1. Measurements and Problem Solving in Chemistry
UNIT 2
Measurements and Problem Solving in Chemistry

2. The Standard Units
Scientists have agreed on a set of international standard units for comparing all our measurements called the SI units
Système International = International System
Quantity
Unit
Symbol
length
meter m
mass
gram g
time
second s
temperature
Kelvin/Celsius
K/°C
volume
liter L
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3. Length Measure of the two-dimensional distance an object covers
often need to measure lengths that are very long (distances between stars) or very short (distances between atoms)
SI unit = meter
About 3.37 inches longer than a yard
Commonly use centimeters (cm)
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4. Mass Measure of the amount of matter present in an object
weight measures the gravitational pull on an object, which depends on its mass
Weight and mass are NOT the same thing
SI unit = gram (g)
Commonly measure mass in grams (g) or milligrams (mg)
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5. Time measure of the duration of an event SI units = second (s)
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6. Volume The amount of space an object takes up.
Could be expressed in units of liters (liquid)
Could be expressed in units of length cubed, m3 (solid)

7. Temperature measure of the average amount of kinetic energy
higher temperature = larger average kinetic energy
heat flows from the matter that has high thermal energy into matter that has low thermal energy
until they reach the same temperature
heat is exchanged through molecular collisions between the two materials
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8. Temperature Scales Fahrenheit Scale, °F Celsius Scale, °C
used in the U.S.
Celsius Scale, °C
used in all other countries
Kelvin Scale, K
absolute scale
no negative numbers
directly proportional to average amount of kinetic energy
0 K = absolute zero
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9. Fahrenheit vs. Celsius
a Celsius degree is 1.8 times larger than a Fahrenheit degree
the standard used for 0° on the Fahrenheit scale is a lower temperature than the standard used for 0° on the Celsius scale
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10. Kelvin vs. Celsius
the size of a “degree” on the Kelvin scale is the same as on the Celsius scale
though technically, we don’t call the divisions on the Kelvin scale degrees; we called them kelvins!
so 1 kelvin is 1.8 times larger than 1°F
the 0 standard on the Kelvin scale is a much lower temperature than on the Celsius scale
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11. Example 1.2 Convert 40.00 °C into K and °F
Find the equation that relates the given quantity to the quantity you want to find
Given:
Find:
Equation:
40.00 °C K
Since the equation is solved for the quantity you want to find, substitute and compute
Find the equation that relates the given quantity to the quantity you want to find
Given:
Find:
Equation:
40.00 °C °F
Solve the equation for the quantity you want to find
Substitute and compute

12. Related Units in the SI System
All units in the SI system are related to the standard unit by a power of 10
The power of 10 is indicated by a prefix multiplier
The prefix multipliers are always the same, regardless of the standard unit
Report measurements with a unit that is close to the size of the quantity being measured
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13. Common Prefix Multipliers in the SI System
Symbol
Decimal
Equivalent
Power of 10
mega- M
1,000,000
Base x 106
kilo- k
1,000
Base x 103
deci- d
0.1
Base x 10-1
centi- c
0.01
Base x 10-2
milli- m
0.001
Base x 10-3
micro-
m or mc
Base x 10-6
nano- n
Base x 10-9
pico p
Base x 10-12
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14. Volume Derived unit Measure of the amount of space occupied
any length unit cubed
Measure of the amount of space occupied
SI unit = cubic meter (m3)
Commonly measure solid volume in cubic centimeters (cm3)
Commonly measure liquid or gas volume in milliliters (mL)
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15. What is the volume of the fish?
Water displacement
What is the volume of the fish?

16. Density

17. Mass & Volume two main physical properties of matter
mass and volume are extensive properties
the value depends on the quantity of matter
extensive properties cannot be used to identify what type of matter something is
if you are given a large glass containing 100 g of a clear, colorless liquid and a small glass containing 25 g of a clear, colorless liquid - are both liquids the same stuff?
even though mass and volume are individual properties, for a given type of matter they are related to each other!
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18. Density Ratio of mass:volume is an intensive property
value independent of the quantity of matter
Density : solids > liquids >>> gases
except ice is less dense than liquid water!
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19. Tro, Chemistry: A Molecular Approach
Mass vs. Volume of Brass
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20. y = 8.38x Volume vs. Mass of Brass Mass, g Volume, cm320 40 60 80
100
120
140
160
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
Volume, cm3
Mass, g
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21. Density
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22. Animation of Density
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23. Example 1. 3 Decide if a ring with a mass of 3. 15 g that displaces 0
Example 1.3 Decide if a ring with a mass of 3.15 g that displaces cm3 of water is platinum
Find the equation that relates the given quantity to the quantity you want to find
Given:
Find:
Equation:
mass = 3.15 g
volume = cm3
density, g/cm3
Since the equation is solved for the quantity you want to find, and the units are correct, substitute and compute
Compare to accepted value of the intensive property

24. Measurement and Significant Figures

25. What Is a Measurement? quantitative observation
comparison to an agreed- upon standard
every measurement has a number and a unit
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26. A Measurement
the unit tells you what standard you are comparing your object to
the number tells you
what multiple of the standard the object measures
the uncertainty in the measurement
scientific measurements are reported so that every digit written is certain, except the last one which is estimated
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27. Reading a Measuring Device using Significant Figures
Record all the numbers you can see
Make ONE Guess!

28. Tro, Chemistry: A Molecular Approach

29. What is the Length? We can see the markings between 1.6-1.7cm
We can’t see the markings between the .6-.7
We must guess between .6 & .7
We record 1.65 cm as our measurement

30. What is the length of the wooden stick?
1) cm
2) cm
3) cm

31. Precision and Accuracy

32. How many significant figures are in each of the following numbers?
0.0035
1.080
2371
2.97 × 105
100,000
Tro's "Introductory Chemistry", Chapter 2

33. How many sig figs? 6 3 5 2 4
All digits count
Leading 0’s don’t
Trailing 0’s do
0’s count in decimal form
0’s don’t count w/o decimal
0’s between digits count as well as trailing in decimal form
48000.
48000
3.982106

34. Determine the Correct Number of Significant Figures for Each Calculation and
1.01 × 0.12 × ÷ 96 = = 0.068
56.55 × ÷ = = 1.52
Result should
have 2 sf.
7 is in place
of last sig. fig.,
number after
is 5 or greater,
so round up.
3 sf
2 sf
4 sf
2 sf
4 sf
Result should
have 3 sf.
1 is in place
of last sig. fig.,
number after
is 5 or greater,
so round up.
3 sf
6 sf
Tro's "Introductory Chemistry", Chapter 2

35. Determine the Correct Number of Significant Figures for Each Calculation and Round and Report the Result, Continued
– 1.22 = =
0.764 – – 5.98 = =
3 dp
Result should
have 1 dp.
8 is in place
of last sig. fig.,
number after
is 5 or greater,
so round up.
1 dp
2 dp
Result should
have 2 dp.
6 is in place
of last sig. fig.,
number after
is 4 or less,
so round down.
3 dp
3 dp
2 dp
Tro's "Introductory Chemistry", Chapter 2

36. Example 1.6—Perform the Following Calculations to the Correct Number of Significant Figures, Continued b)
Tro's "Introductory Chemistry", Chapter 2

37. Uncertainty in Measured Numbers
uncertainty comes from limitations of the instruments used for comparison, the experimental design, the experimenter, and nature’s random behavior
to understand how reliable a measurement is we need to understand the limitations of the measurement
accuracy is an indication of how close a measurement comes to the actual value of the quantity
precision is an indication of how reproducible a measurement is
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38. Accuracy vs. Precision