1. Updated Aug 2006Created by C. Ippolito August 2006 Measurement Objectives: list three requirements for making a measurement express measurements in the International System of Units (SI) list the seven basic SI units be able to combine SI units to form SI derived units determine the amount of uncertainty in a measured quantity correctly apply the terms accuracy and precision determine the number of significant digits for a given calculation or measurement calculate the percent error of an experimental result

2. Updated Aug 2006Created by C. Ippolito August 2006 Chemical Quantities Chemistry –science that studies the structure and nature of matter –describes characteristics or properties of matter –Qualitative characteristics that can be described using words –Quantitative characteristics that can be measured and described using a standard numerical unit

3. Updated Aug 2006Created by C. Ippolito August 2006 Measurements Requirements for Measuring 1.know what is being measured 2.have a standard to compare measurement to 3.have a method of making comparison Measurements –comparison between quantity measured and a standard unit

4. Updated Aug 2006Created by C. Ippolito August 2006 International System of Units International agreement –determined a set of standard units to be used in scientific measurements –based on older French system used in Europe –a.k.a. metric system advantages –calculations easier with use of decimals –units change from larger to smaller and from smaller to larger in multiples of ten

5. Updated Aug 2006Created by C. Ippolito August 2006 SI Base Units QuantityUnitSymbol lengthmeterm masskilogramkg timeseconds amount of substancemolemol temperaturekelvinK electric currentampereA luminous intensitycandelacd

6. Updated Aug 2006Created by C. Ippolito August 2006 SI Prefixes used with base units to form new units that are greater than or less than the base unit units increase or decrease by some multiple of 10

7. Updated Aug 2006Created by C. Ippolito August 2006 Prefixes for Greater Units PrefixSymbol Multiply by exa-E1 000 000 000 000 000 000 peta-P1 000 000 000 000 000 tera-T1 000 000 000 000 giga-G1 000 000 000 mega-M1 000 000 kilo-k1 000 hecto-h100 deca-da10

8. Updated Aug 2006Created by C. Ippolito August 2006 Prefixes for Lesser Units PrefixSymbol Multiply by deci-d0.1 centi-c0.01 milli-m0.001 micro-μ0.000 001 nano-n0.000 000 001 pico-p0.000 000 000 001 femto-f0.000 000 000 000 001 atto-a0.000 000 000 000 000 001

9. Updated Aug 2006Created by C. Ippolito August 2006 Simple Conversion conversion from one unit to another is as simple as moving the decimal point left –move decimal point to left to convert to larger units right –move decimal point to right to convert to smaller units 10 18 10 15 10 12 10 9 10 6 10 3 10 2 10 1 10 -1 10 -2 10 -3 10 -6 10 -9 10 -12 10 -15 10 -18 EPTGMkhda1dcmμnpfa

10. Updated Aug 2006Created by C. Ippolito August 2006 Derived vs Fundamental Units Fundamental UnitsFundamental Units –measure or describe basic qualities of any physical object or phenomena mass length time Derived Units –ones formed from new mathematical expressions needed to quantify qualities of a physical object area density volume speed concentration

11. Updated Aug 2006Created by C. Ippolito August 2006 SI Derived Unit Quantities QuantityNameSymbolBase Unit area square meter m2m2 m2m2 volume cubic meter m3m3 m3m3 speed meter per second m/s density kilogram per cubic meter kg/m 3 concentration mole per cubic meter mol/m 3 force newton Nm●kg/s 2 pressure pascal Pakg/m●s 2 energy joule Jm 2 ●kg/s 2

12. Updated Aug 2006Created by C. Ippolito August 2006 Common Non SI units QuantityNameSymbol time minute hour day min h d volume liter milliliter L mL density gram per milliliterg/mL temperature degree Celsius oCoC distance angstrom  pressure millimeter of mercury atmosphere mm Hg atm energy caloriecal

13. Updated Aug 2006Created by C. Ippolito August 2006 Uncertainty in Measurement limited by the accuracy of the tools being used to make them some digits are certain and the final digit is an estimate –6.25 --- 6.2 is certain the.05 is estimate

14. Updated Aug 2006Created by C. Ippolito August 2006 Accuracy Versus Precision AccuracyAccuracy –quality of the measuring instrument as compared with the standard for that measurement –how close is the measurement to the actual standard PrecisionPrecision –the degree of exactness with which a measurement is taken –reproducibility of measurements –uncertainty of measurement

15. Updated Aug 2006Created by C. Ippolito August 2006 Significant Figures all the digits that are well known plus one estimated figure represent the significant figures in a measurement using a millimeter ruler (6.25) gives more significant digits (3) and greater precision that a centimeter (6.1) ruler with less significant digits (2)

16. Updated Aug 2006Created by C. Ippolito August 2006 Use of Plus or Minus Notation Scientist’s use a ± notation to describe the degree of uncertainty –cm ruler 6.1 cm ±.5 cm or 61 mm ±.5 mm –mm ruler 6.25 cm ±.05 cm or 62.5 mm ±.05 mm

17. Updated Aug 2006Created by C. Ippolito August 2006 Calculating and Significant Figures Multiplication/ Division RuleMultiplication/ Division Rule –express product or quotient to same number of significant figures as the measurement with the fewest significant figures i.e.

18. Updated Aug 2006Created by C. Ippolito August 2006 Calculating and Significant Figures Addition/ Subtraction RuleAddition/ Subtraction Rule –round the sum or difference so that it has same number of significant figures as the measurement with the fewest significant figures i.e.

19. Updated Aug 2006Created by C. Ippolito August 2006 Percent Error Observed ValueObserved Value –value based on laboratory measurement True ValueTrue Value –most probable value based on generally accepted references Absolute ErrorAbsolute Error –difference between observed and true value Percent ErrorPercent Error –(absolute error/true value) x 100

20. Updated Aug 2006Created by C. Ippolito August 2006 Calculating Percent Error Boiling point of water –observed value 105.25 o C –true value 100.0 o C

21. Updated Aug 2006Created by C. Ippolito August 2006 Scientific Notation makes working with large or small numbers is easier –all numbers expressed as the product of a number between 1 and 10 and a whole number power of 10 (M x 10 n ) –i.e. 2000 cm becomes 2 x 10 3 cm

22. Updated Aug 2006Created by C. Ippolito August 2006 Calculations in Scientific Notation Multiplication –(1 x 10 -2 ) (3 x 10 5 ) (2 x 10 12 ) = ? multiply M values –(1 x 3 x 2 = 6) add exponents –(-2+5+12 = 15) (1 x 10 -2 ) (3 x 10 5 ) (2 x 10 12 ) = 6 x 10 15 Division –(6 x 10 5 )  (2 x 10 12 ) = ? divide M values –(6  2 = 3) subtract denominator exponent from numerator exponents –(5-12 = -7) (6 x 10 5 )  (2 x 10 12 ) = 3 x 10 -7