Unit 2- Measurements, Math, and the Mole

Unit 2- Measurements, Math,
and the Mole
“No human endeavor can be called
science if it cannot be demonstrated
mathematically”
- Leonardo Da Vinci
Modified from sciencegeek.net
Nature of Measurement
Measurement - quantitative observation
consisting of 2 parts
Part 1 - number
Part 2 - scale (unit)
Examples:
20 grams
6.63 x 10-34 Joule seconds
Significant Figures
Measuring and Significant Figures
Significant figures = indicate precision in a measurement.
How to: record all digits in a measurement that are known
with certainty on the device plus one final digit, which is
an estimation.
Ruler
Units are in Centimeters (the arrow is the end of the object)
2.83 cm
Known (because of markings on Estimated (you must include)
the ruler)
Practice- What are the best
measurements?
Ex. 1
Ex. 2
6
a. 3 cm
b. 3.0 cm
c. 3.00 cm
Answer: 3.0 cm
5
a. 5.29 mL
b. 5.290 mL
Answer: 5.29 mL
Measuring Practice
Thermometer
graduated cylinder
Answer: 21.7 °C
Answer: 30.0 mL
Rules for identifying Significant
Figures
#1= Non-zero integers always count
as significant figures.
ex: 3456 has 4 sig
ex: 300 has 1 sig
figs
fig
Zeros (placeholders vs. Accuracy)
#2 =sandwiched zeros always count as
significant figures.
ex: 16.07 has 4 sig figs.
Rules for Counting Significant
Figures - Details
Zeros
Leading zeros NEVER count as
significant figures (they are
placeholders).
#3-
Ex:
0.0486 has 3 sig figs.
Rules for Counting Significant
Figures - Details
Zeros
#4= Trailing zeros are significant
only if the number contains a
decimal point.
Ex: 9.300 has 4 sig figs.
Ex: 2000 has 1 sig fig (no decimal)
Ex: 2000. has 4 sig figs (decimal)
Ex: 0.02020 has 4 sig figs (decimal)
Sig Fig Practice #1
How many significant figures in each of the following?
1.0070 m 
5 sig figs
17.00 kg 
4 sig figs
100,890 L 
5 sig figs
3.29 x 103 s 
3 sig figs
0.0054 cm 
2 sig figs
320 cm
2 sig figs
Multiplying & Dividing with Sig Figs
Multiplication and Division: # sig figs in the
result equals the number in the least precise
measurement used in the calculation.
Ex: 6.38 x 2.0 =
12.76  13 (2 sig figs)
Ex 2: 570
÷ 2.5 =
228  230 (2 sig Figs)
Sig Fig Practice #2
Calculation
Calculator says:
Answer
3.24 m x 7.0 m
22.68 m2
100.0 g ÷ 23.7 cm3
4.219409283 g/cm3 4.22 g/cm3
23 m2
0.02 cm x 2.371 cm 0.04742 cm2
0.05 cm2
710 m ÷ 3.0 s
236.6666667 m/s
240 m/s
1818.2 lb x 3.23 ft
5872.786 lb·ft
5870 lb·ft
1.030 g ÷ 2.87 mL
0.35888 g/mL
0.359 g/mL
Adding and Subtracting with Sig
Figs (fyi only…don’t need to know)
Addition and Subtraction: The number
of decimal places in the result equals the
number of decimal places in the least
precise measurement.
6.8 + 11.934 =
18.734  18.7 (3 sig figs)
Metrics
Commonly Used (SI) Metric Units
Quantity
Name
Abbreviation
Mass
Gram
g
Length
meter
m
Kelvin or Celsius
K or °C
Volume
Liters or centimeter3
L or cm3
Density
Grams per centimeter3
g/ cm3
mole
mol
Temperature
Amount of
Substance
3 countries don’t use metrics: Burma,
Liberia, and the USA
A List of the Metric Prefixes
Prefix
yotta
zetta
exa
peta
tera
giga
mega
Multiplier
Symbol Numerical
Exponential
Y
1,000,000,000,000,000,000,000,000
Z
1,000,000,000,000,000,000,000
E
1,000,000,000,000,000,000
P
1,000,000,000,000,000
T
1,000,000,000,000
G
1,000,000,000
M
1,000,000
kilo
k
1,000
hecto h
100
deca
da
10
no prefix means:
deci
d
0.1
centi
c
0.01
milli
m
0.001
micro µ
0.000001
nano
pico
femto
atto
zepto
yocto
n
p
f
a
z
y
0.000000001
0.000000000001
0.000000000000001
0.000000000000000001
0.000000000000000000001
0.000000000000000000000001
1024
1021
1018
1015
1012
109
106
103
102
101
10¯1
10¯2
10¯3
10¯6
10¯9
10¯12
10¯15
10¯18
10¯21
10¯24
Scientific Notation
Scientific Notation… why??
In science, we deal with some very
LARGE numbers:
1 mole = 602000000000000000000000
In science, we deal with some very
SMALL numbers:
Mass of an electron =
0.000000000000000000000000000000091 kg
Imagine the difficulty of calculating
the mass of 1 mole of electrons!
0.000000000000000000000000000000091 kg
x 602000000000000000000000
???????????????????????????????????
How to Write in Scientific Notation
A method of representing very large or
very small numbers in the form:
M x 10n
M is a number between 1 and 10 (can
be a decimal too)
 n is an integer
Ex: 6.3 x 103
.
2 500 000 000
9 8 7 6 5 4 3 2 1
Step #1: Insert an understood decimal point
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n
2.5 x
9
10
The exponent is the
number of places we
moved the decimal.
0.0000579
1 2 3 4 5
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n
5.79 x
-5
10
The exponent is negative
because the number we
started with was less
than 1.
Practice: Convert the following
into or out of scientific notation.
1. 6, 000, 000, 000
2. 0. 000 000 006
3. 6 x 108
4. 5, 234, 000
5. 0. 00120
6. 7.49 x 10-4
7. 80, 080, 100,
000
1. 6 x 109
2. 6 x 10-9
3. 600, 000, 000
4. 5.234 x 106
5. 1.20 x 10-3
6. 0.000749
7. 8.00801 x 1010
PERFORMING
CALCULATIONS
IN SCIENTIFIC
NOTATION
Multiplying
EX: (4 x 106)
X (3 x 105)
12 x 1011
Multiply the M factors
together and the
exponents are added
together.
Change to correct Scientific
notation format: 1.2 x 1012
Best answer with Sig Figs : 1 x 10
12
Practice Problem
(8 x 106m)
X (3 x 104 m)
Answer: 24 x 1010 m2
… but it’s not quite
correct.
M must be a number between 1-10, right now
it’s 24. So, you must make 24 into 2.4 and
move the decimal one more place.
Best answer: 2.4 x 1011 m2
Dividing
EX: (4 x 106)
÷ (2 x 105)
2 x 101
Divide the M factors
together and the exponents
are subtracted from each
other.
Practice Problem
6
10
(8 x
g)
4
÷ (2 x 10 mL)
4x
2
10 g/mL
Another way of seeing it written
Multiply top and divide by bottom
6 X 10
8 m
x
2 x 10
3 X 10
= 12 X 10 11 m2
3 X 10 4 s
m
3
4
s
= 4 x 10 7 m2 / s
How to use your calculator with
Scientific Notation
1. Practice (6.0 x 105) x (4.0 x 103) on your
calculator
2. Punch the number (the digit number) into
your calculator.
3. Push the EE or EXP button. Do NOT type
in x10 or use the 10x buttons!!
4. Enter the exponent number. Use the +/button to change its sign.
Answer= 2.4 x 109
(some calculators will show this for the answer:
2.49 -you have to know it is 2.4 x 109)
Practice with Calculator
(5.23 X106)
X (7.1 x 10-2)
5 , but
5
3.7133
x
10
3.7133 x 10 ,there
but
are 2 sig figs
there
are
2
sig
figs
5
Best answer: 3.7 x 10
Adding and Subtracting with
Scientific Notation
(FYI ONLY… don’t really use Chem.)
IF the exponents are
(4 x
6
+ (3 x 10 ) the same, we simply
add
or
subtract
the
7 x 106 numbers in front and
6
10 )
bring the exponent
down unchanged.
106)
(4 x
+ (3 x 105)
If the exponents
are NOT the
same, we must
move a decimal
to make them
the same.
6
10
4.00 x
6
+ .30 x 10
4.30 x
6
10
YES!
A Problem for you…
Scientific Notation
-6
(2.37 x 10 )
+ (3.48 x
-4
10 )
Solution…
-4
0.0237 x 10
-4
+ 3.48 x 10
-4
3.5037 x 10
Calculating Density
Weight Vs. Mass
Mass = amount of matter
something contains
» Doesn’t change in outer
space
Weight = measurement of the
pull of gravity on an
object.
» Changes in outer space.
Density= Mass / Volume
• How much “stuff” per unit
volume
•The density of a substance is unique and never
changes regardless of it’s size or shape.
Ex: Gold’s density = 19.3 g/ mL
(same for the ring & gold bar)
Density
• Is a physical property
that is unique to each
material
• Can be used to identify
a substance
Density of ice= .92g/cm3
Volume- amount of space an object
occupies
Can find by:
1) Using a ruler
•
only if it’s a certain shape
(ex: cube)
•
Measured in : cm3
2) Water displacement
•
Use for odd shaped objects
•
Measure in: mL
*1 cm 3 = 1 mL (volume is the
same regardless of which
way you measure it)
Ex: Muscle is more dense than fat
Muscle density= 1.06 g/ml
Fat density= 0.9 g/ml
This is why
people who
start
exercising
don’t always
lose weight,
but clothes
fit
differently
Dimensional Analysis
Sample Problems to Solve
A) How many seconds has a 16 year old been
alive?
B) How many liters of water will Kate consume in
1 year? Kate drinks 8 glasses of water in 1 day
& 1 glass = 300 mL. There are 1000 mL in 1
L.
The Math behind Dimensional Analysis
6 zooms
x
4 zetas
3 zooms
=
6 x 4 Zetas
3
= 24 Zetas = 8 Zetas
3
This is the level of math you will need to know in this unit.
You would cancel out everything on the top and bottom
that are the same (including words).
 In the end, multiply everything on the top and divide it by
everything that has been multiplied on the bottom.
Dimensional Analysis
• It is a method to solve conversion type problems
• Uses Conversion Factors (relate 2 things to each other)
• These are either given to you or assumed to be known
– Ex: 4 laps = 1 mile (they are equal to each other)
Can also be written as a fraction:
4 Laps
Or
1 mile
• Can be written in
1
1 mile =
either direction
4 laps
When solving problems use this method:
GIVEN X CONVERSION FACTOR = Find
Sample Dimensional Analysis Problem
Ex: Convert 15 cm into meters
Given x conversion factor = Find
Ex: 15 cm x 1 meter =
100 cm
.15 meter
Dimensional Analysis
Sample Problem #2
•You're throwing a pizza party for 15 people.
•each person might eat 4 slices.
•each pizza will cost you $14.78
•1 pizza will be cut into 12 slices.
•How much is the pizza going to cost you?
Starting x conversion factors
= find
15 people
4 slices
1 person
1 pizza
12 slices
14.78 dollars
1 pizza
=
$73.90
$ 74
dollars
Good use of D.A. - performed by a
senior planning a trip
A group of friends are going to Disneyland for
graduation. Driver wants to know how much to
charge his friends the trip to cover his gas costs?
It’s 876.8 miles round trip.
-Car gets 18 miles/ gallon
$ 4.30/ 1 gallon gas
-6 people
DIMENSIONAL ANALYSIS REVIEW

If an amoeba needs to eat 4 cyanobytes to be full.
How many amoebas can you feed if you have 6.0
cyanobytes?
6 cyanobytes
1 amoeba
4 cyanobytes
= 1.5 amoebas
DIMENSIONAL ANALYSIS REVIEW

If you have 3 drimples, how many blobs could you
make if it takes 1 drimple to make 4 clomps and
6 clomps to make a blob?
3 drimples
4 clomps
1 blob
1 drimple 6 clomps
= 2 blobs
DIMENSIONAL ANALYSIS REVIEW

If you have 8.0 grams of a substance, how many
moles would you have if 1 mole has a mass of 32
grams?
8.0 grams
1 mole
32 grams
= 0.25 moles
DIMENSIONAL ANALYSIS REVIEW

If 3 amoebas need 5 x 10-2 meters2 of living space.
How many amoebas can you have if you have a
petri dish that is 20. x 10-2 meters2?
20. x 10-2 m2
3 ameobas
5 x 10-2 m2
= 12 amoebas
DIMENSIONAL ANALYSIS REVIEW

If you have 10. grams of a substance, how many
atoms would you have if 1 mole has a mass of 40
grams and 1 mole contains 6 x 1023 atoms?
10. g
1 mol
6 x 1023 atoms
40 g
1 mol
= 1.5 x 1023 atoms
DIMENSIONAL ANALYSIS REVIEW
What would be the mass of 1.5 x 1023 molecules, if
6 x 1023 molecules equals 1 mole and 1 mole is 80
grams?
DIMENSIONAL ANALYSIS REVIEW
How many moles are in 116 grams of magnesium
hydroxide, Mg(OH)2?
DIMENSIONAL ANALYSIS REVIEW
How many atoms are in 44 grams of boron?
The Mole
naked mole rat
What is the Mole?
It’s an amount, like a dozen (1 dozen = 12)
1 mole = 6.02 x 1023 particles
(a.k.a. Avogadro’s Number)
Amedeo
Avogadro
Experiments are performed with moles of atoms
(not individual atoms).
A mole is defined as: amount of a substance
that contains as many particles as there are atoms
in 12 g or Carbon-12.
Using the “mole” by weighing
Ex: a scientist wants 1 mole of Na and 1 mole of Cl
to make NaCl.
Is he or she going to count out 6.02 x 1023 Na and Cl
atoms?
NO WAY!
Chemists can "count" atoms or molecules by knowing
how much 1 mole of every substance weighs…
The molar mass! It’s on the periodic table
How big is Avogadro’s #?
• An Avogadro's number of soft drink cans would
cover the surface of the earth to a depth of over
200 miles.
• If you spread Avogadro's number of unpopped
popcorn kernels across the USA, the entire
country would be covered in popcorn to a depth of
over 9 miles.
• If we were able to count atoms at the rate of 10
million per second, it would take about 2 billion
years to count the atoms in one mole.
Molar Mass
Atomic mass
Mass of 1 atom
of C= 12.01 amu
Molar Mass
Mass of 1 mole of C atoms (6.02 x 1023 atoms)
12.01 g/ mol
Here’s How do we know?
It weighs 12.01 grams on a balance
Practice with the Mole Concept
1
H
1.01
1. What weighs more, a mole of Hydrogen or
a mole of Oxygen? Oxygen (16.00 grams /mole)
(Because a Hydrogen atom weighs more than
an Oxygen atom) Note: only units change
8
2. Which has more atoms, a mole of Oxygen or
a mole of Hydrogen?
23 atoms
Both
have
6.02x
10
16.00
O
3. What’s the molar mass of H2O? 18.02 g/ mol (see demo)
4. Mass of 1 molecule of H2O? = 18.02 amu
The Mole vs. a Dozen
1 dozen cookies = 12 cookies
1 mole of cookies = 6.02 X 1023 cookies
1 dozen cars = 12 cars
1 mole of cars = 6.02 X 1023 cars
1 dozen Al atoms = 12 Al atoms
1 mole of Al atoms = 6.02 X 1023 atoms
Note that the NUMBER is always the same, but the MASS is
very different!
Mole is abbreviated mol (gee, that’s a lot quicker to write,
huh?)
Using the Mole in Chemistry
The Mole- a conversion factor
**1 mole = 6.02 x 10 23 particles **
1 mole
6.02 x 10
23
particles**
OR
6.02 x 10 23 particles**
1 mole
**Particles = atoms or molecules **
Molar Mass- a conversion factor
Since 6.02 X 10 23 is impossible to count, chemists know the mass of a
mole (the molar mass)
1 mole
x grams
OR
X grams
1 mole
use periodic table to determine the mass because every substance is different.
Ex: Write the molar mass of Ca as a conversion factor
40.08 grams
1 mole Ca
Or
1 mole Ca
40.08 grams
**Can also be written 40.08 g/ mol**
Molar mass of Compounds
Ex: Write the molar mass of H2O as a conversion factor
Ex : H2O = 18.02 grams
(you need to add)
2 Hydrogen’s : (1.01) 2 = 2.02
1 Oxygen: (16.00) 1 = 16.00
= 18.02 g
Molar mass of H2O= 1 mole
18.02 g
“Mole Map” for Calculations
Grams
use molar mass
g/ mol
Moles
use Avogadro’s number
1 mol/ 6.02 x 10
particles
23
(use the periodic table)
Everything must go through Moles!!!
Converting Moles and Atoms
What is the # of moles of S in 1.8 x 1024 S atoms?
GIVEN X CONVERSION FACTOR = Find**
1.8 X 10
24 Atoms
x
1 mole
6.02 X 10
= 1.8 X 10 24 mole
6.02 X 10 23
=
23
Atoms
3.0 mole
= # of Moles
Converting Moles and Grams
How many grams of Al are in 3.00 moles of Al?
You will need:
1. Molar mass of Al … 1 mole Al = 27.00 g Al
2. Conversion factors for Al
27.00g Al
1 mol Al
or
1 mol Al
27.00 g Al
3. GIVEN X CONVERSION FACTOR=
Find
3.00 moles Al x 27.00 g Al = 81.00 g Al
1 mole Al
Sample of Atoms/Molecules and
Grams
How many atoms of Cu are present in 35.4 g of
Cu?
35.4 g Cu
1 mol Cu
63.5 g Cu
6.02 X 1023 atoms Cu
1 mol Cu
= 3.4 X 1023 atoms Cu
Dimensional Analysis Fun…
from Lewis Caroll’s Through the looking Glass
If there are 5 frumious Bandersnatches,
how many Jabberwocks are there?
There are 20 tumtum trees in the tulgey wood.
In each tulgey wood is one frumious Bandersnatch.
There are 5 slithy toves in 2 borogoves.
There are 2 mome raths per Jabberwock.
There are 2 Jubjub birds in 200 tumtum trees.
There are 200 mome raths in each borogove.
There are 5 Jubjub birds per slithy tove.