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In-Class Problems & HW
CHM 111
Chapter E - Essentials
Chapter E Goals
• Use the SI prefix multipliers to convert between them.
• Report Scientific Measurements to the Correct Digit of Uncertainty
• Determine the Number of Significant Figures in a Number
• Follow Significant Figure Rules in Calculations
• Use Conversion Factors to Convert Quantities from One Unit to Another
• Solve Problems Involving Equations
• Calculate the Density of a Substance
• Rearrange algebraic equations to solve for unknown variables
• Distinguish between intensive and extensive properties of matter
• Distinguish between accuracy and precision in measurements and calculations
Measurement Types: Qualitative and Quantitative
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–
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observations are descriptive in nature
Changes in color and physical state
observations are:
–
–
Measurements
• Numerical values obtained from instrumentation, glassware, and other
measuring devices
• Varying precision and accuracy
– Counted values
• Number of cats per household in the United States
The nature of the measurement (qualitative vs. quantitative) dictates the types of
statistics that can be used during data analysis.
–
What Are Measurements?
• All measurements consist of two parts.
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Scalar or
unit
– Units may be part of the International System of Units (SI), based on the metric
system or the English system.
– Example: 5.9 m means 5.9 meters, and 3.7 kg conveys 3.7 kilograms.
–
value
Reflects the precision of the instrument or piece of glassware used to make the
measurement
Example: 25.0 cm or 1.00 ft
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–
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Standard Units of Measures (SI)
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Length:
–
Mass:
–
Time:
–
Temperature:
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Amount of substance:
Metric System Prefixes:
Prefix
Symbol
Decimal
Power of 10
MegaKiloDeciCentiMilliMicroNanoPicoTemperature Calculations
•
To go from Celsius (°C) to kelvin (K) use the equation:
_____________________________________________
‒
•
Examples:
• Determine the body temperature in kelvin
37.00 °C + 273.15 = 310.15 K
• Liquid nitrogen boils at 77 K. What is this temperature in Celsius?
77 K – 273.15 = –196 °C
To go from Celsius (°C) to Fahrenheit (°F) use the equation:
_____________________________________________
‒
Example: Your younger brother has a temperature of 40.0 °C. What is this temperature
in Fahrenheit?
°F = 1.8(40.0°C) + 32 = 104.0 °F
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Example E.1
Converting between Temperature Scales
A sick child has a temperature of 40.00 °C. What is the child’s temperature in (a) K and (b) °F?
For Practice E.1
Gallium is a solid metal at room temperature but will melt to a liquid in your hand. The melting point of
gallium is 85.6 °F. What is this temperature on (a) the Celsius scale and (b) the Kelvin scale?
Reliability of Measurements: Precision vs. Accuracy and Uncertainty
•
Precision:
– NOTE: You can be precise but not accurate in measurements
•
Accuracy:
–
NOTE: You can have accuracy in overall measurement but
not be precise.
Significant Figures and Measurements
•
Uncertainty
– The uncertain digit depends on the instrument being used.
– Reported as (+/–)
– Example: 23.45 +/– 0.05 mL indicates the last digit of the measured value is estimated to
be within 0.05 mL of the true value. True value lies within 23.40 to 23.50 mL
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•
•
Reporting of significant figures in an answer is dependent on the precision of the
values given in the problem (precision of the glassware or lab equipment
used).
Conversion factors are treated as
values.
– Exact values are measurements that have an infinite number of significant figures.
– Examples:
1 in = 2.54 cm
100 pennies = $1
12 pieces = 1 dozen
Significant Figure Rules
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All
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•
–
–
–
•
values are significant.
Example: 536 has three significant figures.
between
Example: 6703 has four significant figures.
digits are significant.
Leading zeroes: Place-holder zeroes to the
• Example: 0.0043 has two significant figures.
digit are NOT significant.
Trailing zeroes:
– Zeroes to the
digit are NOT significant.
• Example: 7000 has only one significant figure.
• Example: 32040 has four significant figures since the interior zero is significant.
–
Zeroes to the right
ARE significant.
• Example: 50.0 has three significant figures; the interior zero is also significant.
• Example: 0.0600 has three significant figures; the leading zeroes are not
significant.
Measurements and Significant Figures
– 50,003 km has
significant figures.
• The three zeroes are between two nonzero numbers.
–
400 L has
significant figure.
• The two zeroes after the value, 4, are place holders.
–
0.04450 m has
significant figures.
• The two zeroes in front of the value, 4, are place holders.
• The zero following the value, 5, is significant.
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–
–
–
100 cm = 1 m has an
number of significant figures.
• There are always 100 cm in 1 m, never 99.99 cm in 1 m.
• 100 is treated as an exact number.
1.000 x 103 s has
significant figures.
• The trailing zeroes after the value, 1, are significant.
3.050 x 10–1 g has
significant figures.
• The zero after the value, 3, is significant.
• The trailing zero after the value, 5, is significant.
Significant Figures and Scientific Notation
• Example:
3010 in scientific notation is 3.01 x 103
– NOTE: The decimal point was moved three places to the left.
• Example:
0.0310 in scientific notation is 3.10 x 10–2
– NOTE: The decimal point was moved two places to the right. Both of these values
indicate THREE significant figures.
Mathematical Operations and Significant Figures
• Mathematical operations dictate the reporting of significant figures in an answer.
– Multiplication and division
•
–
The
measured value
determines the number of significant figures in the reported answers.
Addition and subtraction
• The value with the
determines the answer’s significant figures.
Example E.3
Determining the Number of Significant Figures
How many significant figures are in each number?
a. 0.04450 m
b. 5.0003 km
c. 10 dm = 1 m
d. 1.000 × 105 s
e. 0.00002 mm
f. 10,000 m
measurement
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For Practice E.3 Determining the Number of Significant Figures
How many significant figures are in each number?
a. 554 km
b. 7 pennies
c. 1.01 × 105 m
d. 0.00099 s
e. 1.4500 km
f. 21,000 m
Example E.4
Significant Figures in Calculations
Perform each calculation to the correct number of significant figures.
a. 1.10 × 0.5120 × 4.0015 ÷ 3.4555
b. 0.355 +105.1 -100.5820
c. 4.562 × 3.99870 ÷ (452.6755 – 452.33)
d. (14.84 × 0.55) – 8.02
For Practice E.4 Significant Figures in Calculations
Perform each calculation to the correct number of significant figures.
a.
3.10007 × 9.441 × 0.0301 ÷ 2.31
b.
0.881+132.1-12.02
c.
2.5110 × 21.20 ÷ (44.11 + 1.223)
d. (12.01 × 0.3) + 4.811
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Density: An Intensive Physical Property of Matter
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physical properties are independent of the amount of substance
being measured.
•
physical properties are dependent on amount
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Density is defined as
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Densities of liquids and gases are affected by
.
.
Example E.5
Calculating Density
A man receives a ring from his fiancée, who tells him that it is made out of platinum. Before the
wedding, he notices that the ring feels a little light for its size and decides to measure its density. He
places the ring on a balance and finds that it has a mass of 3.15 g. He then finds that the ring displaces
0.233 cm3 of water. Is the ring made of platinum? Assume that the measurements occurred at 20 °C.
For Practice E.5
The fiancée in Example E.5 is shocked that the ring is fake and returns it. She buys a new ring that has a
volume of 0.212 cm3. If the new ring is indeed pure platinum, what is its mass?
For More Practice E.5
A metal cube has an edge length of 11.4 mm and a mass of 6.67 g. Calculate the density of the metal and
refer to Table E.4 to determine the likely identity of the metal.
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Strategy for Solving Dimensional Analysis
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Take
•
•
Start with what you can
• Write the measurement (what you can “hold in your hand”) as the starting point for the
calculation.
•
Know your
• Write the “=“ and units of the answer you want
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•
•
•
&
Make a list of all numbers with units
units
the Trip
Review conversion factors and cancel each unwanted unit one at a time.
Do the
• Carefully multiply top numbers and write it down.
• Carefully multiply bottom numbers and write it down.
• Divide top (numerator) by bottom (denominator)
•
the units and answer
Example E.6 Unit Conversion
Convert 1.76 yards to centimeters.
Example E.7
Unit Conversion
Convert 1.8 quarts to cubic centimeters.
For Practice E.7
Convert 9255 cm3 to gallons.
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Example E.8
Unit Conversions Involving Units Raised to a Power
Calculate the displacement (the total volume of the cylinders through which the pistons move) of a 5.70L automobile engine in cubic inches.
For Practice E.8
How many cubic centimeters are there in 2.11 yd3?
For More Practice E.8
A vineyard has 145 acres of Chardonnay grapes. A particular soil supplement requires 5.50 g for every
square meter of vineyard. How many kilograms of the soil supplement are required for the entire
vineyard? (1 km2 = 247 acres)
Example E.9
Density as a Conversion Factor
The mass of fuel in a jet must be calculated before each flight to ensure that the jet is not too heavy to
fly. A 747 is fueled with 173,231 L of jet fuel. If the density of the fuel is 0.768 g/cm3, what is the mass of
the fuel in kilograms?
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For Practice E.9
Backpackers often use canisters of white gas to fuel a cooking stove’s burner. If one canister contains
1.45 L of white gas and the density of the gas is 0.710 g/cm3, what is the mass of the fuel in kilograms?
For More Practice E.9
A drop of gasoline has a mass of 22 mg and a density of 0.754 g/cm3. What is its volume in cubic
centimeters?
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Chapter E Tables and Formulas
Metric System: Prefix Multipliers
To go from Celsius (°C) to kelvin (K) use the equation:
T (K) = T(°C) + 273.15
To go from Celsius (°C) to Fahrenheit (°F) use the equation:
°F = 1.8 (°C) + 32
Accuracy and Precision
Dimensional Analysis:
1.
2.
3.
4.
5.
6.
Take INVENTORY and TRANSLATE units
Start with what you can MEASURE
Know your FINAL DESTINATION
PLAN the trip
Do the MATH
CHECK the units and the answer
Significant Figure Rules
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•
•
•
•
All nonzero values are significant.
Zeroes between nonzero digits are significant.
Place-holder zeroes to the left of a nonzero digit are NOT significant.
Zeroes to the right after a nonzero digit are NOT significant.
Zeroes to the right after a decimal point ARE significant.
Mathematical Operations and Significant Figures
Multiplication and division: lowest number of SIGNIFICANT FIGURES
Addition and subtraction: lowest number of DECIMAL PLACES.
Density:
𝒅=
𝒎
𝑽