Scientific Measurement Chapter 3 Scientific Measurement

Section 3.1 Measurements and Their Uncertainty Objectives Convert measurements to scientific notation Distinguish among accuracy, precision, and error of a measurement Determine the number of significant figures in a measurement and in a calculated answer

Using and Expressing Measurements Measurements are fundamental to the experimental sciences Qualitative measurements are words such as heavy or hot Quantitative measurements involve numbers (quantities) Quantitative measurements depend on: The reliability of the measuring instrument The care with which it is read – this is determined by you! Scientific Notation Coefficient raised to the power of 10 Reviewed early this year

Accuracy, Precision, and Error It is necessary to make good, reliable measurements in the lab that are both correct and reproducible Accuracy How close a measurement is to the true value (correct) Precision How close the measurements are to each other (reproducibility)

Accuracy, Precision, and Error To evaluate the accuracy of a measurement, the measured value must be compared to the correct value To evaluate the precision of a measurement, you must compare the value of 2 or more repeated measurements

Accuracy, Precision, and Error Precision and Accuracy Neither accurate nor precise Precise but not accurate Precise and accurate

Accuracy, Precision, and Error Accepted Value The correct value based on reliable references Experimental Value The value measures in the lab Error Accepted value – experimental value Can be positive or negative

Accuracy, Precision, and Error Percent Error The absolute value of the error divided by the accepted value, then multiplied by 100% accepted value – experimental value accepted value % error = X 100

Why is there uncertainty? Measurements are performed with instruments, and no instrument can be read to an infinite number of decimal places

Significant Figures in Measurements In a measurement significant figures include all of the digits that are known, plus one more digit that is estimated Measurements MUST be reported to the correct number of significant figures

How many significant figures are reported in each measurement?

Rules for Counting Significant Figures 1st question you must ask yourself… Is there a decimal point present? Answer? Absent or present Think of our country… We have 2 oceans on our coasts … the pacific and the atlantic Atlantic Pacific

Rules for Counting Significant Figures If the decimal point is absent you start counting significant figures from the atlantic side (right – left) If the decimal point is present you start counting significant figures from the pacific side (left – right)

Rules for Counting Significant Figures 2nd question to ask yourself … Which numbers are significant? THE RULES! All non-zero numbers are significant Example – 4,398 has 4 significant figures Zeros appearing between non-zero digits are significant Example – 709 has 3 significant figures

Rules for Counting Significant Figures THE RULES When a decimal point is present – begin counting from the left to the right (pacific side) with the first non-zero number. All numbers after the first non-zero number are significant, including zeros at the end of the number Examples: 0.76 has 2 significant figures 0.0001885 has 4 significant figures 0.065700 has 5 significant figures 5.308 has 4 significant figures

Rules for Counting Significant Figures THE RULES When a decimal point is absent – begin counting from the right to the left (atlantic side) with the first non-zero number Examples: 189 has 3 significant figures 9,008 has 4 significant figures 23,000 has 2 significant figures 6,090 has 3 significant figures

Rules for Counting Significant Figures 2 special situations Counted numbers 23 people, 5 dogs 2. Exactly defined quantities 60 minutes = 1 hour 100 cm = 1 m Have an unlimited number of significant figures

Significant Figures Practice #1 How many significant figures in the following examples? 1.0070 m  17.10 kg  100,890 L  3.29 x 103 s  0.0054 cm  3,200,000  8 cats 

Significant Figures in Calculations In general – a calculated answer cannot be more precise than the least precise measurement from which it was calculated Sometimes calculated values need to be rounded off Example If you are asked to find the area of a floor and your 2 measurements are 7.7 m and 5.4 m (2 sig fig’s each) your answer 41.58 (4 sig fig’s) must be rounded to have only 2 significant figures – 42 m

Rounding Calculated Answers Decide how many significant figures are needed Depends on the given measurements and the mathematical process Round to that many digits, counting from the left Is the next digit less than 5? Drop it if so Is the next digit 5 or greater Increase by 1

Rounding Calculated Answers Practice problem Round each measurement to the number of significant figures shown in parentheses. Write the answer in scientific notation 314.721 meters (four) 0.001 775 meters (two) 8792 meters (two)

Rounding Calculated Answers Addition and Subtraction The answer should be rounded to the same number of decimal places as the least number of decimal places in the problem Practice Problem Calculate the sum of the three measurements. Give the answer to the correct number of significant figures. 12. 52 m + 349. 0 m + 8.24 m = the answer can only have one decimal place 369. 76 must be rounded to 369. 8

Rounding Calculated Answers Multiplication and Division Round the answer to the same number of significant figures as the least number of significant figures in the problem Position of decimal place has nothing to do with the rounding process Practice Problem perform the following operations. Give the answer to the correct number of significant figures. 2. 10 m x 0. 34 m = the answer (1.47) can only have 2 significant figures correct answer is 1.5 m2

Significant Figures Practice #2 Calculation 3.24 m x 7.0 m 100.0 g / 23.7 cm3 0.02 cm x 2.371 cm 710 m / 3.0 s 1818.2 lb x 3.23 ft 1.030 g x 2.87 mL Calculator Says 22.68 m2 4.219409283 g/cm3 0.04747 cm2 236.6666667 m/s 5872.786 lb/ft 2.9561 g/ml Answer 23 m2 4.22 g/cm3 0.05 cm2 240 m/s 5870 lb/ft 2.96 g/mL

Significant Figures Practice #3 Calculation 3.24 m + 7.0 m 100.0 g - 23.73 g 0.02 cm + 2.371 cm 713.1 L - 3.872 L 1818.2 lb + 3.37 lb 2.030 mL - 1.870 mL Calculator Says 10.24 m 76.27 g 2.391 cm 709.228 L 1821.57 lb 0.16 mL Answer 10.2 m 76.3 g 2.39 cm 709.2 L 1821.6 lb 0.160 mL

Section 3.2 The International System of Units Objectives List SI units of measurement and common SI prefixes Distinguish between the mass and weight of an object Convert between the Celsius and Kelvin temperature scales

International System of Units Measurements depend upon units that serve as reference standards The standards of measurement used in science are those of the metric system

International System of Units The metric system is now revised and renamed as the International System of Units (SI) as of 1960 It is based on 10 or multiples of 10 There are 7 base units Only five commonly used in chemistry: meter, kilogram, kelvin, second, and mole

International System of Units

International System of Units We use prefixes for units larger or smaller than the base unit SI prefixes common to chemistry Prefix Unit Abbreviation Meaning Exponent Kilo- k thousand 103 Deci- d tenth 10-1 Centi- c hundredth 10-2 Milli- m thousandth 10-3 Micro-  millionth 10-6 Nano- n billionth 10-9

Nature of Measurements Quantitative observation consisting of 2 parts: Number Unit Example: 20 grams 6.63 x 10-34 Joule seconds

International System of Units Sometimes Non – SI units are used Liters, Celsius, calorie Some are derived units They are made of joining other units Speed = miles/hour Density = grams/mL

Length Length In SI units, the basic unit of length is the meter (m) The distance between 2 objects Measured with a ruler In SI units, the basic unit of length is the meter (m)

Volume 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 1 mL = 1 cm3

Devices for Measuring Liquid Volume Graduated Cylinder Volumetric Flask Buret Pipets

The Volume Changes! Volumes of solid, liquid, or gas will generally increase with temperature Much more prominent with gases Therefore, measuring instruments are calibrated for specific temperatures, usually 20 degrees Celsius, which is about room temperature

Mass Mass Measure of the quantity of matter present Weight is a force that measures the pull by gravity It changes with location Mass is constant regardless of location SI unit = kilogram Measuring instrument is the balance scale

Temperature Temperature Measure of how hot or cold an object is When 2 objects are in contact - heat moves from the object at the higher temperature to the object at the lower temperature We use 2 units of temperature Celsius Kelvin

Units of Temperature Celsius scale Kelvin Scale Defined by the freezing point of water (0 0C) and the boiling point of water (100 0C) Kelvin Scale Does not use the degree sign, it is just represented as K Absolute zero = 0 K Formula to convert: K = 0C + 273

Energy Energy The ability to do work, or to produce heat Energy can also be measured 2 common units SI unit of energy = Joule (J) Calorie (cal) = heat needed to raise 1 gram of water by 1 0C Conversion between joules and calories: 1 calorie = 4.184 J

Section 3.3 Conversion Problems Objectives Construct conversion factors from equivalent measurements Apply the technique of dimensional analysis to a variety of conversion problems Convert complex units, using dimensional analysis

Conversion Factors Conversion Factors A ratio of equivalent measurements Why do we use conversion factors? Quantities can be expressed in several ways 1 dollar = 4 quarters = 10 dimes = 100 pennies 1 meter = 10 decimeters = 100 centimeters = 1000 millimeters These are all expressions or measurements representing the same amount of money and length

Conversion Factors Conversion Factors Start with two things that are the same One meter is one hundred centimeters Write it as an equation 1m = 100 centimeters Whenever 2 measurements are equivalent, a ration of the two measurements will equal 1

Conversion Factors 1 m = 100 cm We can divide on each side of the equation to come up with two ways of writing the number “1” 1m = 100 cm 1m 1m 1m = 100 cm The measurement in the numerator is equivalent to the measurement in the denominator = 1 = 1 100 cm 100 cm

Conversion Factors A unique way of writing the number 1 In the same system they are defined quantities so they have an unlimited number of significant figures Equivalence statements always have this relationship Big #/Small unit = Small #/Big unit 1000 mm = 1 m When a measurement is multiplied by a conversion factor, the numerical value is generally changed, but the actual size of the quantity measured remains the same

Conversion Factors Practice by writing the two possible conversion factors for the following Between kilograms and grams Between feet and inches Using 1.096 qt. = 1.00 L

Conversion Factors What are conversion factors good for? We can multiply by the number “one” creatively to change the units Question: 13 inches is how many yards? We know that 36 inches = 1 yard 1 yard 36 inches 13 inches X 1 yard = 1

Conversion Factors We can multiply by a conversion factor to change the units Question: 13 inches is how many yards? Known: 36 inches = 1 yard 1 yard 36 inches 13 inches X 1 yard = 1 = 0.36 yards

Conversion Factors Called conversion factors because they allow us to convert units Really just multiplying by one, in a creative way

Dimensional Analysis Dimensional Analysis A way to analyze and solve problems by using units (or dimensions) of the measurement Dimension = a unit (g, L, mL) Analyze = to solve Using the units to solve the problem If you the unit of your answer are right, chances are you did the math right

Dimensional Analysis Dimensional analysis provides an alternative approach to problem solving, instead of with an equation or algebra A ruler is 12.0 inches long. How long is it in cm? You must know the conversion factor to answer the question ( 1 inch = 2.54 cm) 12.0 inches x 2.54 cm 1 inch = 30.48 cm

Dimensional Analysis A race is 10.0 km long. How far is this in miles if: 1 mile = 1,760 yards 1 meter = 1.094 yards

Dimensional Analysis Converting Between Units Problems in which measurements with one unit are converted to an equivalent measurement with another unit are easily solved using dimensional analysis Question: convert 750 dg to grams

Dimensional Analysis Converting between units Many complex problems are best solved by breaking the problem into manageable parts Break the solution down into steps, and use more than one conversion factor if necessary

Dimensional Analysis Converting Complex Units Complex units are those that are expressed as a ration of two units Speed = meters/hour Convert 15 meters/hour to cm/sec

Section 3.4 Density Objectives Calculate the density of a material from the experimental data Describe how density varies with temperature

Density Which is heavier – a pound of lead or a pound of feathers? Most people will answer lead, but the weight is exactly the same They are normally thinking about equal volumes of the two The relationship here between mass and volume is called density

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

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

Density and Temperature Water is an important exception Over certain temperatures, the volume of water increases as the temperature decreases Does ice float in liquid water Why?