Units of Measurement

OBJECTIVES Distinguish between a quantity, a unit, and a measurement standard. Name and use SI units for length, mass, time, volume, and density. Distinguish between mass and weight. Perform density calculations. Transform a statement of equality into a conversion factor.

KEY TERMS Quantity SI Weight Derived unti Volume Density Conversion factor Dimensional analysis

UNITS OF MEASUREMENT Chef recipe Measurements represent quantity QUANTITY: is something has magnitude, size or amount. Not the same as a measurement EX: A quantity represented by a teaspoon is volume teaspoon  measurement Volume quantity

Scientists worldwide use SI measurements Scientists all over the world have agreed on a single measurement system called Le Systéme International d’Unités, abbreviated SI. Adopted in 1960 by General Conference on Weights and Measures 7 base units Most other units are derived Non-SI units still commonly used

Scientists worldwide use SI measurements SI units are defined in terms of standards of measurements. Standards are objects or natural phenomena that are of a constant value, easy to preserve and reproduce, and particular in size. International organizations monitor the defining process US: National Institute of Standards and Technology (NIST) 75 000 NOT 75,000 Becuase coma in other countries is used to represent the decimal point.

Prefixes added to SI base units indicate larger or smaller quantities Seven SI base units are listed in the table below. Quantity Quantity Symbol Unit Name Unit Abbreviation Length L Meter m Mass M Kilogram kg Time t Second s Temperature T Kelvin K Amount of substance N Mole mol Electric Current I Ampere A Luminous Intensity Iv candela cd

Prefixes added to SI base units indicate larger or smaller quantities All other SI units can be derived from these 7 fundamental units Prefices added to the names of SI base unkits are used to represent quantities that are larger or smaller than the base units. EX: Prefix centi-, abreviated c, represents exponential factor 10-2, which equals 1/100 1 centimeter  1 cm = 0.01 m

Prefix Unit abbreviation Exponential factor Meaning Example Tera T 1012 1 000 000 000 000 1 Tm = 1 x 1012 m Giga F 109 1 000 000 000 1 Gm = 1 x 109m Mega M 106 1 000 000 1 Mm = 1 x 106 m Kilo k 103 1000 1 km = 1000 m Hecto h 102 100 1 hm = 100 m Deka da 101 10 1 dam = 10 m 1 1 m Deci d 10-1 1/10 1 dm = 0.1 m Centi c 10-2 1/100 1 cm = 0.01 m Milli m 10-3 1/1000 1 mm = 0.001 Micro µ 10-6 1/1 000 000 1 µm = 1 x 10-6 m Nano n 10-9 1/1 000 000 000 1 nm = 1 x 10-9 m Pico p 19-12 1/1 000 000 000 000 1 Pm = 1 x 10-12 m Femto f 10-15 1/1 000 000 000 000 000 1 fm = 1 x 10-15 m atto a 10-18 1/1 000 000 000 000 000 000 1am = 1 x 10-18 m

Mass MASS: a measure of the quantity of matter SI standard base unit for mass is kilogram Standard of mass are used to calibrate balances all over the world The unit of mass equal to the mass of the international prototype of the kilogram A kilogram is 2.2 pounds The gram, g, is 1/1000 of a kilogram More useful for measurement of small objects About the mass of a paper clip Milligram, mg, used for tiny quantities 1/1000 of a gram

Mass vs. Weight Mass often confused with weight Mass measure of the amount of matter WEIGHT: a measure of the gravitational pull of matter. Mass determined by comparing the mass of an object with a set of standard masses on two sides of the balance. When mass on each are the same, the sides balance. Mass does not depend on the gravity Weight changes as gravitational forces change Mass does not change

Mass vs. Weight Mass measured on instrument called a balance Weight typically measured on a spring scale Involves reading the amount that an object pulls down on a spring As force of gravity increases on an object , the object´s weight increases. Weight of an object on the Moon is about 1/6 of weight on Earth.

Length SI standard unit for length is the meter 1 m is about the width of an average doorway For longer distances, a kilometer is used 1 km = 1000 m For shorter distances, a centimeter is used About the size of a paper clip 1 cm = 1/100 m

SI base units combine to form derived units Combinations of SI base units form DERIVED UNITS. Produced by multipying or dividing standard units EX: Area  length times width  m x m = m2

Derived SI Units Quanity Quanity Symbol Unit Unit Abbreviation Derivation Area A Square meter m2 Length x width Volume V Cubic meter m3 length x width x height Density D Kilograms per cubic meter kg/m3 Mass volume Molar Mass M Kilograms per mole kg/mol amount of substance Molar Volume Vm Cubic meters per mole m3/mol Amount of a substance Energy E joule J Force x length

SI base units combine to form derived units Some combinations of units are given their own names Pressure kg/m·s2 Pascal, Pa Prefixes also added to derived units Area cm2 or mm2

Volume VOLUME is the amount of space occupied by an object. Derived SI unit of volume is cubic meters, m3. Large unit inconvenient in chemistry lab Cubic centimeter, cm3 1 m3 = 1 000 000 cm3 Chemists use non-SI units for liquids and gases Liter, L 1 L = 1000 cm3 Milliliter, mL For smaller volume 1000 mL = 1 L Cubic centimeter and milliliter are interchangeable

Density Cork lighter than lead even though same size Liquid mercury heavier than water Different substances contain different masses per volume DENSITY is the ratio mass to volume, or mass divided by volume DENSITY density = mass volume

DENSITY

Density SI unit for density is devied from the base units for mass and volume kg/m3 Units are large for laboratory use g/cm3 or g/mL Physical property of a substance Doesn´t depend on amount of sample As mass increases, volume increases (proportional) Ratio of mass to volume is constant Helps to identify a substance

DENSITIES OF SOME MATERIALS Solids Density at 20°C (g/ml) Liquids Density a 20°C (g/ml) Cork 0.24 Gasoline 0.67 Butter 0.86 Ethyl alchohol 0.791 Ice 0.92* Kerosene 0.82 Sucrose 1.59 Turpentine 0.87 Bone 1.85 Water 0.998 Diamond 3.26 Sea water 1.025** Copper 8.92 Milk 0.0131** Lead 11.35 Mercury 13.6 * Measured at 0°C ** measured at 15°C

Sample Problem: Density A sample of alumininum metal has a mass of 8.4 g. The volume of the sample is 3.1 cm3. Calculate the density of aluminum ANALYZE m = 3.4 g, v = 3.1 cm3, d =? PLAN Density = mass/volume SOLVE Density = 8.4 g/ 3.1 cm3 = 2.7 g/cm3 CHECK YOUR WORK

Practice Problems: Density What is the density of a block of marble that occupies 310. cm3 and has a mass of 853 g? Diamond has a density of 3.26 g/cm3. What is the mass of a diamond that has a volume of 0.351 cm3. 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?

Conversion Factors change one unit to another A CONVERSION FACTOR is a ratio derived from the equality between two different units that can be used to convert from one unit to the other. ALWAYS equals 1 Have to equivalent to each other EX: How many quarter are there in a dollar?

Conversion Factors change one unit to another Use conversion factors to solve problems through dimensional analysis DIMENSIONAL ANALYSIS is a mathematical technique that allows you to use units to solve problems involving measurements. Quantity sought = quantity given x conversion factor

Deriving Conversion Factors You can derive conversion factors if you know the relationship between the unit you have and the unit you want. Deci- means “1/10”, its 1/10 of a meter 1 m = 10 dm

Sample Problem: Conversion Factors Express a mass of 5.712 g in mg and kg. ANALYZE 1 g = 1000 mg, 1 kg = 1000 g 5.712 g PLAN SOLVE 5.712 g x (1000 mg/1 g) = 5712 mg 5.712 g x (1 kg/1000 mg) = 0.005712 kg CHECK YOUR WORK

Practice: Conversion Factors Express a length of 16.45 m in centimeters and in kilometers. Express a mass of 0.014 mg in grams.