Name:
Regents Chemistry: Mr. Palermo
Notes: Unit 1: Math
and Measurement
www.mrpalermo.com
8/9/15 UNIT 1 MATH AND
MEASUREMENT
M R . PA L E R M O
OBJECTIVE: BY THE END OF THIS VIDEO
YOU WILL BE ABLE TO:
LESSON 1: METRIC
CONVERSIONS
ü  Identify base units of measurement.
ü  Convert between units of
measurement.
W W W. M R PA L E R M O . C O M
WHAT IS CHEMISTRY?
MATTER CAN BE DESCRIBED AS:
•  The study of Matter and the changes
it undergoes…..
•  Qualitative measurements: descriptive,
non-numerical observations
•  What is Matter?
•  Quantitative Measurements: are in the
form of NUMBERS and UNITS.
-  Matter is anything that has mass and
takes up space.
1 8/9/15 QUANTITATIVE MEASUREMENTS:
TABLE D (BASE UNITS)
•  The METRIC SYSTEM (SI): System of
measurement used in science and in
most countries
•  The BASE UNITS of measurement:
(Found on Reference Table D)
PREFIXES:
•  Used to modify base units of
measurement. (Found on Reference
Table C)
CHECK YOUR UNDERSTANDING:
ü  Can you identify the base unit of
measurement?
Example:
gram (g)
CONVERTING UNITS USING TABLE C
WHERE ARE THE BASE UNITS?
1. Find the difference between the
exponents of the two prefixes on Table C.
2. Move the decimal that many places.
To the left
or right?
2 8/9/15 TRICK: TURN THE TABLE ON ITS
SIDE
EXAMPLE 1: CONVERT 5.2 CM = ____ MM •  The difference between the two factors (-­‐2 and -­‐3) is 1. •  Since you are moving from a larger prefix to a smaller prefix you move the decimal one place to the right. EXAMPLE 2: CONVERT 45.5 MM = ____ M •  The difference between the two factors (-­‐3 and 0) is 3. •  Since you are moving from a smaller prefix to a larger prefix you move the decimal three places to the leH. CHECK YOUR UNDERSTANDING:
ü  Can you convert between units of
measurement?
EXAMPLE 3
Convert the following:
20 cm = ____________ m
YOU SHOULD BE ABLE TO:
ü  Identify base units of measurement.
ü  Convert between units of
measurement.
3 8/9/15 OBJECTIVE: BY THE END OF THIS VIDEO
YOU WILL BE ABLE TO:
ü  Determine the volume of a substance
ü  Calculate density/mass/volume
LESSON 2: DENSITY
W W W. M R PA L E R M O . C O M
QUANTITATIVE CALCULATIONS:
•  Mass: the amount of matter an
object contains. (This is different than
weight, which is mass plus gravity)
HOW DO WE MEASURE MASS IN THE
LAB?
•  Electronic Balance
•  Volume: The amount of space a
substance occupies
HOW CAN WE MEASURE VOLUME?
•  l x w x h (regular solid)
-  ex. V =
READING A MENISCUS
line
10 mL
1cm3
•  Graduated cylinder (liquids)
li
of s
ight
too
high
proper line of sight
w
o lo
ht to
f sig
ne o
10
high
too
ding
8 rea
reading correct
6 readin
g to
o lo
w
-  Read bottom of MENISCUS
-  ex. V = 27.5 mL
graduated
cylinder
4 8/9/15 MEASURING VOLUME: IRREGULAR
SOLID
EXAMPLE: WHAT IS THE VOLUME OF
THE SOLID?
Water displacement
method
1. Measure initial
volume
2.  Measure final volume
with object
3.  The Difference is the
volume of the object
CHECK YOUR UNDERSTANDING:
ü  Can you Determine the volume of a
substance?
DENSITY
•  Ratio of mass of an object to its
volume
•  Use density formula
•  Located on Table T
EXAMPLE 1 What is the density of an object with
a mass of 60 g and a volume of 2
cm3?
D=
D=
M
V
CHECK YOUR UNDERSTANDING:
ü  Can you calculate density/mass/
volume
M
V
5 8/9/15 EXAMPLE 2 An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass. M D
= CHECK YOUR UNDERSTANDING:
ü  Can you calculate density/mass/
volume
V
HOW TO SOLVE FOR MASS OR
VOLUME IF DENSITY IS NOT GIVEN:
USE TABLE S
Example:
The volume of an aluminum sample is
251 cm3. What is the mass of the
sample?
CHECK YOUR UNDERSTANDING:
ü  Can you calculate density/mass/
volume
The density of aluminum on table S is
2.70g/cm3
YOU SHOULD BE ABLE TO:
•  Determine the volume of a substance
•  Calculate density/mass/volume
LESSON 3: TEMPERATURE
CONVERSIONS
W W W. M R PA L E R M O . C O M
6 8/9/15 OBJECTIVE: BY THE END OF THIS VIDEO
YOU WILL BE ABLE TO:
ü  Differentiate between Kelvin and
Celsius Scales
ü  Convert between Celsius and Kelvin
temperature
TEMPERATURE SCALES
TEMPERATURE:
•  Measure of average kinetic
Energy
CELSIUS SCALE
•  Freezing point of water at 0°C.
•  Boiling for water at 100°C.
•  Below 0 is NEGATIVE.
KELVIN SCALE
•  Water freezes at 273K and boils at 373K
•  Theoretical point of ABSOLUTE ZERO is when
all molecular motion stops
•  NO NEGATIVE NUMBERS
•  Divisions (degrees) are the same as in Celsius
7 8/9/15 CHECK YOUR UNDERSTANDING:
ü  Can you differentiate between Kelvin
and Celsius Scales
CONVERTING BETWEEN
TEMPERATURE SCALES
•  Formula: K = °C + 273
•  Located on Table T
EXAMPLE 2:
What is the temperature in Celsius of an
object that is 150 K?
EXAMPLE 1:
What is the temperature in Kelvin of an
object that is 55°C ?
CHECK YOUR UNDERSTANDING:
ü  Can you convert between Celsius
and Kelvin temperature
8 8/9/15 YOU SHOULD BE ABLE TO:
ü  Differentiate between Kelvin and
Celsius Scales
ü  Convert between Celsius and Kelvin
temperature
LESSON 4: PERCENT ERROR
W W W. M R PA L E R M O . C O M
OBJECTIVE: BY THE END OF THIS VIDEO
YOU WILL BE ABLE TO:
ACCURACY VS. PRECISION
ü  Differentiate between accuracy and
precision
ü  Calculate percent error
•  Accuracy - how close a measurement is
to the accepted or true value
EXAMPLE •  Precision - how close a series of
measurements are to each other
EXAMPLE: These students were asked to determine the density of sucrose. Sucrose has a density of 1.59 g/cm3. Which student is more accurate? Student A
(g/cm3)
Student B
(g/cm3)
Student C
(g/cm3)
Trial 1
1.54
1.40
1.70
Trial 2
1.60
1.68
1.69
Trial 3
1.57
1.45
1.71
Avg.
1.57
1.51
1.70
Range
0.06
0.28
0.02
9 8/9/15 CHECK YOUR UNDERSTANDING:
ü  Can you differentiate between
accuracy and precision
PERCENT ERROR
•  Measurement of ACCURACY
-  the % that the measured value is “off”
from accepted value
•  Measured value = value you “get”
•  Accepted value = value you “should
get”
Formula is found on Table in your
Reference Table:
•  If answer is negative, your measured value is
LESS THAN the accepted value
•  If answer is positive, your measured value is
GREATER THAN the accepted value
EXAMPLE 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. CHECK YOUR UNDERSTANDING:
ü  Can you calculate percent error
YOU SHOULD BE ABLE TO:
ü  Differentiate between accuracy and
precision
ü  Calculate percent error
10 8/9/15 OBJECTIVE: BY THE END OF THIS VIDEO
YOU WILL BE ABLE TO:
LESSON 5: PRECISION &
SIGNIFICANT FIGURES
ü  Identify the precision of a measuring
device
ü  Identify the amount of significant
figures in a number
W W W. M R PA L E R M O . C O M
SIGNIFICANT FIGURES •  Indicate PRECISION of a measurement.
•  Recording Sig Figs
-  Sig figs in a measurement include the known
digits plus a final estimated digit (precision of
instrument)
2.38 cm
EXAMPLE MEASURING LENGTH:
•  We know for sure that the object is
more than ____, but less than ____
•  We know for sure that the object is
more than ____, but less than ____
•  This ruler allows us to estimate the
length to ______
2 RUNNERS FINISH THE RACE IN 8
SECONDS. WHO WON?
1
2
11 8/9/15 EXAMPLE:
WHAT IS THE LENGTH OF THE RED LINE?
Runner 1
Runner 2
0
cm
2
3
4
5
RULES FOR COUNTING SIG FIGS CHECK YOUR UNDERSTANDING:
ü  Can you identify the precision of a
measuring device
1
1. All non-­‐zero digits are significant. 2. Leading zeros are never significant. ex. 0.421 (3 sig figs) 3. All capTve zeros are significant. (Cap+ve is a zero between 2 other non-­‐zero digits.) ex. 4012 (4 sig figs) 4. For Trailing zeros: (zeros aHer last non-­‐zero digit) -­‐ Decimal point → significant -­‐No decimal point → not significant ex. 114.20 (5 sig figs)
ex. 11,420 (4 sig figs)
HOW TO COUNT SIG FIGS 1.  Start counTng from LEFT to RIGHT at first NONZERO number. 2.  If decimal point is present then count any trailing zeros 3.  If decimal is not present don’t count trailing zeros EXAMPLE
1) 2545.300 g (7 sig figs) 2) 4530 km (3 sig figs) 3) 0.00453 m (3 sig figs) 12 8/9/15 CHECK YOUR UNDERSTANDING:
ü  Can you identify the amount of sig
figs in a number
YOU SHOULD BE ABLE TO:
ü  Identify the precision of a measuring
device
ü  Identify the amount of significant
figures in a number
OBJECTIVE: BY THE END OF THIS VIDEO
YOU WILL BE ABLE TO:
ü  Round answers to proper sig figs in
calculations
LESSON 6: ROUNDING SIG
FIGS IN CALCULATIONS
W W W. M R PA L E R M O . C O M
WHAT DO I ROUND MY ANSWER TO?
•  Every measurement has some error in
it. When performing calculations AN
ANSWER CAN NEVER BE MORE
PRECISE THAN YOUR LEAST PRECISE
MEASUREMENT
ROUNDING: SIG FIG IN CALCULATIONS •  MulTply/Divide -­‐ Round answer to the
least number of significant figures. Example: (13.91g/cm3)(23.3cm3) = 324.103g
4 SF
3 SF
3 SF
324 g
13 8/9/15 CHECK YOUR UNDERSTANDING:
ü  Can you round answers to proper sig
figs in calculations
CALCULATING SIG FIGS (CON’T) •  Add/Subtract – Round to the least place value Example: 3.75 mL
+ 4.1 mL
7.85 mL → 7.9 mL
224 g
+ 130 g
354 g → 350 g
YOU SHOULD BE ABLE TO:
ü  Round answers to proper sig figs in
calculations
LESSON 7: SCIENTIFIC
NOTATION
W W W. M R PA L E R M O . C O M
OBJECTIVE: BY THE END OF THIS VIDEO
YOU WILL BE ABLE TO:
ü  Convert numbers into scientific
notation and standard notation
ü  Calculate mathematical operations
using scientific notation
SCIENTIFIC NOTATION
•  A way to represent large or small
numbers
For example:
•  The mass of a hydrogen atom is
0.00000000000000000000000167g.
•  2 g of H2 contains
602,000,000,000,000,000,000,000
molecules. 14 8/9/15 SCIENTIFIC NOTATION IS WRITTEN AS:
• The product of two numbers: a coefficient
and a 10 raised to a power.
• The coefficient (number written first) is
always a number from 1 to 9
Example:
1.67 x 10-24 g
2 g of H2 is composed of 6.02 x 1023
molecules.
CONVERTING FROM EXPANDED FORM
INTO SCIENTIFIC NOTATION
1.  For #’s greater than 1 move decimal to
the LEFT until there’s 1 digit to its left.
The number of places moved =
exponent number
Example: 45,450 g =
CHECK YOUR UNDERSTANDING:
2. For #’s less than 1 move decimal to
RIGHT stopping after the first non zero
number. The number of places
moved = negative exponent number
ü  Can you convert numbers into
scientific notation and standard
notation
Example: 0.00453 ml = 4.53 x 10-3 ml
CONVERTING FROM SCIENTIFIC
NOTATION TO STANDARD NOTATION
1.  Move the decimal place the number
of times indicated by the exponent.
2.  To the right if it is positive.
3.  To the left if it is negative.
CHECK YOUR UNDERSTANDING:
ü  Can you convert numbers into
scientific notation and standard
notation
Example:
4.5 x 10-2 = 0.045
15 8/9/15 CALCULATING WITH SCI NOTATION
USING A CALCULATOR
Ex. (5.44 × 107 g) ÷ (8.10 × 104 mol) =
Type on your calculator:
5.44
EXP
EE
7
÷
8.10
EXP
EE
4
EXE
CHECK YOUR UNDERSTANDING:
ü  Can you calculate mathematical
operations using scientific notation
ENTER
= 671.60493
= 672 g/mol
= 6.72 × 102 g/mol
YOU SHOULD BE ABLE TO:
ü  Convert numbers into scientific
notation and standard notation
ü  Calculate mathematical operations
using scientific notation
16