Dimensional analysis and Units of Measurements
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Transcript of Dimensional analysis and Units of Measurements
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Dimensional analysisand Units of Measurements
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Dimensional analysis
• Dimensional analysis uses conversion factors to convert from one unit to another.
• Also called Factor Label (and railroad tracks)
• You do this in your head all the time– How many quarters are in 4 dollars?
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Dimensional analysis practice
3 Big Mac = 7 salads9 salads = 2 slices of pepperoni pizza
22 slices of pepperoni pizza = 27 Sonic cokes Ex. 1) What number of Big Macs equal 365.4 salads? Ex. 2) How many sonic cokes do you have to drink to
equal 11 salads?
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Units of MeasurementMeter m
Liter L
Celsius C
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Mass is the amount of matter, weight is a measure of the gravitational pull on matter
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SI UnitsPrefix Symbol Scientific
notationFactor Example
Mega M 1 x 106 1,000,000 megagram (Mg)
Kilo k 1 x 103 1,000 kilometer (km)
Hecto h 1 x 102 100 hectoliter (hL)
Deka da or (D) 1 x 101 10 dekagram (Dg)
BASE UNIT 1 x 100 1 meter
Deci d 1 x 10-1 .1 deciliter (dL)
Centi c 1 x 10-2 .01 centimeter (cm)
Milli m 1 x 10-3 .001 milligram (mg)
Micro u 1 x 10-6 .000001 microgram (ug)
Nano n 1 x 10-9 .000000001 nanometer (nm)
Pico p 1 x 10-12 .000000000001 picogram (pg)
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PracticeIn each pair below, circle the larger
Millimeter Centimeter
picometer Micrometer
kilogram Hectogram
deciliter millileter
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PracticeIn each pair below, circle the larger
Millimeter Centimeter
picometer Micrometer
kilogram Hectogram
deciliter millileter
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PracticeIn each pair below, circle the larger
Millimeter Centimeter
picometer Micrometer
kilogram Hectogram
deciliter millileter
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PracticeIn each pair below, circle the larger
Millimeter Centimeter
picometer Micrometer
kilogram Hectogram
deciliter millileter
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PracticeIn each pair below, circle the larger
Millimeter Centimeter
picometer Micrometer
kilogram Hectogram
deciliter millileter
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Basic SI UnitsQuantity Base unitLength meter (m)Mass gram (g)Time second (s)Volume Liter (L)Temperature Kelvin (K) or Celsius (C)Amount of substance mole (mol)Heat & Energy joule (J)
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Metric Conversions Practice
Ex. 3) 2.435 g __________________cg
Ex. 4) 23.8 mL = ________________kL
Ex. 5) 23.5 cs = ________________ns
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Some Useful Conversions
Length:1 in = 2.54 cm1 mi = 5280 ft
Volume:1 cm3 = 1 mL1 L = 1.06 qt
Weight:1 kg = 2.2 lb16 oz = 1 lb1 ton = 2000 lb
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Temperature
• 20°C = K
Use both the Kelvin and Celsius scale, to convert
Celsius + 273 = Kelvin
Kelvin -273 = Celsius
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Temperature
• 20°C = 293 K
Use both the Kelvin and Celsius scale, to convert
Celsius + 273 = Kelvin
Kelvin -273 = Celsius
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Temperature
• 20°C = 293 K• 373 K = °C
Use both the Kelvin and Celsius scale, to convert
Celsius + 273 = Kelvin
Kelvin -273 = Celsius
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Temperature
• 20°C = 293 K• 373 K = 100 °C
Use both the Kelvin and Celsius scale, to convert
Celsius + 273 = Kelvin
Kelvin -273 = Celsius
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Volume: measured in cubic centimeters (cm3) or liters
• 1 liter (L) = 1 cubic decimeter (dm3) = 1000 millileters (mL)• 1 mL= 1 cm3
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• Volume can be measure by Length x x or the Water Displacement method
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• Volume can be measure by Length x width x or the Water Displacement method
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• Volume can be measure by Length x width x height or the Water Displacement method
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• Volume can be measure by Length x width x height or the Water Displacement method
Know the relationship between the following volume units…
L = mL = cm3 (or cc in medical lingo)
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• Volume can be measure by Length x width x height or the Water Displacement method
Know the relationship between the following volume units…
1 L = mL = cm3 (or cc in medical lingo)
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• Volume can be measure by Length x width x height or the Water Displacement method
Know the relationship between the following volume units…
1 L = 1000 mL = cm3 (or cc in medical lingo)
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• Volume can be measure by Length x width x height or the Water Displacement method
Know the relationship between the following volume units…
1 L = 1000 mL = 1000 cm3 (or cc in medical lingo)
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Density
• Is the ratio of mass per unit of volume. How much matter is packed into a given amount of space
• Density = mass/volume
• D= m/v
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• The Density of a substance stays regardless of the size of the sample. For example: if you cut a block of copper in half, you have decreased both the mass and volume, the ratio of the 2 stays the same. This is called an Intensive Physical Property.
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• The Density of a substance stays constant regardless of the size of the sample. For example: if you cut a block of copper in half, you have decreased both the mass and volume, the ratio of the 2 stays the same. This is called an Intensive Physical Property.
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• The appropriate units of density are:
• for solids• for liquids
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• The appropriate units of density are:
• g/cm3 for solids• for liquids
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• The appropriate units of density are:
• g/cm3 for solids• g/mL for liquids
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Example problems:
• A sample of aluminum metal has a mass of 8.4g. The volume of the sample is 3.1 cm3. Calculate the Density of aluminum.
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Example problems:
• A sample of aluminum metal has a mass of 8.4g. The volume of the sample is 3.1 cm3. Calculate the Density of aluminum.
• 8.4 g/3.1 cm3 =
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Example problems:
• A sample of aluminum metal has a mass of 8.4 g. The volume of the sample is 3.1 cm3. Calculate the Density of aluminum.
• 8.4 g/3.1 cm3 = 2.7 g/cm3
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Example problems:
• Diamond has a density of 3.26 g/cm3. What is the mass of a diamond that has a volume of 0.350 cm3?
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Example problems:
• Diamond has a density of 3.26 g/cm3. What is the mass of a diamond that has a volume of 0.350 cm3?
• 3.26 g/cm3 x 0.350 cm3 =
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Example problems:
• Diamond has a density of 3.26 g/cm3. What is the mass of a diamond that has a volume of 0.350 cm3?
• 3.26 g/cm3 x 0.350 cm3 = 1.14 g
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Example problems:
• What is the volume of a sample of liquid mercury that has a mass of 76.2 g, given that the density of mercury is 13.6 g/mL?
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Example problems:
• What is the volume of a sample of liquid mercury that has a mass of 76.2 g, given that the density of mercury is 13.6 g/mL?
76.2 g = 13.6 g/mL
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Example problems:
• What is the volume of a sample of liquid mercury that has a mass of 76.2 g, given that the density of mercury is 13.6 g/mL?
76.2 g = 5.60 mL13.6 g/mL
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Reliable Measurements
• refers to the closeness of the measure value is to the , or real, value.
• refers to how a series of measurements are to one another.
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Reliable Measurements
• Accuracy refers to the closeness of the measure value is to the , or real, value.
• refers to how a series of measurements are to one another.
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Reliable Measurements
• Accuracy refers to the closeness of the measure value is to the accepted, or real, value.
• refers to how a series of measurements are to one another.
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Reliable Measurements
• Accuracy refers to the closeness of the measure value is to the accepted, or real, value.
• Precision refers to how a series of measurements are to one another.
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Reliable Measurements
• Accuracy refers to the closeness of the measure value is to the accepted, or real, value.
• Precision refers to how close a series of measurements are to one another.
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• is calculated by subtracting the value from the value.
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• Error is calculated by subtracting the experimental value from the accepted value.
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• The is the ratio of an error to an accepted value.
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• The percent error is the ratio of an error to an accepted value.
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% error = error x 100 = accepted value – experimental value x 100 accepted value accepted value
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Example
• An experiment finds the density of lead to be 10.95 g/cm3. The literature value for the density of lead is 13.34 g/cm3.
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The error: accepted value – experimental value=• 13.34 – 10.95 =
An experiment finds the density of lead to be 10.95 g/cm3. The literature value for the density of lead is 13.34 g/cm3.
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The error: accepted value – experimental value=
• 13.34 – 10.95 = 2.39
An experiment finds the density of lead to be 10.95 g/cm3. The literature value for the density of lead is 13.34 g/cm3.
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The error: accepted value – experimental value=• 13.34 – 10.95 = 2.39
The % error: error x 100 = accepted value
2.39 x 100 =13.34
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The error: accepted value – experimental value=• 13.34 – 10.95 = 2.39
The % error: error x 100 = accepted value
2.39 x 100 = 17.9%13.34
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Practice
• Sara’s lab shows the atomic mass of aluminum to be 28.9. What is her percent error if the accepted value is 27.0?
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Practice
• Sara’s lab shows the atomic mass of aluminum to be 28.9. What is her percent error if the accepted value is 27.0?
• 28.9 – 27.0 =
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Practice
• Sara’s lab shows the atomic mass of aluminum to be 28.9. What is her percent error if the accepted value is 27.0?
• 28.9 – 27.0 = 1.90
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Practice
• Sara’s lab shows the atomic mass of aluminum to be 28.9. What is her percent error if the accepted value is 27.0?
• 28.9 – 27.0 = 1.90• 1.90/27.0 x 100% =
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Practice
• Sara’s lab shows the atomic mass of aluminum to be 28.9. What is her percent error if the accepted value is 27.0?
• 28.9 – 27.0 = 1.90• 1.90/27.0 x 100% = 7.04%
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Practice
• What is the percent error in a measurement of the boiling point of bromine if the textbook value is 60.8 °C and the lab value is 40.6 °C?
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Practice
• What is the percent error in a measurement of the boiling point of bromine if the textbook value is 60.8 °C and the lab value is 40.6 °C?
• 60.8 °C – 40.6 °C =
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Practice
• What is the percent error in a measurement of the boiling point of bromine if the textbook value is 60.8 °C and the lab value is 40.6 °C?
• 60.8 °C – 40.6 °C = 20.2 °C
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Practice
• What is the percent error in a measurement of the boiling point of bromine if the textbook value is 60.8 °C and the lab value is 40.6 °C?
• 60.8 °C – 40.6 °C = 20.2 °C• 20.2 °C / 60.8 °C x 100% =
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Practice
• What is the percent error in a measurement of the boiling point of bromine if the textbook value is 60.8 °C and the lab value is 40.6 °C?
• 60.8 °C – 40.6 °C = 20.2 °C• 20.2 °C / 60.8 °C x 100% = 33.2%