Units of Measurement Chapter 2 Section 2 Objectives: Distinguish between a quantity, a unit, and a measurement standard. Distinguish between a quantity, a unit, and a measurement standard. Name and use SI units for length, mass, time, volume, and density. Name and use SI units for length, mass, time, volume, and density. Distinguish between mass and weight. Distinguish between mass and weight. Perform density calculations. Perform density calculations. Transform a statement of equality into a conversion factor. Transform a statement of equality into a conversion factor.

Would you be breaking the speed limit in a 40 mi/h zone if you were traveling 60 km/h?

Measurements are quantitative information. Measurements are quantitative information. Measurements are more than just numbers. Measurements are more than just numbers. Example: Example: 1 salt 2 sugar 2 flour 4 butter Measurements represent quantities. Measurements represent quantities. A quantity is something that has magnitude, size, or amount. A quantity is something that has magnitude, size, or amount. A quantity is not the same thing as measurement. A quantity is not the same thing as measurement. The quantity represented by a teaspoon is volume. The quantity represented by a teaspoon is volume. The teaspoon is a unit of measurement, while volume is a quantity. The teaspoon is a unit of measurement, while volume is a quantity.

SI Units Scientists use a single measurement system called Le Systèm International d’Unitès, abbreviated SI. Scientists use a single measurement system called Le Systèm International d’Unitès, abbreviated SI. SI Units are defined in terms of standards of measurement. SI Units are defined in terms of standards of measurement. There are seven base units, and most other units are derived from these seven. There are seven base units, and most other units are derived from these seven.

Quantity Quantity Symbol Unit Name UnitAbbrev. Defined standard LengthlMeterm The length of the path traveled by light in a vacuum during a time interval of 1/ of a second. MassmKilogramkg Unit of mass equal to the mass of the international prototype. TimetSeconds Duration of periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.

Quantity Quantity Name Unit Name Unit Abbrev. Defined Standard TemperatureTkelvinK The fraction 1/ of the thermodynamic temperature of the triple point of water. Amount of Substance nmolemol The amount of substance of a system which contains as many elementary entities as there are atoms in kilogram of carbon-12.

Quantit y Quantity Symbol Unit Name Unit Abbrev. Defined Statement Electric Current I ampere A The constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2x10 -7 newton per meter of length. Luminous Intensity IvIv Candela Cd The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540x10 12 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

SI Base Units (LENGTH) The SI unit for length is the meter (m). The SI unit for length is the meter (m). A distance of 1 m is about the width of an average doorway. A distance of 1 m is about the width of an average doorway. Longer distances can be expressed using the kilometer, km. One km equals 1000m. Longer distances can be expressed using the kilometer, km. One km equals 1000m. For shorter distances, the centimeter is often used. For shorter distances, the centimeter is often used.

SI Base Units (MASS) Mass is a measure of the quantity of matter. Mass is a measure of the quantity of matter. The SI standard unit is the kilogram (kg). The SI standard unit is the kilogram (kg). The mass of typical textbook is 1 kg. The gram (g), which is 1/1000 of a kilogram, is more useful for measuring masses of small objects, such as flasks and beakers. The mass of typical textbook is 1 kg. The gram (g), which is 1/1000 of a kilogram, is more useful for measuring masses of small objects, such as flasks and beakers. Mass is often confused with weight. Mass is often confused with weight. Weight is a measure of the gravitational pull on matter. Weight is a measure of the gravitational pull on matter. Mass does not depend on gravity. Mass does not depend on gravity.

Using the SI Prefix Chart Using the SI Prefix Chart SI prefixes are based on powers of 10. SI prefixes are based on powers of 10. To change between one prefix to another requires the decimal point to be moved in either direction. To change between one prefix to another requires the decimal point to be moved in either direction. For example: Convert 4.0 km into cm. For example: Convert 4.0 km into cm. 1 st put your finger on the km space. Count how many spaces it takes to get to centimeters. 1 st put your finger on the km space. Count how many spaces it takes to get to centimeters. Move your decimal point this many spaces. Move your decimal point this many spaces. If you are counting spaces from left to right, the decimal point is moved to from left to right. (The number should get bigger.) If you are counting spaces from left to right, the decimal point is moved to from left to right. (The number should get bigger.) If you are counting spaces from right to left, the decimal point is moved from right to left. (The number should get smaller.) If you are counting spaces from right to left, the decimal point is moved from right to left. (The number should get smaller.) 4.0 km = cm SI Prefixes

Complete the following conversions. Complete the following conversions g = _______ kg 17.5 g = _______ kg 2.34 km = _______ m 2.34 km = _______ m 3.21 μg = __________ g 3.21 μg = __________ g 6.23 mol = ______________ pmol 6.23 mol = ______________ pmol 2.3 L = _________ mL 2.3 L = _________ mL

Derived SI Units Many SI units are combinations of the quantities shown in the first table. Many SI units are combinations of the quantities shown in the first table. Combinations of SI base units form derived units. Combinations of SI base units form derived units. Derived units are produced by multiplying or dividing standard units. For example, area, a derived unit, is length times width. Derived units are produced by multiplying or dividing standard units. For example, area, a derived unit, is length times width. If both length and width are expressed in meters, the area unit equals meters times meters, which is square meters, abbreviated m 2. If both length and width are expressed in meters, the area unit equals meters times meters, which is square meters, abbreviated m 2.

Derived SI Units QuantityQuantity Symbol UnitUnit Abbr. Derivation AreaAsquare meterm2m2 length x width VolumeVcubic meterm3m3 length x width x height DensityDkilograms per cubic meter kg m 3 mass/volume Molar massMkilograms per mol kg mol mass/amount of substance Molar volume VmVm cubic meters per mol m 3 mol volume/amount of substance EnergyEJouleJforce x length

Derived Units (VOLUME) Volume is the amount of space occupied by an object. Volume is the amount of space occupied by an object. The derived SI unit is cubic meters, m 3. The derived SI unit is cubic meters, m 3. One cubic meter is equal to the volume of a cube who edges are 1 m long. One cubic meter is equal to the volume of a cube who edges are 1 m long. Chemists measure the volumes of liquids and gases using the non-SI unit liter (L). Chemists measure the volumes of liquids and gases using the non-SI unit liter (L). 1 L = 1000 cm 3 Another non-SI unit is the milliliter, mL and it is used for smaller volumes. Another non-SI unit is the milliliter, mL and it is used for smaller volumes mL = 1L = 1000 cm 3

Derived Units (DENSITY) Density is the ratio of mass to volume, or mass divided by volume Mathematically it is written as: density = mass or D = m volume V The SI unit for Density is kg/m 3 or g/cm 3 for small density measurements. m D V

Density Density is a characteristic physical property of a substance. It does not depend on the sample size because as the sample’s mass increases its volume increases proportionately, and the ratio is constant. Density can be used to identify a substance.

Density Problems A sample of aluminum metal has a mass of 8.4 g. The volume of the sample is 3.1 cm 3. Calculate the density of aluminum. Solution: Given: mass (m) = 8.4g volume (V ) = 3.1 cm 3 volume (V ) = 3.1 cm 3 Unknown: density (D ) Unknown: density (D ) density = mass = 8.4g = 2.7 g/cm 3 volume 3.1cm 3 volume 3.1cm 3

Density Problems What is the density of a block of marble that occupies 310. cm 3 and has a mass of 853 g? Solution: Given: volume (V) = 310. cm 3 mass (m) = 853 g mass (m) = 853 g D = m = 853 g _ = V 310. cm 3 V 310. cm 3

Density Problems Diamond has a density of 3.26 g/cm 3. What is the mass of a diamond that has a volume of cm 3 ? Solution: Given: density (D) = 3.26 g/cm 3 volume (V) = cm 3 volume (V) = cm 3 D = m V m = (D)(V) = (3.26 g/cm 3 )(0.351 cm 3 ) = (3.26 g/cm 3 )(0.351 cm 3 ) = m DV

Conversion Factors