Conversion Problems Density Measurements and their Uncertainty Do any of these signs list a measurement Measurements contain BOTH a number and a unit All measurements depend on units that serve as reference standards The standards of measurement used in science are those of the m ID: 674585
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Slide1
Scientific Measurements
Units of Measurements
Conversion Problems
Density
Measurements and their Uncertainty Slide2
Do any of these signs list a measurement?
- Measurements contain BOTH a
number
and a
unit
.Slide3
All measurements depend on units that serve as reference standards. The standards of measurement used in science are those of the metric system.
Based on multiples of 10
The International System of Units (abbreviated SI, after the French name, Le
Système
International
d’Unités) is a revised version of the metric system.
1. Measuring with SI UnitsSlide4
What do the SI prefixes deci,
centi
, and
milli mean? Think about the word decimal
,
century, and millennium. Slide5Slide6
The five SI base units commonly used by chemists are the meter, the kilogram, the
kelvin
, the second, and the mole.Slide7
What metric units are commonly used to measure length, volume, mass, temperature and energy?
Units & Quantities Slide8
In SI, the basic unit of length, or linear measure, is the
meter (m)
.
For very large or and very small lengths, it may be more convenient to use a unit of length that has a prefix.
Units of LengthSlide9
Volume
- space occupied by any sample of matter
Units of Volume
How do you calculate the volume of a cube?
The
SI unit of volume
is the amount of space occupied by a cube that is 1 m along each edge. This volume is the
cubic meter (m)
3Slide10
Units of Volume
The liter is a NON SI unit of measurement!
A
liter (L)
is the volume of a cube that is 10 centimeters (10 cm) along each edge (10 cm
10 cm 10 cm = 1000 cm3 = 1 L).
What unit of volume are you most familiar with?
“I’ll have a liter of cola”Slide11
Common quantities
Units of Volume
The volume of 20 drops of liquid from a medicine dropper is approximately 1
mL.
A sugar cube has a volume of 1 cm
3
. 1
mL
is the same as 1 cm
3
.Slide12
The mass of an object is measured in comparison to a standard mass of 1
kilogram (kg),
which is the basic
SI unit of mass.
Common metric units of mass include kilogram, gram, milligram, and microgram.Unit of MassSlide13
How does weight differ from mass?
Unit of Mass
Weight
is a force that measures the pull on a given mass by gravity.
Mass
is a measure of the quantity of matter. (the space it occupies)Slide14
Units of Temperature
Temperature
-
is a measure of how hot or cold an object is.
Thermometers are used to measure temperature.
Substances expand with an increase in temperature. Slide15
When 2 objects at different temperatures are in contact, heat travels from:
Heat of Transfer
Lower temperature
Higher
temperatureSlide16
Scientists commonly use two equivalent units of temperature, the degree
Celsius
and the
Kelvin.
Units of Temperature
Celsius
Kelvin
Reference points
Fahrenheit Slide17
The zero point on the Kelvin scale, 0 K, or
absolute zero
, is equal to
273.15 °C.
Units of TemperatureSlide18
Because one degree on the Celsius scale is equivalent to one Kelvin on the Kelvin scale, converting from one temperature to another is easy. You simply add or subtract 273, as shown in the following equations.
Units of TemperatureSlide19
Converting Between Temperature Scales
Normal human body temperature is 37
C. What is that temperatures in
kelvins
?
Analyze: List the known and the unknown.KnownTemperature in C = 37CUnknown
Temperature in K = ?K
Equation
: K= C + 273
Calculate
:
Solve for the unknown.
K= C + 273
37 + 273 = 310K
Practice –
Converting Between Temperature ScalesSlide20
Liquid nitrogen boils at 77.2 K. What is this temperature in degrees Celsius?
Analyze
:
List the known and the unknown.
Calculate
: Solve for the unknown.Practice –
Converting Between Temperature Scales
-196
CSlide21
Energy
- the capacity to do work or to produce heat.
The joule and the calorie are common units of energy.
Joule (J) is the SI unit of energy.1 calorie (cal) is the quantity of heat that raises the temperature of 1g of pure H2O by 1C.
Units of Energy
1 J = 0.2390 cal
1 cal= 4.184 JSlide22
1. Which of the following is not a base SI unit?
meter
gram
second
mole
Were you paying attention?Slide23
2. If you measured both the mass and weight of an object on Earth and on the moon, you would find that
both the mass and the weight do not change
.
both the mass and the weight change.
the mass remains the same, but the weight changes.
the mass changes, but the weight remains the same.
Were you paying attention?Slide24
3. A temperature of 30 degrees Celsius is equivalent to
303 K.
300 K.
243 K.
247 K.
Were you paying attention?
K =
C + 273Slide25Slide26
Can you think of any other examples in which quantities can be expressed in several different ways?Slide27
Consider the conversion units of distance:
1 meter = 10 decimeters = 100 centimeters = 1000 millimeters
When 2 measurements are equivalent, a ratio of the 2 measurements equals 1
Conversion factor
or
Remember: even though the numbers in the measurements 1 m and 100 cm differ, both measurements represent the same lengthSlide28
What happens when a measurement is multiplied by a conversion factor?
When a measurement is multiplied by a conversion factor, the numerical value is generally
changed
, but the actual size of the quantity measured
remains the same
.2. Conversion ProblemsSlide29
3.3
Conversion Factors
A
conversion factor
is a ratio of equivalent measurements.The ratios 100 cm/1 m and 1 m/100 cm are examples of conversion factors.
Fig. 3.11Slide30
3.3
Conversion Factors
The scale of the micrograph is in nanometers. Using the relationship 10
9
nm = 1 m, you can write the following conversion factors.Slide31
Dimensional analysis
is a way to analyze and solve problems using the units, or dimensions, of the measurements.
Why is dimensional analysis useful?
An alterative way to problem solving
Dimensional AnalysisSlide32
How many seconds are in a workday that lasts exactly eight hours?
Analyze
:
List the
knowns
and the unknown.KnownTime worked = 8 h1 hour = 60 min1 minute = 60 sUnknownSeconds worked = ? sCalculate
:
Solve for the unknown.
Example of Using Dimensional Analysis
Sample Problem 3.5Slide33
1.) How many minutes are there in exactly one week?
Analyze
:
List the knowns
and the unknown.
KnownUnknownCalculate: Solve for the unknown.2.) How many seconds are in exactly a 40-hour work week?
Analyze
:
List the
knowns
and the unknown.
Known
Unknown
Calculate
:
Solve for the unknown.
1.0080x10
4
min
1.44000x10
5
sSlide34
1.) The directions for an experiment ask each student to measure 1.84g of copper (Cu) wire. The only copper wire available is a spool with a mass of 50.0g. How many students can do the experiment before the copper runs out?
2.) A 1.00-degree increase on the Celsius scale is equivalent to a 1.80-degree increase on the Fahrenheit scale. If a temperature increase by 48.0
C, what is the corresponding temperature increase on the Fahrenheit scale?
27 students
86.4
FSlide35
What types of problems are easily solved by
using dimensional analysis?
Problems in which a measurement with one unit is converted to an equivalent measurement with another unit are easily solved using dimensional analysis.
Converting Between unitsSlide36
Converting Between Metric Units
Express 750 dg in grams.
Analyze
:
List the
knowns
and the unknown.
Known
Mass = 750 dg
1 g = 10 dg
Unknown
Mass = ? g
Calculate
:
Solve for the unknown.
Conversion unitSlide37
Practice Problems
Convert the following.
15 cm
3
to liters
7.38 g to kilograms6.7 s to milliseconds94.5 g to micrograms
1.5 x 10
-2
L
7.38 x 10
-3
kg
6.7 x 10
3
ms
9.45 x 10
7
gSlide38
Sports Stats
Entertainment & Chemistry Learning Network
Purpose
: to use dimensional analysis to convert between English and metric units.
Procedure
: Using the player stats for the New England Patriots, convert heights and weights into heights and masses expressed in meters and kilograms, respectively.
You must document your approach:
Identify the known, unknown, and conversion factor.
Must show all calculations.
2.54 cm = 1 inch
454g = 1 lb
ECLNSlide39
Multistep Problems
What is 0.073 cm in micrometers?
Analyze
:
List the
knowns and the unknown.Known
Length = 0.073 cm = 7.3x10
-2
cm
10
2
cm = 1m
1m = 10
6
m
Unknown
Length = ?
m
Calculate
:
Solve for the unknown.Slide40
The radius of a potassium atom is 0.227nm. Express the radius to the unit centimeters.
The diameter of Earth is 1.3 x 10
4
km. What is the diameter expressed in decimeters?
Practice Problems
1.3 x 10
8
dm
2.27 x 10
-8
cmSlide41
The mass per unit volume of a substance is a property called density. The density of manganese, a metallic element, is 7.21 g/cm
3
. What is the density of manganese expressed in units kg/m
3?
Converting Complex Units
Analyze: List the
knowns
and the unknown.
Known
Density of manganese = 7.21 g/cm
3
10
3
g = 1kg
10
6
cm
3
= 1
m
3
Unknown
Density manganese = ?
kg/m3Slide42
Calculate
:
Solve for the unknown.
Density of manganese = 7.21 g/cm
3
103 g = 1kg106cm3 = 1m
3
g/cm
3
kg/m
3
7.21 x 10
3
kg/m
3Slide43
Gold has a density of 19.3 g/cm
3
. What is the density in kilograms per cubic meter?
There are 7.0 x 10
6
red blood cells (RBC) in 1.0 mm3 of blood. How many red blood cells are in 1.0 L of blood?Practice Problems
g/cm
3
10
3
g = 1 kg
10
6
cm
3
= 1 m
3
1.93 x 10
4
kg/m
3
7.0 x 10
12
RBC/L
mm
3
= 1 m
3
10
6
cm
3
= 1 m
3
1cm
3
= 1
mL
10
3
mL = 1 LSlide44
1
Mg = 1000 kg. Which of the following would be a correct conversion factor for this relationship
?
1000
.
1/1000. ÷ 1000
.
1000 kg/1Mg.
Were you paying attention?Slide45
The
conversion factor used to convert joules to calories changes
the quantity of energy measured but not the numerical value of the measurement.
neither the numerical value of the measurement nor the quantity of energy measured.
the numerical value of the measurement but not the quantity of energy measured.
both the numerical value of the measurement and the quantity of energy measured.
Were you paying attention?Slide46
How
many
g are in 0.0134 g
?
1.34 10–4
1.34
10
–6
1.34
10
6
1.34
10
4
Were you paying attention?Slide47
Express
the density 5.6 g/cm
3
in kg/m
3
.5.6 106kg/m3
5.6
10
3
kg/m
3
0.56 kg/m
3
0.0056 kg/m
3
Were you paying attention?Slide48
Which is heavier, a pound of lead or a pound of feathers?Slide49
Why can boats made of steel float on water when a bar of steel sinks?Slide50
What determines the density of a substance?
Density
is the ratio of the mass of an object to its volume.
3. Determining DensitySlide51
Each of these 10-g samples has a different volume because the densities vary.
Density
Which substance has the highest ratio of mass to volume?Slide52
Define what an intensive property is.
Provide 3 examples of an intensive property.
Provide 2 examples of an extensive property.
Bell Ringer
Date: 10/11/2012Slide53
Density is an intensive property that depends only on the composition of a substance, not on the size of the sample.
DensitySlide54
For example, a 10.0-cm
3
piece of lead has a mass of 114 g. What is the density of lead?
Unit of density: g/cm
3Slide55
What would happen if corn oil is poured into a glass containing corn syrup?
OIL
SYRUPSlide56
Determining Density
Simulation 1
Rank materials according to their densities.
ChemASAP
/dswmedia
/
rsc
/asap1_chem05_cmsm0301.htmlSlide57
Volume as temperature
The mass remains the same despite the temperature and volume changes.
Recall:
Density and Temperature
If volume changes
with temperature and mass stays the same, then
density
must change.
Slide58
The density of a substance generally decreases as its temperature increases.
DENSITY
TEMPERATURE
50
F
100
F
0
FSlide59
A copper penny has a mass of 3.1 g and a volume of 0.35 cm3
. What is the density of copper?
Sample Problem
Analyze
:
List the knowns and the unknown.KnownMass = 3.1 gVolume = 0.35 cm
3
Unknown
Density = ?
g/cm
3
8.8571
g/cm
3
Slide60
A student finds a shiny piece of metal that she thinks is aluminum. In the lab, she determines that the metal has a volume of 245 cm
3
and a mass of 612g. Calculate the density. Is the metal aluminum?
A bar of silver has a mass of 68.0g and a volume 6.48 cm
3
. What is the density of silver?Practice Problems
2.50
g/cm
3
- NO
10.5
g/cm
3
Slide61
What is the volume of a pure silver coin that has a mass of 14 g? The density of silver (Ag) is 10.5
g/cm
3.
Practice Problem
Using Density to Calculate Volume
Analyze: List the knowns and the unknown.
Known
Mass of coin = 14 g
Density of silver = 10.5 g/cm
3
Unknown
volume of coin= ?
cm
3
1.3
cm
3
of Ag
Slide62
Use dimensional analysis and the given densities to make the following conversions.
14.8 g of boron to cm
3
of boron. The density of boron is 2.34 g/cm
3
.4.62 g of mercury to cm3 of mercury. The density of mercury is 13.5 g/cm3
.
Rework the preceding problems by applying the following equation.
Practice Problems
Volume of B = 6.32
cm
3
Volume of Hg = 0.342
cm
3Slide63
Make the following conversions:
2.53 cm
3
of gold to grams
(density of gold = 19.3 g/cm
3)1.6 g of oxygen to liters (density of oxygen = 1.33 g/L)
25.0 g of ice to cubic centimeters
(density of ice = 0.917 g/cm
3
)
48.8
g
1.2 L
27.3
cm
3Slide64
If
50.0
mL
of corn syrup have a mass of 68.7 g, the density of the corn syrup
is
0.737 g/mL.
0.727 g/
mL.
1.36 g/
mL.
1.37 g/
mL.
Were You Paying Attention?Slide65
What
is the volume of a pure gold coin that has a mass of 38.6 g? The density of gold is 19.3 g/cm
3
.
0.500 cm
3
2.00 cm
3
38.6 cm
3
745 cm
3
Were You Paying Attention?Slide66
As
the temperature increases, the density of most
substances
increases.
decreases.
remains the same.
increases at first and then decreases
.
Were You Paying Attention?Slide67
Today’s current weather in Eastville
is
The Weather Channel projected
forcast:
Eastern Shore News
Slide68
What everyday activities involve measuring?
Recall which units of measure are related to each of the examples you provide.
Estimate how tall you are
in inches.
Have your lab partner estimate how tall you are with a yard stick.
Compare
the estimates with the yard stick value.Slide69
A
measurement
is a quantity that has both a number and a unit.
Ex.
Height Weight
4. Measurements and Their Uncertainty
Measurements are fundamental to the experimental sciences. For that reason, it is important to be able to make measurements and to decide whether a measurement is correct.
Cooking
Speed Slide70
In
scientific notation
, a given number is written as the product of two numbers: a coefficient and 10 raised to a power.
Using and Expressing Measurements
Example:
602,000,000,000,000,000,000,000
Scientific notation = 6.02x10
23Slide71
3.1
What is the difference between accuracy & precision?Slide72
Accuracy
- a measure of how close a measurement comes to the actual or true value of whatever is measured.
Precision
- a measure of how close a series of measurements are to one another.Slide73
To evaluate the accuracy of a measurement, the
measured value
must be compared to
the correct value.
To evaluate the precision of a measurement, you must
compare the values of two or more repeated measurements.Slide74
3.1
Accuracy, Precision, and Error
Determining
Error
Suppose you are using a thermometer to measure the boiling point of pure H
2O at STP. The thermometer reads 99.1
C. The true, or accepted value of the boiling point of pure
H
2
O under these conditions (STP) is actually 100
C.
Which is the accepted value?
Which is the experimental value?
What is the error?Slide75
The
accepted value
is the correct value based on reliable references. The
experimental value
is the value measured in the lab. The difference between the experimental value and the accepted value is called the error.
Error can be positive or negative depending on whether the experimental value is greater than or less than the accepted value.Slide76
The
percent error
is the absolute value of the error divided by the accepted value, multiplied by 100%.Slide77
Suppose you are using a thermometer to measure the boiling point of pure H
2
O at STP. The thermometer reads 99.1
C. The true, or accepted value of the boiling point of pure H
2
O under these conditions (STP) is actually 100 C.Slide78
Just because a measuring device works, you cannot assume it is accurate. The scale below has not been properly zeroed, so the reading obtained for the person’s weight is inaccurate.Slide79
Suppose you estimate a weight that is between 2.4 lb and 2.5 lb to be 2.46 lb. The first two digits (2 and 4) are known. The last digit (6) is an estimate and involves some uncertainty. All three digits convey useful information, however, and are called significant figures.
The
significant figures
in a measurement include
all of the digits that are known, plus a last digit that is estimated.Significant Figures in MeasurementsSlide80
Measurements MUST ALWAYS be reported to the correct number of significant figures because calculated answers often depend on the number of significant figures in the values used in the calculation.
Animation
See how the precision of a calculated result depends on the sensitivity of the measuring instruments.Slide81
Significant Figures in Measurements
3.1Slide82
How many significant figures are in each measurement?
123 m
40.506 mm
9.8000 x 10
4
m22 meter sticks0.07080 m 98,000 m
Counting Significant Figures in Measurements
3 sig figs (rule 1)
5 sig figs (rule 2)
5 sig figs (rule 4)
Unlimited (rule 6)
4 sig figs (rule 2, 3,4 )
2 sig figs (rule 5)Slide83
How many significant figures are in each length?
0.05730 meters
8765 meters
0.00073 meters
40.007 meters
How many significant figures are in each measurement?143 grams
0.074 meter
8.750 x 10
-2
gram
1.072 meter
4 sig figs
4 sig figs
2 sig figs
5 sig figs
3 sig figs
2 sig figs
4 sig figs
4 sig figsSlide84
How does the precision of a calculated answer compare to the precision of the measurements used to obtain it?
Significant Figures in Calculations Slide85
Significant Figures in Calculations
In general, a calculated answer cannot be more precise than the least precise measurement from which it was
calculated.
The
calculated value must be rounded to make it consistent with the measurements from which it was calculated.
3.1Slide86
To round a number, you must first decide how many significant figures your answer should have
. The answer depends on the given measurements and on the mathematical process used to arrive at the answer.
Rounding
If the digit immediately to the right of the last significant digit is less than 5, it is simply dropped and the value of the last significant digit stays the same.
If the digit in question is 5 or greater, the value of the digit in the last significant place is increased by 1
2.691 m
2.69 m
294.8
mL
295
mLSlide87
Round off each measurement to the number of significant figures shown in parentheses. Write the answer in scientific notation.
314.721 meters (4)
0.001775 meter (2)
8792 meters (2)
Sig. Fig.’s - Rounding MeasurementsSlide88
Round each measurement to
three significant figures
. Write your answers in scientific notation.
87.073 meters
4.3621 x 10
8 meters0.01552 meter9009 meters1.7777 x 10-3 meter
629.55 meters
Practice Problems
8.71 x 10
1
m
4.36 x 10
8
m
1.55 x 10
-2
m
9.01 x 10
3
m
1.78 x 10
-3
m
6.30 x 10
2
mSlide89
The answer to an addition or subtraction calculation should be rounded to the
same number of decimal places
(not digits) as the measurement with the least number of decimal places.
Example:
12.52 meters + 349.0 meters + 8.24 meters
Step 1 – align the decimal points and identify least # of decimal places.
12.52 meters
349.0 meters
+ 8.24 meters
369.76 meters
Sig. Fig.’s - Addition and Subtraction
- 2 decimal places
- 1 decimal places
- 2 decimal places
369.8 meters
or 3.698 x 10
2
metersSlide90
Perform each operation. Express your answers to the correct number of significant figures.
61.2 meters + 9.35 meters + 8.6 meters
9.44 meters – 2.11 meters
1.36 meters + 10.17 meters
34.61 meters – 17.3 meters
Practice
79.2 m
7.33 m
11.53 m
17.3 mSlide91
In calculations involving multiplication and division, you need to round the answer to the same number of significant figures as the measurement with the
least number of significant figures.
The position of the decimal point has nothing to do with the rounding process when multiplying and dividing measurements.
Sig. Fig.’s - Multiplication and Division Slide92
Perform the following operations. Give the answers to the correct number of significant figures.
7.55 meters x 0.34 meter
2.10 meters x 0.70 meter
2.4526 meters ÷ 8.4
Practice
= 2.576 (meter)
2
(3)
2.6 m
2
(2)
= 1.47 (meter)
2
(3)
Step 1 – determine # of sig figs
Step 2 – calculate answer
Step 3 – determine answer w/ correct # of sig figs.
(2)
1.5 m
2
(5)
(2)
= 0.291976 meter
0.29 mSlide93
Were You Paying Attention?
In
which of the following expressions is the number on the left NOT equal to the number on the right
?
0.00456
10
–8
= 4.56
10
–11
454
10
–8
= 4.54
10
–6
842.6
104 = 8.426 106 0.00452 10
6
= 4.52
10
9
Slide94
Were You Paying Attention?
Which
set of measurements of a 2.00-g standard is the most precise
?
2.00 g, 2.01 g, 1.98 g
2.10 g, 2.00 g, 2.20 g
2.02 g, 2.03 g, 2.04 g
1.50 g, 2.00 g, 2.50 g Slide95
A
student reports the volume of a liquid as 0.0130 L. How many significant figures are in this measurement
?
2
3
4
5
Were You Paying Attention?