale is 0
(-273 oC) referred to as the absolute zero
TEMPERATURE
Fahrenheit Scale: Water freezes at 32oF and boils at 212oF
- 180 degree interval
K  o C  273
o
C
5 o

F32 
9
o
or
or
o
C  K  273
F
9 o

C   32
5
10o, 40o, 60o may be considered as 2 significant figures
100o may be considered as 3 significant figures
TEMPERATURE
Convert 29 oC to K
K  29  273  302 K
Convert 29 K to oC
o
C  29  273  - 244 o C
Convert 29 oF to oC
5
5
o
C  29  32  (3)   1.7   2o C
9
9
Convert 29 oC to oF
9
o
F  29  32  52.2  32  84.2  84 o F
5
TEMPERATURE
Heat
A form of energy necessary to raise the temperature of a substance
Units: Calorie (cal) or joules (J) [1 cal = 4.184 J]
Specific Heat
The quantity of heat energy necessary to raise the temperature of
1 gram of a substance by 1 oC
Units: cal/g.oC
TEMPERATURE
Calorie
The amount of heat energy needed to raise the temperature
of 1 gram of water by 1 degree Celsius
Heat (cal) 
specific heat(cal/g . C) x mass(g)  x temperatur e change  C
o
o
PERCENTAGE
- per one hundred
part of interest
percent (%) 
x 100
total (sum of all parts)
The chemistry class at CSU is made up of 39 females
and 12 males. What percentage of the class are
females and males
39
% female 
x 100  76 %
(39  12)
% male 
12
x 100  24 %
(39  12)