Scientific Measurement

Importance of Measurement Qualitative & Quantitative Measurements Qualitative: SubjectiveSubjective ObservationalObservational DescriptiveDescriptive Non-numericalNon-numerical Quantitative: ObjectiveObjective Expressible as a quantityExpressible as a quantity NumericalNumerical Has specific unitsHas specific units

Scientific Notation Number written as product of 2 numbers A coefficientA coefficient 10 raised to a power10 raised to a power 36,000 written as 3.6 X 10 4     coefficient 10 to power of 4 coefficient 10 to power of 4 Coefficient is always between 1-10

Scientific Notation Make very large /small numbers user- friendly Avagadro’s Number (number of molecules /mole) 602,000,000,000,000,000,000, ,000,000,000,000,000,000, X X 10 23

Scientific Notation Coefficient is always between 1-10 If number is >10 Exponent is positiveExponent is positive # places decimal moved to left# places decimal moved to left 4,870,000 = 4.87 X 10 6 If number is < 1 exponent is negativeexponent is negative # placed decimal moved to right# placed decimal moved to right = 4.87 X 10 -6

Scientific Notation To multiply in Scientific Notation Multiply the coefficientsMultiply the coefficients Add the exponentsAdd the exponents (3.5 X 10 4 ) X (2.0 X 10 3 ) = 7.0 X 10 7 (3.5 X 10 4 ) X (2.0 X ) = 7.0 X (3.5 X ) X (2.0 X ) = 7.0 X

Scientific Notation To divide in Scientific Notation Divide the coefficientsDivide the coefficients Subtract the exponent of denominator from exponent of numeratorSubtract the exponent of denominator from exponent of numerator (7.0 X 10 8 )  (2.0 X 10 3 ) = 3.5 X 10 5 (7.0 X 10 4 )  (2.0 X ) = 3.5 X (7.0 X )  (2.0 X 10 8 ) = 3.5 X (7.0 X )  (2.0 X ) = 3.5 X 10 4

Scientific Notation Addition & Subtraction Make the exponents the sameMake the exponents the same Add or subtract coefficientsAdd or subtract coefficients Exponent remains unchangedExponent remains unchanged (5.40 X 10 3 ) + (6.0 X 10 2 ) = (5.40 X 10 3 ) + (0.60 X 10 3 ) = 6.00 X 10 3

Accuracy& Precision Accuracy Closeness to true valueCloseness to true valuePrecision Ability to repeat a measurementAbility to repeat a measurement closeness of series of measurements to each othercloseness of series of measurements to each other

ErrorError Indicator of accuracy &/or precision of a measurementIndicator of accuracy &/or precision of a measurement Error = experimental value - accepted value accepted value = assumed or known correct value experimental value = measured value

Percent Error Percent error: a measure of relative error Error = experimental value - accepted value % error = (  error  /accepted value) x 100 Why would you want to know the error associated with an instrument or a procedure? Allows assessment of accuracyAllows assessment of accuracy

Percent Error ex. thermometer measures BP of H 2 O at sea level as 99.2 O C error = 100 O C O C = 0.8 O C % error = (0.8 O C /100 O C) X 100 % = 0.8 % If same thermometer gave BP of unknown liquid as 85 O C,If same thermometer gave BP of unknown liquid as 85 O C, True BP is 85 O C % or O C = 85.7 O CTrue BP is 85 O C % or O C = 85.7 O C

Significant Figures A calculated answer cannot be more accurate than the measurements used to make the calculation.

Significant Figures ex. density = mass/volume Given: mass = 10.0 g & volume = 53.0 cm 3 By calculator: density = g/cm 3 Implies we know the density accurately to the nearest 1 millionth of a g/cm 3 Instrument accuracy: 0.1g and 0.1 cm 3

Example 5.45 cm 9.85 cm Use calculator to determine area Implies can measure to nearest.0001 cm 9.85 cm x 5.45 cm = cm 2 Can only estimate to.01 cm Round cm 2 to 53.7 cm 2

Known digits + 1 estimated digit cm scale mm indicated between cm On cm scale Know: 9 cm Est: 9.8 cm 2 sig. figures With mm scale Know: 8 mm Est: 8.5 mm 3 sig. figures Final measure: 9.85 cm

Significant Figures 1. Every nonzero digit is significant 2. 0s between nonzero digits are significant (ex 30.45, ) 3. Leftmost 0s in front of nonzero digits are not significant (ex 0.45, ) 4. 0s at the end of a number after a decimal point are significant (ex 24.00, 3.200)

Significant Figures 5. Rightmost 0s at end of number (left of understood decimal point) are not significant (ex 300) 6. Unlimited significant figures a) counting (ex 15 rats) b) defined quantities (ex 1 hr = 60 min)

Significant Figures meters meters 40,506 meters X 10 4 meters

Significant Figures 3 Unlimited meters 22 meter sticks meters 98,000 meters

Significant Figures in Calculations 1. Determine the number of significant figures in the answer 2.Round the answer to that number of significant figures

Count that number of figures from left a) if next digit is  5,  the last significant digit by 1 b) if next digit is < 5, last significant digit stays the same To round to a given number of significant figures

Practice Rounding Round the following to 4 sig figures: <   ,382,900 9  5 2,383, <

Determining Number of Significant Figures Addition & Subtraction Round to number of decimal places as measurement with least number of sig figures after decimalRound to number of decimal places as measurement with least number of sig figures after decimal

Ex: Addition Need 2 digits after decimal point Need 2 digits after decimal point st digit after 2 is a 7, 7>5 1 st digit after 2 is a 7, 7>5 Final answer is Final answer is  2 significant figures after decimal point

Determining Number of Significant Figures Multiplication & Division Round to same number of sig figures as measurement with least number of significant figuresRound to same number of sig figures as measurement with least number of significant figures

Ex: multiplication x5.21 x5.21 Can have 3 sig figures  3 sig figures  6 sig figures st digit after 0 is a 2, 2<5 Final answer is 120 No, must rewrite as 1.20 x 10 2 ?

International System of Units (SI) Based on metric system. Know: length = mlength = m volume = m 3volume = m 3 mass = kgmass = kg density = g/cm 3 = g/mLdensity = g/cm 3 = g/mL temperature = Ktemperature = K Common prefixes & metric relationships Tables pp 64-67

The Seven SI Base Units Physical QuantityName of UnitSymbol MassKilogram kg LengthMeter m TimeSecond s Electric currentAmpere A TemperatureKelvin K Luminous intensity Candela cd Quantity of substance Mole mol Required for Chem A & B

SI Prefixes Factor Prefix Symbol exa E petaP teraT 10 9 gigaG 10 6 mega M 10 3 kilo k 10 2 hecto h 10 1 deka da MUST KNOW

SI Prefixes Factor Prefix Symbol deci d centi c milli m micro  nano n pico p femto f atto a MUST KNOW

Density Density = mass/ volume Physical characteristic Can be used for identification Commonly given as g/cm 3 at 20 O C solids and liquidsg/cm 3 at 20 O C solids and liquids g/L at 20 O C gasesg/L at 20 O C gases Why specify temperature? As temp , volume ,  density 

Determining Density mass = gmass = g volume = 53.0 cm 3volume = 53.0 cm 3 density = m/vdensity = m/v = g/cm = 3 significant figures53.0 = 3 significant figures Round to 3 significant figuresRound to 3 significant figures density = 1.89 g/cm 3density = 1.89 g/cm 3

Specific Gravity Specific gravity = density of substance  density of H 2 O Density of H 2 O is  g/ml at 3.98 O C (0.997 g/ml at 25 O C) Specific gravity of substance  density of substance

Specific Gravity Units of density = g/cm 3 What are units of specific gravity? No units substance g/cm 3 water g/cm 3

Hydrometer Liquid Reading Hydrometer Measures specific gravity of liquidsMeasures specific gravity of liquids

Temperature Degree of hotness or coldness Celsius scale BP of H 2 O = 100 O C (at sea level) MP of H 2 O = 0 O C

Kelvin Scale 0 K = absolute 0 0 K = absolute 0 0 K = absence of heat 0 K = -273 O C K = O C O C = K - 273