Unit 2- Measurements, Math, and the...
Transcript of Unit 2- Measurements, Math, and the...
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
Part 1 - numberPart 2 - scale (unit)
Examples:20 grams
6.63 x 10-34 Joule seconds
Measurement - quantitative observation consisting of 2 parts
Measuring and Significant Figures
Units are in Centimeters (the arrow is the end of the object)
Ruler
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.
2.83 cm
Known (because of markings on the ruler)
Estimated (you must include)
Practice- What are the best measurements?
a. 3 cm
b. 3.0 cm
c. 3.00 cm5
6Ex. 2
a. 5.29 mL
b. 5.290 mLAnswer: 3.0 cm
Answer: 5.29 mL
Ex. 1
Rules for identifying Significant Figures
#1= Non-zero integers always count as significant figures.
ex: 3456 has 4 sig figsex: 300 has 1 sig 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#3- Leading zeros NEVER count as
significant figures (they are placeholders).
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 #1How 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
3.24 m x 7.0 m
Calculation Calculator says: Answer
22.68 m2 23 m2
100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3
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)
Commonly Used (SI) Metric Units
Quantity Name Abbreviation
Mass Gram g
Length meter m
Temperature Kelvin or Celsius K or °C
Volume Liters or centimeter3 L or cm3
Density Grams per centimeter3 g/ cm3
Amount of
Substance
mole mol
3 countries don’t use metrics: Burma, Liberia, and the USA
A List of the Metric PrefixesMultiplier
Prefix Symbol Numerical Exponential yotta Y 1,000,000,000,000,000,000,000,000 1024
zetta Z 1,000,000,000,000,000,000,000 1021
exa E 1,000,000,000,000,000,000 1018
peta P 1,000,000,000,000,000 1015
tera T 1,000,000,000,000 1012
giga G 1,000,000,000 109
mega M 1,000,000 106
kilo k 1,000 103
hecto h 100 102
deca da 10 101
no prefix means: deci d 0.1 10¯1
centi c 0.01 10¯2
milli m 0.001 10¯3
micro µ 0.000001 10¯6
nano n 0.000000001 10¯9
pico p 0.000000000001 10¯12
femto f 0.000000000000001 10¯15
atto a 0.000000000000000001 10¯18
zepto z 0.000000000000000000001 10¯21
yocto y 0.000000000000000000000001 10¯24
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
Scientific Notation… why??
Imagine the difficulty of calculating the mass of 1 mole of electrons!
0.000000000000000000000000000000091 kgx 602000000000000000000000
???????????????????????????????????
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 integerEx: 6.3 x 103
How to Write in Scientific Notation
2 500 000 000
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
123456789
Step #4: Re-write in the form M x 10n
0.0000579
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
1 2 3 4 5
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
Multiplying
Multiply the M factors together and the exponents are addedtogether.
EX: (4 x 106)X (3 x 105)
12 x 1011
Best answer with Sig Figs : 1 x 10 12
Change to correct Scientific notation format: 1.2 x 1012
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)
Divide the M factors together and the exponents are subtracted from each other.
2 x 101
Another way of seeing it written
6 X 10 8 m x 2 x 10 3 m
3 X 10 4 s
= 12 X 10 11 m2
3 X 10 4 s = 4 x 10 7 m2 / s
Multiply top and divide by bottom
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.
(some calculators will show this for the answer: 2.49 -you have to know it is 2.4 x 109)
Answer= 2.4 x 109
Practice with Calculator
(5.23 X106)
X (7.1 x 10-2)
3.7133 x 105 , but there are 2 sig figs3.7133 x 105 , but there are 2 sig figs
3.7133 x 105 , but there are 2 sig figs
Best answer: 3.7 x 105
(4 x 106)+ (3 x 106)
IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged.
7 x 106
(4 x 106)+ (3 x 105)
If the exponents are NOT the same, we must move a decimal to make them the same.
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
Ex: Gold’s density = 19.3 g/ mL
(same for the ring & gold bar)
•The density of a substance is unique and neverchanges regardless of it’s size or shape.
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/mlFat density= 0.9 g/ml
This is why people who start exercising don’t always lose weight, but clothes fit differently
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 zoomsx
4 zetas
3 zooms=
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.
6 x 4 Zetas
3= 24 Zetas
3= 8 Zetas
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
1 mile = 1Or 1 mile
4 laps
• Can be written in
either direction
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?
15 people 4 slices 1 pizza 14.78 dollars
1 person 12 slices 1 pizza
Starting x conversion factors = find
= $73.90$ 74dollars
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 = 1.5 amoebas
4 cyanobytes
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 = 2 blobs
1 drimple 6 clomps
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 = 0.25 moles
32 grams
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 = 12 amoebas
5 x 10-2 m2
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 = 1.5 x 1023 atoms
40 g 1 mol
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?
What is the Mole?
1 mole = 6.02 x 1023 particles(a.k.a. Avogadro’s Number)
Experiments are performed with moles of atoms (not individual atoms).
Amedeo Avogadro
A mole is defined as: amount of a substance that contains as many particles as there are atoms in 12 g or Carbon-12.
It’s an amount, like a dozen (1 dozen = 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
Here’s How do we know?
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
It weighs 12.01 grams on a balance
Practice with the Mole Concept
1
H
1.01
8
O
16.00
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
2. Which has more atoms, a mole of Oxygen or a mole of Hydrogen?
Both have 6.02x 10 23 atoms
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 cookies1 mole of cookies = 6.02 X 1023 cookies
1 dozen cars = 12 cars1 mole of cars = 6.02 X 1023 cars
1 dozen Al atoms = 12 Al atoms1 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?)
The Mole- a conversion factor
**1 mole = 6.02 x 10 23 particles **
1 mole
6.02 x 10 23 particles**
6.02 x 10 23 particles**
1 moleOR
**Particles = atoms or molecules **
Molar Mass- a conversion factorSince 6.02 X 10 23 is impossible to count, chemists know the mass of a
mole (the molar mass)
use periodic table to determine the mass because every substance is different.
1 mole
x gramsOR
X grams
1 mole
Ex: Write the molar mass of Ca as a conversion factor
40.08 grams
1 mole Ca
Or1 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
1 mole18.02 g
Molar mass of H2O=
use molar mass use Avogadro’s numberGrams Moles particles
Everything must go through Moles!!!
“Mole Map” for Calculations
g/ mol
(use the periodic table)
1 mol/ 6.02 x 10 23
Converting Moles and Atoms
What is the # of moles of S in 1.8 x 1024 S atoms?
GIVEN X CONVERSION FACTOR = Find**
= # of Moles1.8 X 10 24 Atoms x 1 mole
6.02 X 10 23 Atoms
= 1.8 X 10 24 mole
6.02 X 10 23= 3.0 mole
How many grams of Al are in 3.00 moles of Al?
Converting Moles and Grams
3. GIVEN X CONVERSION FACTOR= Find
3.00 moles Al x 27.00 g Al1 mole Al
1. Molar mass of Al … 1 mole Al = 27.00 g Al
You will need:
2. Conversion factors for Al27.00g Al or 1 mol Al1 mol Al 27.00 g Al
= 81.00 g 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 6.02 X 1023 atoms Cu
63.5 g Cu 1 mol Cu
= 3.4 X 1023 atoms Cu
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.
Dimensional Analysis Fun…
from Lewis Caroll’s Through the looking Glass