Chapter 2 – Section 2 Suggested Reading Pages 33-42 Units of Measurement Chapter 2 – Section 2 Suggested Reading Pages 33-42

Making Measurements Measurements must have a number and a unit. The unit depends on the quantity being measured.

SI Measurement Le Systeme International d’Unites See Table of SI Base units – Page 34 See Table of SI Prefixes – Page 35

Standard SI Units Length = meter (m) Mass = kilogram (kg) Time = second (s) Temperature = Kelvin (K) Amount of substance = mole (mol)

Derived SI Units Produced by multiplying or dividing standard units. Area = square meter (m2) Volume = cubic meter (m3) Density = kilograms per cubic meter (kg/m3)

Definitions Mass – a measure of the quantity of matter in an object. Weight – a measure of the gravitational pull on matter. Volume – the amount of space occupied by an object. Density – the ratio of mass to volume

The object with the lowest density will float. The density of an object is calculated by dividing the mass of the object by its volume. The object with the lowest density will float.

Density is a Derived Unit Combination of base units Mass (g or kg) Volume (m3 or cm3) length  length  length 1 cm3 = 1 mL 1 dm3 = 1 L Density (kg/m3 or g/cm3 or g/mL) mass per volume D = M V

Density Mass (g) Volume (cm3)

Density V = 825 cm3 M = DV D = 13.6 g/cm3 M = (13.6 g/cm3)(825cm3) An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass. GIVEN: V = 825 cm3 D = 13.6 g/cm3 M = ? WORK: M = DV M = (13.6 g/cm3)(825cm3) M = 11,200 g We will talk about how to round correctly soon!

Density D = 0.87 g/mL V = M V = ? M = 25 g V = 25 g 0.87 g/mL A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? M = 25 g WORK: V = M D V = 25 g 0.87 g/mL V = 29 mL

Dimensional Analysis – The technique of converting between units.

Six Steps that May Help You: Write down the starting number with unit, draw a horizontal line under it, and a vertical line next to it.

Look at the unit and write down conversion factors that might work Look at the unit and write down conversion factors that might work. (You have to THINK of these.) 3. Write down UNITS for conversion factors ABOVE & BELOW the line so the unit you started with will CANCEL OUT.

4. Fill in the numbers that go with the conversion factors. 5. Cancel out units as required. 6. Do the math & don’t forget to round correctly at the end & put the correct unit on your final answer.

Example: Convert 14 cm to meters 14 cm 1. Write it down, draw the lines.

Example: Convert 14 cm to meters 14 cm Our factor that we think will work is 100 cm = 1 meter Write down the factor.

Example: Convert 14 cm to meters m 14 cm cm Conversion Factor: 100 cm = 1 meter 3. Fill in the units from the factor so that the starting unit will cancel out.

4. Fill in the numbers from the conversion factor. Example: Convert 14 cm to meters 14 cm 1 m 100 cm Conversion Factor: 100 cm = 1 meter 4. Fill in the numbers from the conversion factor.

Example: Convert 14 cm to meters 14 cm 1 m 100 cm 5. Cancel out units. Conversion Factor: 100 cm = 1 meter 5. Cancel out units.

 Example: Convert 14 cm to meters 14 cm 1 m = 14 x 1 100 100 cm m = Don’t forget units! m = 0.14 6. Do the math. Multiply all numbers across the top, divide by each number across the bottom.

Some Problems Require Many Steps … Just draw a longer line! Example: Convert 4.7 kg to pounds

Example: Convert 4.7 kg to pounds 4.7 kg 1. Write it down, draw the lines.

Example: Convert 4.7 kg to pounds 4.7 kg Our factors that we think will work are 454 g = 1 lb 1000g = 1 kg Write down the factors.

Example: Convert 4.7 kg to pounds g lb 4.7 kg kg g Conversion Factors: 454 g = 1 lb and 1000g = 1 kg 3. Fill in the units from the factors so that the starting unit will cancel out.

4. Fill in the numbers from the conversion factors. Example: Convert 4.7 kg to pounds g 1000 1 lb 4.7 kg 1 kg 454 g Conversion Factors: 454 g = 1 lb and 1000g = 1 kg 4. Fill in the numbers from the conversion factors.

Example: Convert 4.7 kg to pounds g 1000 1 lb 4.7 kg 1 kg 454 g Conversion Factors: 454 g = 1 lb and 1000g = 1 kg 5. Cancel out units.

  454 *Example: Convert 4.7 kg to pounds 4.7 kg 1000 g 1 lb = 1 454 10. lb Don’t forget units! 6. Do the math. Multiply all numbers across the top, divide by each number across the bottom.

How to measure Mass – balance Weight – a spring scale Volume – volumetric flask