Transcript Making Measurements

Making Measurements
S
Day 1- Tuesday
Measurements in Life
S What are some examples of situations in your
life that require making measurements?
S Amount of time it takes to do something
S Body temperature when you’re sick
S Speed of a thrown baseball
S Distance between the line of scrimmage and
the goal
2 Types of Measurements
S There are 2 types of measurements that can be made:
S Qualitative
S Quantitative
S Qualitative: measurements that do NOT involve the
use of numbers and concern characteristics of an
object.
S Quantitative: measurements that involve numbers and
must be determined with an apparatus of some sort.
Qualitative or Quantitative?
S It is hot outside.
Qualitative
S Yesterday I ran 3 miles.
Quantitative
S It was 102° outside this afternoon.
Quantitative
S The balloon was big and blue.
Qualitative
S The paper felt soft on my skin.
Qualitative
S I need 3.25mm of string for my project.
Quantitative
S I am 3 foot 4 inches tall.
Quantitative
S Wow you’re short!!
Qualitative
Don’t Forget…
S Why are units just as important in communicating a
quantitative measurement as the number is?
S A number without a unit is meaningless
S Ex: 35 °F is cold and 35 °C is hot
Accuracy vs Precision
S Accuracy: refers to how close a measured value is
to an accepted value
S Precision: refers to how close a series of
measurements are to one another
Accuracy vs Precision
Ken
Sue
Jon
Trial 1
(g/cm3)
1.54
1.40
1.70
Trial 2
(g/cm3)
1.60
1.68
1.69
Trial 3
(g/cm3)
1.57
1.45
1.71
Average
(g/cm3)
1.57
1.51
1.70
Accepted Value = 1.59 g/cm3
S
Who collected the most accurate
data?
Ken, because his average is
closest to the accepted
value.
S
Who collected the most precise
data?
Jon, because his values varied
by the smallest amount (0.02
g/cm3.
Scientific Notation Rules
1. The first figure is a number from 1-9.
2. The first figure is followed by a decimal point
and then the rest of the figures.
3. Then multiply by the appropriate power of 10.
Scientific Notation
Given: 289,800,000
 Use: 2.898 (moved 8 places)
 Answer: 2.898 x 108
Given: 0.000567
 Use: 5.67 (moved 4 places)
 Answer: 5.67 x 10-4
Learning Check
S
Express these numbers in Scientific Notation:
4.05789 x 105
1) 405789
3.872 x 10-3
2) 0.003 872
3) 3,000,000,000
3 x 109
4) 0.000 000 02
2 x 10-8
5) 0.478260
4.7826 x 10-1
Tuesday – Exit Ticket
S Convert the following number to scientific
notation
S 1.) 0.000 000 000 276
S 2.) 150, 000, 000
S 3.) Determine if the following set of data is
accurate, precise or both.
The bug is 2.59 cm long
3.58 cm
3.59 cm
3.57 cm
Day 2- Wednesday
Significant Figures
S What is the difference between
S 75.00 mL
S 75.0 mL
S 75 mL
S Are they all the same number or are they different?
Significant Figures
S How do we read the ruler?
S 4.5515 cm?
S 4.551 cm?
S 4.55 cm?
S 4.5 cm?
S 4 cm?
S We needed a set of rules to decide
1
2
3
4
5
Significant Figure
Rules
Rule #1: All real numbers (1, 2, 3, 4, etc.)
count as significant figures.
S Therefore, you only have to be
concerned with the 0
S Whether a 0 is significant or not
depends on the location of that 0 in the
number
Which zeros count?
Rule #2: Zeros at the end of a
number without a decimal point
don’t count
12400 g (3 sig figs)
Rule #3: Zeros after a decimal
without a number in front are not
significant.
0.045 g (2 sig figs)
Which zeros count?
Rule #4: Zeros between other sig figs do
count.
1002 g (4 sig figs)
Rule #5: Zeroes at the end of a number
after the decimal point do count
45.8300 g (6 sig figs)
Significant Figures
Pacific Ocean
Atlantic Ocean
S
When the decimal is Present,
start counting with the first
nonzero number on the left.
S
When the decimal is Absent,
start counting with the first
nonzero number on the right.
S
Keep counting until you fall off
S
Keep counting until you fall off.
Other Information
about Sig Figs
S Only measurements have sig figs.
S A a piece of paper is measured 11.0 inches tall.
S Counted numbers are exact
S A dozen is exactly 12
S Being able to locate, and count significant figures is
an important skill.
Learning Check
A. Which answers contain 3 significant figures?
1) 0.4760 cm
2) 0.00476 cm
3) 4760 cm
B. All the zeros are significant in
1) 0.00307 mL 2) 25.300 mL
3) 2.050 x 103 mL
C. 534,675 g rounded to 3 significant figures is
1) 535 g
2) 535,000 g
3) 5.35 x 105 g
Learning Check
In which set(s) do both numbers contain the same
number of significant figures?
1) 22.0 and 22.00
2) 400.0 and 40
3) 0.000015 and 150,000
NO
NO
YES- 2
4) 63,000 and 2.1
YES- 2
5) 600.0 and 144
NO
6) 0.0002 and 2000
YES-1
Rounding rules
S Look at the number behind
the one you’re rounding.
S If it is 0 to 4 don’t change
it
S If it is 5 to 9 make it one
bigger
Rounding
S 5.87192
S Round 2 digits
5.9
S Round 3 digits
5.87
S Round 4 digits
5.872
S 7.9237439
S Round 1 digits
8
S Round 2 digits
7.9
S Round 4 digits
7.924
S Round 5 digits
7.9237
Learning Check
How many sig figs are in the following
measurements?
658 g
3
6850. g
4
6850 g
0.0685 g
0.006085 g
60.006085 g
3
3
4
8
Calculations Using Sig Figs
Addition/ Subtraction
Multiplication/ Division
S
The least accurate measurement
determines the accuracy of the
answer.
S
The least precise measurement
determines the accuracy of the
answer.
S
Keep only as many decimal
places as the least accurate
measurement.
S
Round your answer to the least
number of significant figures in
any of the factors.
S
Ex: 12.01 + 35.2 + 6 = 53
S
Ex: 1.35 x 2.467 = 3.33
Another Example
If 27.93 mL of NaOH is added to 6.6 mL
of HCL, what is the total volume of your
solution?
 First line up the decimal
places
27.96 mL
 Then do the adding
+ 6.6 mL
 Find the estimated numbers
in the problem
34.56 mL
 This answer must be rounded
to the tenths place
34.6 mL
Example:
135 cm x 32 cm = 4320 cm2
3 S.F.
2 S.F.
Round off the answer to 4300
cm3 which is 2 sig figs.
Learning Check
1.
2.19 m X 4.2 m =
A) 9 m2 B) 9.2 m2 C) 9.198 m2
2. 4.311 cm2 ÷ 0.07 cm =
A) 61.58 cm B) 62 cm C) 60 cm
3.
(2.54 mL X 0.0028 mL)
=
0.0105 mL X 0.060 mL
A.) 11.3 mL
B)11 mL C) 0.041mL
Percent Error
S Percent error is a way for scientists to express how far off a
lab value is from the commonly accepted value.
S The formula is:
S % Error = |Accepted value – Experimental Value| x 100 %
Accepted Value
Percent Error
S Example 1:
S Experimental Value = 1.24 g
S Accepted Value = 1.30 g
S % Error = |Accepted value – Experimental Value| x 100 %
Accepted Value
S % Error = |1.30 – 1.24| x 100 %
1.30
= 4.62 %
Wednesday- Exit Ticket
S How many sig figs are in the following
number
S 1.) 45.00
S 2.) 4,500
S 3.) 0.04500
S 4.) 0.000 00045
Day 3- Thursday
Why do we need common
units?
S It is important for scientists around the world to be able to
communicate with each other!
S If we all used a different set of units, communication would
be different if not impossible.
S Therefore...
International System of Units
S The common system of units scientists have devised in
order to communicate with each other even when they’re
from different places is called the Systemme Internationale
(International System in French) or SI.
S This system has seven base units that are based on an object
or event in the physical world.
SI Base Units
Quantity
SI Base Unit
Symbol
Time
second
s
Length
meter
m
Mass
kilogram
kg
Temperature
Kelvin
K
Amount of Substance
moles
mol
Electric Current
Ampere
A
Luminous Intensity
candela
cd
Time
S The SI base unit for time is the second, s.
S How is this unit officially defined?
S The frequency of microwave radiation given off by a cesium-
133 atom is the physical standard used to establish the length
of a second.
S This is why atomic (cesium) clocks are more accurate than the
standard clocks and stopwatches we normally used to measure
time.
Length
S The SI base unit for length is the meter, m.
S How is this unit officially defined?
S
A meter is the distance that light travels through a vacuum in
1/299792458 of a second.
S If you need to measure length that is longer than this base
unit… you’d measure in kilometers (km).
S If you need to measure length that is a shorter distance than
the base unit… you’d measure in centimeters (cm) or
millimeters (mm).
Mass
S Mass is the measure of the amount of matter in a sample.
S The SI base unit for mass is the kilogram, kg.
S How is this officially defined?
S The kilogram is defined by a platinum-iridium metal cylinder
stored in Sevres, France. A copy is kept at the National
Institute of Standards and Technology in Gaithersburg,
Maryland.
Mass
S What units are you most
likely to use to measure
mass in lab?
S The masses measured in
lab are often much smaller
than a kg, for those cases
we use grams (g) or
milligrams (mg)
Temperature
S The SI base unit for temperature is the Kelvin, K.
S This scale was calibrated so that changing one unit on the
Kelvin scale is the same as changing a temperature by one
degree Celsius.
S Defining temperature points
S Celsius: 0° water freezes, 100° water boils
S Kelvin: 273 water freezes, 0 all motion stops
Temperature
S Why was the Kelvin scale invented/ why is it useful?
S We needed an “absolute zero scale” so that we could do calculations
without negative numbers.
S Convert between Kelvin and Celsius
S K = °C + 273
S °C = K – 273
S A third temperature scale that we will not use in the lab is
Fahrenheit.
S How do you convert between Celsius and this scale?
S °F = (1.8 x °C) + 32
S °C = (°F-32) / 1.8
History of Temperature
Lord Kelvin
Anders Celsius
Derived Units
S Not all quantities can be measured with base units.
S Example: the SI unit for speed is meters per second (m/s).
S Notice that this includes 2 base units- the meter and the
second.
S A unit that is defined by a combination of base units is
called a derived unit.
Volume
S Volume is space occupied by an object.
S The derived SI unit for volume is the cubic meter, m3, which is
represented by a cube whose sides are all one meter in length.
S This unit is much larger than what will commonly be needed in the
lab so a more useful derived unit, the cubic centimeter, cm3 is used.
S The unit cm3 works well for solid objects with regular dimensions, but
not as well for liquids or for solids with irregular shapes. The metric
unit for volume is the Liter, L.
S What are the conversions between volume units?
S 1000m = 1 L; 1 cm3 = 1 mL; (memorize 1 cm3  1 mL)
Metric Dimensional Analysis
Trick
Name/ Symbol
Factor
King
Kilo (K)
1000 or 103
Henry
Hecto (H)
100 or 102
Died
Deca (D)
10
By
base
1
drinking
deci (d)
1/10
chocolate
centi (c)
1/100 or 1/102
milk
milli (m)
1/1000 or 1/103
Micro (µ)
1/1000000 or 1/106
Nano (n)
1/1000000000 or 1/109
S Mass, distance, time, volume, and quantity (amount) are the ones
most common to chemistry.
S
These measurements each have their own base unit.
We want to know/
measure
What it’s
called
Standard system
Metric Base Unit
Abbreviation
How much something
weighs
Mass
Pounds, ounces,
tons
Gram
g
How long/short
something is
Distance
Inches, feet, miles
Meter
m
How much space
something takes
up
Volume
Pints, gallons,
quarts, cups
Liter
L
Time
Seconds, minutes,
hours
Second
s
Quantity
Dozen, gross
Mole
mol
How long something
takes
How many of
something we
have
#2
The greater unit
gets the 1
Symbol
S 950 g = ________ kg
950 g
x
1
K
1000
H
100
D
10
b
1
d
1/10
c
1/100
m
1/1000
kg
1000 g
Factor
=
0.95 kg
The greater unit
gets the 1
#1
Symbol
S
35 mL = _________ cL
S TWO prefixes = TWO steps
35 mL
x
1
L
1000 mL
x
Factor
K
1000 or 103
H
100 or 102
D
10
b
1
d
1/10
c
1/100 or 102
m
1/1000 or 103
μ
1/1000000 or 106
100 cL
1 L
=
3.5 cL
The greater unit
gets the 1
#8
Symbol
S
0.005 kg= _________ dag
S TWO prefixes = TWO steps
0.005 kg
x
103
g
1 kg
x
Factor
K
1000 or 103
H
100 or 102
D
10
b
1
d
1/10
c
1/100 or 102
m
1/1000 or 103
μ
1/1000000 or 106
106 μg
1
g
=
5x106 μg
Friday- Exit Ticket
S Perform the following metric conversion
S 180 ns to ks
S 77.2 cm3 to L
S Round the following number to 3 sig figs
S 45674
Extra Dimensional Analysis
Dimensional Analysis
S Many problems in chemistry do not have a simple formula
that you can plug the data into and get the answer. Instead,
solving a chemistry problem requires planning, much like
taking a trip. You must determine where you are going
(what you are solving for) and how you are going to get
there (what do you need to know to solve the problem).
Dimensional Analysis
S In chemistry most data is in the form of a measurement. A
measure contains two parts - the number and the UNIT!
S Many problems involve converting measurements from one
unit (or dimension) to another. These units help you to plan
the solution to the problem you are trying to solve. The
technique of converting between units is called
DIMENSIONAL ANALYSIS.
Dimensional Analysis
S When you use dimensional analysis to solve chemistry
problems you will keep track of the units involved in the
calculations you use. When you multiply or divide numbers
with units you also multiply or divide the units. You cancel
units the same way that you cancel the numerators and
denominators of fractions.
S A conversion factor is a relationship between different units
of measure.
Dimensional Analysis
S Give an example of a conversion factor and show 3 ways of
writing it.
S Inches and feet
S Minutes and seconds
Dimensional Analysis
1.
Write the given.
2.
Set up your conversion factor your units will cancel out.
3.
Multiply by factors on the top and divide by factors on the
bottom.
S Be sure your units are cancelling out and that the unit you’re
left with is the desired unit.
Dimensional Analysis
S How many inches are equal to 4.5 feet?
S How many steps? 1 (12 in = 1 ft)
4.50 ft
x
12 in
1 ft
=
54 in
Dimensional Analysis
S How many dollars are in 140 dimes?
S How many steps? 1 (1 dollar = 10 dimes)
140 dimes
x
1 dollar
10 dimes
= 14 dollars
Dimensional Analysis
S Pistachio nuts cost $6.00 per pound. How many pounds of
nuts can be bought for $20.00?
S How many steps? 1 (1 pound = $6.00)
20 dollars
x
1 pound
6 dollars
=
3.33 pounds
Dimensional Analysis
S How much does 4.15 pounds of pistachio nuts cost?
S How many steps? 1 (1 pound = $6.00)
4.15 pounds
x
6 dollars
1 pound
=
24.90 dollars