Download Chapter 5 - Measurements

Chapter 3 - Measurements
You’ll learn it in the summer,
If not, it’ll be a bummer.
You’ll need to know conversions,
For units, Euro version.
Metrics are powers of ten,
And you might cry when,
You’re forced to use sig figs,
No one will do any jigs.
You’ll want to know about Kelvins,
And Celsius degrees,
Don’t get frustrated with rate factors,
Or calculations of density.
- Ben Nichols
Learning Targets :
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




Students should understand and apply the law of conservation of mass.
Students should be able to use and determine the accuracy and precision of measurements made
by various measuring instruments.
Students should be able to recognize and manipulate significant digits correctly when making
measurements and using them in the lab.
Students should be able to utilize scientific notation.
Students should be able to perform metric conversions.
Students should be able understand and calculate density.
Students should be able to analyze experimental results to determine the amount of error.
Scientific notation
3.2 x 103
740900000000000
5.5 x 10-4
0.084
SI Units:
Basic SI Units: length – meter (m)
mass - kilogram (kg)
time
- second (s)
electric current - ampere (A)
temperature - Kelvin (K)
amount of a substance – mole (mol)
luminous intensity – candela (cd)
All other are “derived” units
Area
Volume
Quantity
Symbol
A
V
Density
D
Molar Mass
M
Energy (heat)
Pressure
E
P
Quantity
SI Unit
Square meter
Cubic meter
Kilograms per
cubic meter
Kilograms per
mole
Joule
Pascal*
SI Unit
Abbreviation
m2
m3
Derivation
length x width
length x width x height
3
mass / volume
kg/mol
mass / amount
J
Pa
force x length
force / area
Metric prefixes
Base units
Mass: grams (g)
prefix
giga
symbol
G
10^
mega
M
kilo
k
Length: meter (m)
deka
Da
Base
0
deci
d
big # small unit =
small #
Volume: liter (L)
centi
c
milli
m
micro
nano
n
Pico
p
big unit
Metric conversions
Examples:
22.6 mm = ______m
12.0 cm2 = _____mm2
1L=
.61 kg = ______cg
78.5 mL = ______L
24.1m3 = _____dm3
1mL =
21 mL = _____cm3
6.3 dm3 = _____L
3.7 L = ____cm3
4.89 dm3 = _____mL
Temperature:
Scientists commonly use two equivalent units of temperature, the Celsius scale and the Kelvin scale. A
change of 1 degree on the Celsius scale is equal to a change of one Kelvin on the Kelvin scale. Absolute
zero is equal to _______ K or _______ oC.
Example:
25 oC = ___________ K
K=
o
C=
312 K = ______________ oC
Density calculations
Mass is a measure of the amount of matter in an object.
 Essentially, how much “stuff” is inside an object.
Weight is the force that mass has as a result of gravity.
 When the gravity changes, the weight will change, but the mass will remain constant
Volume is the amount of space an object occupies.
 This remains constant for solids and liquids.
Density is the amount of matter per the amount of space. It is calculated by dividing the mass by the
volume.
 Density is an intensive property; it will remain the same no matter how much of the substance
there is.
 The density of an object will determine if it will float or sink in another phase. If an object floats,
it is less dense than the other substance. If it sinks, it is denser.
The formula for density looks like a heart with a line through it:
D
m
V
Example: What is the volume of a substance with a mass of 75.8g and a density of 7.87 g/cm3?.
Name: ________________
Period: _____
SIGNIFICANT FIGURES
Every value is an estimation limited to our _____________________. Scientists try to obtain accurate and
precise measurements. __________________ refers to how close a measurement approaches the true value.
__________________ refers to obtaining a constant value.
A significant figure is one which is known to be reasonably reliable. If you have a measurement to the nearest
tenth of 15.7 cm, this means that is is between 15.65 and 15.75 cm.
1. Rules for recording data you measured
The number of significant figures here is the number of digits you are able to read with certainty from the measuring
device plus ________________ digit you estimate. EXCPTION: ____________ measuring devices – record all the
numbers displayed and do not add an estimated digit.
2. Rules for reading and interpreting data reported by others.
1.
If YES, find the ________________most end of the entire number and look to the ___________ until you reach the last
"NONZERO" digit. This digit and all others to the left are significant.
Ex. 12.050 L has _____ sig figs
0.00050 mL has ______ sig figs
12.24 g has ____ sig figs
2.
If NO, reverse the instructions from above (find the __________most end of the entire number and look to the
_________ until you reach the last non-zero digit. This digist and all others to the right are significant.
Ex. 230 kg has ______ sig figs
10000 mL has _____ sig fig
1204 mg has ______ sig figs
3. Rules for calculations
Addition and subtraction
In addition and subtraction we consider the significant figures on the right side of decimal point. This
means that only as many digits are to be retained to the right side of decimal point as the number
with fewest digits to the right of the decimal point.
For example:
+
4.345
23.5
=27.845 (calculator answer)
Honors Chemistry
Answer after rounding off: ___________
Ch 5 – Measurements
Page 5
Name: ________________
Period: _____
Multiplication and Division
In multiplication and division , the number obtained after calculation of two or more numbers
must have no more significant figure than that number used in multiplication or division.
For example:
4.3458
x
2.7
11.73366
(calculator answer)
Answer after rounding off: ________
(because 2.7 has only two significant figures
Significant Figures are only limited for measurments. Counting numbers or defined quantities have
an infinite number of significant figures. Ex: 12 students, 1 m = 100 cm.
4. Rounding
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o
o
o
If the number to be rounded is greater than 5 – round ____________.
If the number to be rounded is less than 5 – round ___________.
If the number to be rounded is equal to 5
if it is followed by nonzero digit, round _________.
if not followed by a nonzero digit and is preceded by an odd digit, round up
if not followed by a nonzero digit and is preceded by an even digit keep the same
Scientific notation
Scientific notation is a way to indicate proper precision. All digits in scientific notation are significant.
3
Example 2100 cm = 2.1 x 10 cm and has ___________significant figures.
Practice Problems
1. How many significant digits do the following measurements contain?
a)
101 g __________
c)
900. cm ________
e)
0.92 mL ________
b)
0.06 m _________
d)
40200 kg _______
f)
90 torr _________
2. Round the number 389.55 to
a) 1 sig fig ________________
b) 2 sig figs ________________
c) 3 sig figs ________________
d) 4 sig figs ________________
3. Convert the following to scientific notation keeping the same number of significant figures.
a) 0.0048 ____________
c) 0.82 ______________
e) 9090 ______________
b) 60.0 ______________
d) 3000 ______________
f) 28050 _____________
4. 6.82 mL + 4.028 mL =
5. You live 3.562 miles away from school. It take you 5.37 minutes to go to school. What is your average speed?
Honors Chemistry
Ch 5 – Measurements
Page 6
Name: _______________________
Period: _____
Worksheet 1 - Scientific Notation/Metric Conversions
1.
Express 205,000,000 mi in scientific notation.
2.
Express 15,545,000 kg in scientific notation.
3.
Express 0.001 s in scientific notation.
4.
Convert 6.02 x 10-2 from scientific notation.
5.
Convert 24.5 cm to m.
6. Convert 68.4 kg to Mg.
7. Convert 8.54 kg to cg.
8. Convert 68.4 g to kg.
9. 3.5oC = ______ K
10 59.9 K = _____ oC
11. 82.4 m = _____ Mm
12. 2100 cg = _____ Mg
13. 2080 g = ______Dag
14. 4082 cm3 = _____ m3
15. 947.0 km2 = ______ m2
16. 21.94 L = ______ cm3
17. 80.0448 cm3 = ______ mL
18. 0.093 mL = ______ dm3
19. What does the following measure and is it base or derived? (Example: 34 cm2: area, derived unit)
a) 12.3 km
b) 14.0 pL
c) 34.5 mol
d) 890.3 mm2
e) 438 in3
f) 74 g/mL
g) -53.4 °C
h) 320 Pa
Honors Chemistry
Ch 3 – Measurements
Page 7
Name: _______________________
Period: _____
Worksheet 2 – Significant Figures in the Lab
1. Read the following ruler measurements.
a) _______________
b) _______________
2. Read the following graduated cylinder measurements.
a) ___________
b) ___________
c) ____________
d) ____________
3. Read the following temperature measurements in degrees Celsius.
a) ___________
Honors Chemistry
b) ___________
c) ____________
Ch 3 – Measurements
d) ____________
Page 8
Name: _______________________
Period: _____
4. In an experiment, the mass of an evaporating dish was recorded. A sample of salt water was added to
the dish, and the mass was recorded. Then, the dish was heated until all of the water evaporated, leaving
the salt behind. The mass of the dish, and remaining salt, was recorded after the dish cooled.
Data Obtained:
Item
Evaporating Dish
Evaporating Dish with salt water
Evaporating Dish with dried salt
Mass (g)
26.54
33.98
29.28
a. Determine the mass of salt water in the evaporating dish.
b. Determine the mass of dried salt remaining in the dish after evaporation.
c. Determine the mass of water which was lost during evaporation.
Honors Chemistry
Ch 3 – Measurements
Page 9
Name: _______________________
Period: _____
Worksheet 3 – Significant Figures Calculations
1.
How many sig figs do the following measurements contain?
a) 12.00 g ___
b) 0.0024 cm ______
c) 108.04 torr _______
d) 3,000m ________
e) 0.84 L _______ ____
f) 60 g ________
g) 6020080 cm ______
h) 0.050 mL__________
j) 0.3 X 106 atm______
2.
i)1.0 x 10 4 s _______
k) 1.080 X103 atm ________
Round the number 682.55 to
a) 1 sig fig ___________
b) 2 sig figs ___________
d) 4 sig figs ____________
e) 5 sig figs _____________
c) 3 sig figs _________
3. Convert the following to scientific notation keeping the same number of significant figures.
a) 0.0048 ___________________
b) 3000 _____________________
c) 60.0 ___________________
d) 8080 _____________________
e) 0.82 ___________________
f) 28050. ______________________
4. Round the following measurements to 3 significant figures
a) 22.77 g ______________
b) 14.62 m ___________
c) 2108.4 L _______________
d) 99.999s ____________
5. Compute the following. Show all your work and express each answer in the proper number of significant figures.
Include units.
a) If 12.00000 grams of carbon contain 6.02 x 1023 atoms, what is the mass of one carbon atom in milligrams?
b) If a glass marble has a mass of 1.275 grams, what will be the mass of a dozen identical marbles? What would be the
mass (in kg) of a "dozen dozen" marbles?
c) 82 cm x 3.00 cm x 10 cm
d) 105 g/0.86 mL
e) 1.054 x 104km + 4.216xl02km
g)
40.821 L-0.86 L
Honors Chemistry
Ch 3 – Measurements
Page 10
Name: _______________________
Period: _____
Worksheet 4 – Density
1.
What is the relationship between mass and volume of a substance called?
2.
Is density of a substance constant? Explain.
3.
Draw particle diagrams of copper at 30oC and copper at 80oC. Use your diagrams to discuss the density of
copper at both temperatures.
4.
Draw a particle diagram of pure water. Draw another particle diagram of salt water. Use your diagrams to
discuss the density of pure water vs. salt water.
5.
Which has a larger density: table salt or lead?
6.
Balloon A is filled with 1.0 x 1022 particles of carbon dioxide. Balloon B is filled with 1.0 x 1022 particles of helium.
Both balloons have the same volume. Carbon dioxide is denser than air and balloon A will fall on the floor.
Helium is less dense than air and balloon B will rise. If both balloons have the same volume and the same
number of particles, how do you explain the difference in densities?
7.
The density of copper is 8.3 g/cm 3. What is the mass of a bar of copper that has a volume of 3.0 cm3.
8.
What is the density of a solution that has a mass of 13.5 g and a volume of 22 mL?
9.
What is the density of a substance that has a mass of 22 kg and a volume of 2.0 L?
10. What is the mass of a substance that has a density of 33.4 kg/gallon and a volume of 2.58 gallons.
11. A cube has a mass of 22.6 g and a density of 3.7 g/cm3. What are the dimensions of the cube?
12. A block has a length of 2.45 cm and a width of 4.52 cm. What is the block’s height if it has a mass of 78.4 g and a
density of 3.54 g/cm3?
Honors Chemistry
Ch 3 – Measurements
Page 11
Name: _______________________
Period: _____
Chapter 3 Sample Questions
1. How many significant figures are in each of the following numbers?
a) 0.0087 __________
b) 400 __________
8
3
d) 45.5 x 10 ________
e) 4.6 x 10 ______
c) 20030 __________
f) 30. __________
2. Round 399.65 to
a) 1 sig. fig. __________________
b) 2 sig. figs. __________________
c) 3 sig. figs. __________________
d) 4 sig. figs. __________________
3. Convert the following to scientific notation keeping the same number of sig. figs.
a) 0.00022 _____________________
b) 340000 __________________
4. Convert the following to long hand keeping the same number of significant figures.
-8
4
a) 3.20 x 10 ______________________
b) 0.002 x 10 ________________
5. Perform the following conversions.
o
3
a) 21 C = ______________ K
c) 38.6 mL = _______________ dm
b) 3400 Dam = _______________ dm
d) 22.2 L = _________________ dm
3
6. Perform the following calculations. Make sure to express your answers with the correct number of significant figures.
Show work and box your final answer.
23
a) The mass of 6.02 x 10 molecule of oxygen gas is equal to 32.06 grams. What is the mass of 1 molecule of oxygen gas?
b) What is the density of a ball that has a volume of 1.62 L and a mass of 3490 grams?
3
c) What is the length of a cube that has a mass of 22.6 grams and a density of 2.825 g/cm ?
1.
2.
3.
4.
5.
6.
Answers
a) 2
b) 1
c) 4
d) 3
2
2
a) 400
b) 4.0 x10
c) 4.00 x10
-4
5
a) 2.2 x10
b) 3.4 x10
a) 0.0000000320
b) 20
a) 294 K
b) 340000
c) 0.0386
-23
a) 5.33x10 grams/molecule
b) 2150 g/L
Honors Chemistry
e) 2
f) 2
d)399.6
d) 22.2
c) 2.00 cm
Ch 3 – Measurements
Page 12
Name: _______________________
Period: _____
Mass Demos
Law of Conservation of mass:
Demo 1
Prediction: _______
Initial mass: _________
Final mass: __________ Change: ________
Observations: _____________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
Explanation: ______________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
Particle diagrams
Initial
Final
Demo 2
Prediction: _______
Initial mass: _________
Final mass: __________ Change: ________
Observations: _____________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
Explanation: ______________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
Particle diagrams
Initial
Final
Demo 3
Prediction: _______
Initial mass: _________
Final mass: __________ Change: ________
Observations: _____________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
Explanation: ______________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
Particle diagrams
Initial
Honors Chemistry
Final
Ch 3 – Measurements
Page 13
Name: _______________________
Period: _____
Demo 4
Prediction: _______
Initial mass: _________
Final mass: __________ Change: ________
Observations: _____________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
Explanation: ______________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
Particle diagrams
Initial
Final
Demo 5
Prediction: _______
Initial mass: _________
Final mass: __________ Change: ________
Observations: _____________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
Explanation: ______________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
Particle diagrams
Initial
Final
Demo 6
Prediction: _______
Initial mass: _________
Final mass: __________ Change: ________
Observations: _____________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
Explanation: ______________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
Particle diagrams
Initial
Honors Chemistry
Final
Ch 3 – Measurements
Page 14
Name: _______________________
Period: _____
Density of Metals Lab
You will use the mass-volume relationship to identify two metals. You will need to come up with your
own procedure.
Tips:



You will need at least 3 data points for each metal.
Remember that your sample sizes need to be large enough to make a significant difference in
volume.
Remember that your sample sizes need to be different so when you graph your data, the points
are not all on top of each other or close together.
Please place the wet metals on the proper labeled paper towel on the back counter.
Here is a list of the possible metals:
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

Silicon
Aluminum
Tin
Zinc
Nickel
Copper
2.33 g/mL
2.70 g/mL
6.99 g/mL
7.13 g/mL
7.81 g/mL
8.96 g/mL
You will need a formal lab report. Remember it needs to be in past tense and passive voice. Use your
syllabus packet and follow the lab report rules. You will need:
 Heading
 Purpose
 Procedure (past tense and passive voice)
 Data Table (don’t forget the units)
 Results – Here you should include:
o Graph for both metals of mass vs. volume (don’t forget to label axes and title your graph)
o Line of best fit (don’t connect the dots)
o Slope of the line. (show your calculation or indicate if you didn’t on excel)
o Densities of both metals (the slopes) and the identity of the metals.
 Conclusion (see lab report rules)
Honors Chemistry
Ch 3 – Measurements
Page 15
Name: _______________________
Honors Chemistry
Period: _____
Ch 3 – Measurements
Page 16
Name: _______________________
Period: _____
Measurement Stations
Station #
Measuring Equipment
Smallest Increment
Measurement
# Sig. Figs.
1
2
3
4
5
6
7
8
9
10
11
12
Honors Chemistry
Ch 3 – Measurements
Page 17