Lecture 2 Fall Units of measurement. Sections 1.4 through Units of Measurement. Must have units – SI units are the Systeme International. This has 7 base units from which all other units are derived:

The 7 base units from which all other units are derived: Physical Unit abbreviation Quantity_______________________ Masskilogramkg LengthMeterm Timesecond s or sec TemperatureKelvinK Amount of SubstanceMolemol

Prefixes are used to indicate decimal fractions or multiples of the above units: PrefixAbbr.meaningexample GigaG10 9 gigameter MegaM10 6 megameter Kilok kilometer Decid deciliter Centic centiliter Millim milligram Microμ microgram Nanon nanometer Picop picogram Femtof femtosecond

Derived SI units: Volume: The volume of a cube is given by the lengths of its sides multiplied together. Thus, the volume of anything has the units m 3, or cm 3. The most commonly used unit of volume in chemistry is the liter, which is a dm 3. 1 mL = 1 cm 3 is interchangeable. a b c Volume = a x b x c Units = meters x meters x meters = m 3 or = cm x cm x cm = cm 3 or ml or cc

Density: Density is mass/volume. Commonly expressed as gm/ml or gm/cc. Densities of some common substances: __________________________________ Air g/ccEthanol: 0.79 Water:1.00Table salt: 2.16 Iron:7.9Gold: 19.32

1.5. Uncertainty in Measurement: Exact numbers: e.g. number of inches in a foot, number of people in the lecture theater. Are usually defined numbers. Inexact Numbers: These are measured numbers, which always have a degree of uncertainty. Suppose ten students measure the mass of the same dime on ten different balances. They will all get slightly different values. (= g. a quarter weighs 5.57 g))

Precision and accuracy: Precision is how closely a set of measurements agree with each other. Accuracy is how closely the set of measurements agree with the correct or true value. good accuracy good precision

Significant Figures: Suppose you measure the weight of a dime on a balance stated to be accurate to g. You could report the weight as ± g. Measured quantities are reported in such a way that only the last digit is uncertain. All digits of a measured quantity are called significant figures.

To determine the number of significant figures in a number start counting digits from the left to the right. Note: Zeroes at the end or in the middle of a number are significant, those at the beginning are not three significant figures 1.030four““ x 10 5 five ““

Significant Figures in Calculations: For multiplication and division: The result contains the same number of significant figures as the measurement with the fewest significant figures: e.g. area = 6.221cm x 5.2 cm = = 32 cm 2. Only two significant figures

Addition and Subtraction. For addition and subtraction: The result contains the same number of decimal places as the result with the fewest decimal places. e.g = = 104.8

Dimensional Analysis Converting inches into cm: Conversion factor: same quantity but in different units the units to be eliminated go on opposite sides of the fraction

Dimensional Analysis Converting m/min into m/s: Conversion factor the units to be eliminated go on opposite sides of the fraction

Dimensional Analysis More than one conversion: A car travels 12 km per liter of gasoline. How many many miles per gallon will it go? =>Convert 12 km/L into mi/gallon =>first, convert length units: km into mi, second, convert volume units: L into gallons

Dimensional Analysis ? ? or

Dimensional Analysis Place conversion factor so units to be removed will cancel

Dimensional Analysis Note: 12 kilometers has only two significant figures, so answer must have only two significant figures

Conversions involving squared and cubic units: The volume of a container is 5.3 m 3. What is the volume in cm 3 ?  Convert m 3 into cm 3  Conversion factor = 100 cm or 100 cm 1 meter 1 m Vol in cm 3 = 5.7 meter 3 x 100 cm x 100 cm x 100 cm 1 meter 1 meter 1 meter = 5,700,000 cm 3 (note: 1 m 3 = 1 m x 1 m x 1 m)