Chapter 3 Scientific Measurement Hingham High School Mr. Clune Full screen view – click screen in lower right corner (Internet Explorer 4.0 & higher)

Measurements Qualitative measurements - words Quantitative measurements – involves numbers (quantities) Depends on reliability of instrument Depends on care with which it is read Scientific Notation Coefficient raised to power of 10

Scientific Notation Multiplication Multiply the coefficients, add the exponents 4 + 7 = 11 (2 X 104) X (3 X 107) 2 X 3 = 6 6 X 1011

2 X 104 8 X 109 9 - 5 = 4 4 X 105 8 4 = 2 Scientific Notation Division Divide the coefficients, subtract the denominator exponent from numerator exponent 8 X 109 4 X 105 9 - 5 = 4 8 4 = 2 2 X 104

Scientific Notation Before adding or subtracting in scientific notation, the exponents must be the same Calculators will take care of this

Scientific Notation Addition Line up decimal; add as usual the coefficients; exponent stays the same (25 X 104) + (3.0 X 106) (25 X 104) + (300. X 104) (325 X 104)

Scientific Notation Subtraction Line up decimal; subtract coefficients as usual; exponent remains the same (25 X 104) - (150. X 103) (25 X 104) - (15.0 X 104) (10 X 104)

Measurements and Their Uncertainty Need to make reliable measurements in the lab Accuracy – how close a measurement is to the true value Precision – how close the measurements are to each other (reproducibility)

Bad Accuracy And Good Precision

Bad Accuracy And Bad Precision

Good Accuracy And Bad Precision

Good Accuracy And Good Precision

Measurements and Their Uncertainty Accepted value – correct value based on reliable references Experimental value – the value measured in the lab Error – the difference between the accepted and experimental values

Measurements and Their Uncertainty Error = accepted – experimental Can be positive or negative Percent error = the absolute value of the error divided by the accepted value, times 100% | error | accepted value % error = x 100%

% Error = 2% % Error Example Accepted Value = 100g Experimental Value = 102g % Error = | Acc – Exp | Acc X 100% % Error = | 100 – 102 | 100 X 100% % Error = 2%

Significant Figures Significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated. Note Fig. 3.4, page 66 Rules for counting sig. figs.? Zeroes are the problem East Coast / West Coast method

2. Zeros between nonzero digits 10003 mL (5) 0.2005 ms (4) Significant Figures 1. All nonzero digits 457 cm (3) 0.35 g (2) 2. Zeros between nonzero digits 10003 mL (5) 0.2005 ms (4)

3. Zeros to the left of the first nonzero digits in a number are Significant Figures 3. Zeros to the left of the first nonzero digits in a number are not significant; they merely indicate the position of the decimal point. 0.02 g (1) 0.0026 cm (2)

4. When a number ends in zeros that are to the right of the decimal Significant Figures 4. When a number ends in zeros that are to the right of the decimal point, they are significant. 0.0200 g (3) 3.0 cm (2)

5. When a number ends in zeros that are not to the right of a decimal Significant Figures 5. When a number ends in zeros that are not to the right of a decimal point, the zeros are not necessarily significant. 130 cm (2) 10,300 g (3)

Counting Significant Fig. Sample 3-1, page 69 Rounding Decide how many sig. figs. Needed Round, counting from the left Less than 5? Drop it. 5 or greater? Increase by 1 Sample 3-2, page 70

Sig. fig. calculations Addition and Subtraction The answer should be rounded to the same number of decimal places as the least number in the problem Sample 3-3, page 60

{ 26.46 + 4.123 30.583 Sig. fig. calculations this has the least digits to the right of the decimal point (2) 26.46 + 4.123  30.583     Rounds off to 30.58

Sig. Fig. calculations Multiplication and Division Round the answer to the same number of significant figures as the least number in the measurement Sample 3-4, page 61

{ 2.61 x1.2 3.132 Sig. Fig. calculations this has the smaller number of significant figures (2) 2.61 x1.2    3.132      Rounds off to 3.1

International System of Units The number is only part of the answer; it also need UNITS Depends upon units that serve as a reference standard The standards of measurement used in science are those of the Metric System

International System of Units Metric system is now revised as the International System of Units (SI), as of 1960 Simplicity and based on 10 or multiples of 10 7 base units Table 3.1, page 63

International System of Units Sometimes, non-SI units are used Liter, Celsius, calorie Some are derived units Made by joining other units Speed (miles/hour) Density (grams/mL)

Common prefixes Kilo (k) = 1000 (one thousand) Deci (d) = 1/10 (one tenth) Centi (c) = 1/100 (one hundredth) Milli (m) = 1/1000 (one thousandth) Micro () = (one millionth) Nano (n) = (one billionth)

Length In SI, the basic unit of length is the meter (m) Length is the distance between two objects – measured with ruler We make use of prefixes for units larger or smaller

Volume The space occupied by any sample of matter Calculated for a solid by multiplying the length x width x height SI unit = cubic meter (m3) Everyday unit = Liter (L), which is non-SI

Volume Measuring Instruments Graduated cylinders Pipet Buret Volumetric Flask Syringe

Volume changes? Volume of any solid, liquid, or gas will change with temperature Much more prominent for GASES Therefore, measuring instruments are calibrated for a specific temperature, usually 20 oC, which is about normal room temperature

Volume – (m3)

Volume (L) 1dm3=1L

Volume

Volume (mL) 1cm3=1mL 1cm

Volume – Liter (L) 1L=1.05qt

Units of Mass Mass is a measure of the quantity of matter Weight is a force that measures the pull by gravity- it changes with location Mass is constant, regardless of location

Mass – KiloGram (kg) 1kg=2.2lbs

Working with Mass The SI unit of mass is the kilogram (kg), even though a more convenient unit is the gram Measuring instrument is the balance scale

Temperature Kelvin (K) Based on Absolute Zero Celsius (°C) Water freezes at 0°C (273K) Water boils at 100°C (373K)

Temperature Water freezes at 0°C (273K) Water boils at 100°C (373K)

BP of H2O FP of H2O Temperature (°C, K) Absolute Zero

°C = K - 273 345K = ? °C °C = 345K – 273 72°C Temperature Convert Kelvin to Celsius °C = K - 273 345K = ? °C °C = 345K – 273 72°C

K = °C + 273 20 °C = ? K K= 20°C – 273 293K Temperature Convert Celsius to Kelvin K = °C + 273 20 °C = ? K K= 20°C – 273 293K

Time – Seconds (s)

The capacity to do work or produce heat Energy The capacity to do work or produce heat Joule (J) Calorie (Cal) Energy needed to raise 1g of 1 °C

Homework Practice Problem 16 Page 78 Section Assessment Questions: 18-27(odd) Page 79 Due: 10/7/04

Dimensional Analysis Converting Units

Conversion Problems 50cm = ?m 100cm = 1m 1m 100cm 100cm 1m

Conversion Problems 1m 100cm 50cm X = 0.50 m

Conversion Problems 0.045kg =? g 1000g = 1kg 1kg 1000g 1000g 1kg

Conversion Problems 1000g 1kg 0.045kg X = 45g

Conversion Problems 2.5hr =? s 60min = 1hr 1hr 60min 60min 1hr

Conversion Problems 2.5hr =? s 60s = 1min 1min 60s 60s 1min

Conversion Problems 60s min 60min 1hr 2.5hr X X = 9000s

Homework Practice Problem 35-37 Pages 82 - 86 Due: 10/7/04

Density Which is heavier- lead or feathers? It depends upon the amount of the material A truckload of feathers is heavier than a small pellet of lead The relationship here is between mass and volume- called Density

The formula for density is: mass volume Common units are g/mL, or possibly g/cm3, (or g/L for gas) Density is a physical property, and does not depend upon sample size Density =

Things related to density What happens when corn oil and water are mixed? Why? Will lead float?

Density and Temperature What happens to density as the temperature increases? Mass remains the same Most substances increase in volume as temperature increases Thus, density generally decreases as the temperature increases

Density and water Sample 3-10,11, page 91-92 Water is an important exception Over certain temperatures, the volume of water increases as the temperature decreases Does ice float in liquid water? Why? Sample 3-10,11, page 91-92

Specific Gravity A comparison of the density of an object to a reference standard (which is usually water) at the same temperature Water density at 4 oC = 1 g/cm3 1g of H2O = 1mL = 1 g/cm3

Formula Note there are no units left, since they cancel each other D of substance (g/cm3) D of water (g/cm3) Note there are no units left, since they cancel each other Measured with a hydrometer – p.72 Uses? Tests urine, antifreeze, battery Specific gravity =

Temperature Heat moves from warmer object to the cooler object Glass of iced tea gets colder? Remember that most substances expand with a temp. increase? Basis for thermometers

Temperature scales Celsius scale- named after a Swedish astronomer Uses the freezing point(0 oC) and boiling point (100 oC) of water as references Divided into 100 equal intervals, or degrees Celsius

Temperature scales Kelvin scale (or absolute scale) Named after Lord Kelvin K = oC + 273 A change of one degree Kelvin is the same as a change of one degree Celsius No degree sign is used

Temperature scales Water freezes at 273 K Water boils at 373 K 0 K is called absolute zero, and equals –273 oC Fig. 3.19, page 75 Sample 3-6, page 75