Chapter 3 – Scientific Measurement

Chapter Preview 3.1 - Importance of Measurement Qualitative/Quantitative measurements Scientific Notation 3.2 - Uncertainty in Measurements Accuracy, precision, & error SIGFIGS! 3.3 - International System of Units Length, Volume, Mass Metric System 3.4 - Density What is it? Calculations 3.5 - Temperature Different scales

Section 3.1 The Importance of Measurement Qualitative measurements – non-numerical measurements Quantitative measurements – measurements in a definite, numerical form… ALWAYS with units. If you don’t put a unit on an answer, it’s wrong.

Measurements: Qualitative or Quantitative? 3 meters Large trash cans 5 car lengths Round Brown basketballs 6 runs Several slugs 98 degrees Millions of stars

Scientific Notation In chemistry and other sciences, very small or large numbers are often used 602,000,000,000,000,000,000,000 Scientific notation is a method of writing these numbers in a shorter, easier form. 6.02 x 1023

Scientific Notation Scientific Notation: M x 10n In scientific notation, a number is written as the product of two numbers: a coefficient and 10 raised to a power. Scientific Notation: M x 10n 1 ≤ M ≤ 9 and n is a whole number 6.02 x 1023 6.02 is the coefficient 1023 moves the decimal place The exponent is the number of decimal places moved

Scientific notation The following are examples of where to locate the scientific notation button and on how to type scientific notation in.

Examples Write each measurement in scientific notation 665,000 0.000425 0.0000000005500

Standard Notation 3 x 104 0.056 x 103 4.56 x 10-9 Write the following measurements in standard notation 3 x 104 0.056 x 103 4.56 x 10-9

Scientific Notation Multiplying and dividing To multiply: Multiply the coefficients to get the new coefficient Add the exponents to get the new exponent Ex: (2.0 x 103)(3.0 x 104) = 6.0 x 107 To divide: Divide the coefficients to get the new coefficient Subtract the exponents to get the new exponent Ex: (10.0 x 105)/(5.0 x 102) = 2.0 x 103

Adding and subtracting The decimal places must be in the same spot on the standard notation number Align the decimal places by shifting the decimal and adjusting the exponent until the exponents are the same Ex: 45.5 x 102 + 2.5 x 103  4.55 x 103 + 2.5 x 103 Then add or subtract. Keep the exponent Ex: 7.05 x 103

Examples (6.50 x 104) x (5.0 x 106) (6.50 x 104) x (5.0 x 10-5)

A scientific calculator has a scientific notation button on your calculator. It will make solving problems in chemistry much easier! TI = Normally select the 2nd button followed by the ee button. Casio = Normally select the exp button.

Section 3.2 Uncertainty in Measurements Objectives: Distinguish among the accuracy, precision, and error of a measurement Identify the number of significant figures in a measurement and in the result of a calculation

Section 3.2 Uncertainty in Measurements All measurements have some degree of uncertainty Meter stick Making precise measurements reliably is important

Uncertainty in Measurements Correctness and reproducibility in measurements have certain terms. Accuracy - how close the measurement is to the actual value. Precision – how consistent a series of measurements is.

Uncertainty in Measurements

Uncertainty in Measurements To evaluate the accuracy of a measurement, you observe the accepted value and experimental value Accepted value – the correct value based on reliable references Experimental value – the value actually measured in the lab

Uncertainty in Measurements Error – the difference between the accepted and experimental value Error = experimental value – accepted value Percent error – shows the error relative to the accepted value

Example You measure the freezing temperature of water to be 2 degrees Celsius. What is the percent error of your measurement? You will need to convert to Kelvin! (Celsius + 273 = Kelvin)

Activity Lab: Percent Error Get into groups of two. Complete each station.

Significant Figures Significant figures include all of the digits that are known, plus a last digit that is estimated.

Significant Figures Rules All nonzero digits are significant. 456 cm 1.982 km Rule #2 All zeros appearing in between nonzero digits are significant. 2,002.3 mi 100.5 lbs

Significant Figures Rules Leftmost zeros appearing in front of nonzero digits are not significant. 0.0037 m 0.000 009 km Rule #4 Rightmost zeros appearing after a nonzero digit with NO decimal are NOT significant. 200 mi 45,000,000 lbs

Significant Figures Rules Rightmost zeros appearing after a nonzero digit WITH a decimal ARE significant. 32.00 m 120.0 km Rule #6 There are two situations in which measurements have an unlimited number of significant figures. Counting items with whole numbers. (i.e. people) Exactly defined quantities. (60 min = 1 hour)

123 meters 30.0 meters 3 sig figs 3 sig figs 0.123 meter Examples 123 meters 3 sig figs 0.123 meter 40,506 meters 5 sig figs 9.8000 x 104 meters 30.0 meters 3 sig figs 22 meter sticks Unlimited 0.07080 meter 4 sig figs 98,000 meters 2 sig figs

Sig Figs in Calculations Rounding Sig Figs An answer cannot be more precise than the least precise measurement from which it was calculated. To round a number, you must first decide how many significant figures the answer should have. It depends on the given measurements.

Rules for Rounding Numbers If the digit following the last digit to be retained is: Then the last digit should: Example (rounded to three significant figures) Greater than 5 Be increased by 1 42.68 g → 42.7 g Less than 5 Stay the same 17.32 m → 17.3 m 5, followed by nonzero digit(s) 2.7851 cm → 2.79 cm 5, not followed by nonzero digit(s), and preceded by an odd digit 4.635 kg → 4.64 kg (because 3 is odd) 5, not followed by nonzero digit(s), and the preceding significant digit is even 78.65 mL → 78.6 mL (because 6 is even)

Examples: Round each measurement to three significant figures. 4.3621 x 108 m 0.01552 m 9009 m 1.7777 x 10-3 m 629.55 m

Sig Figs in Calculations Addition & Subtraction Add / Subtract Normally Find the least place value that all given numbers have in common Round to that least place value.

Examples 12.52 m + 349.0 m + 8.24 m 74.626 m – 28.34 m

Sig Figs in Calculations Multiplication & Division Multiply / Divide Normally Count the number of sig figs in each given number. Round to the least amount of sig figs.

Examples 7.55 m x 0.34 m 2.4526 g ÷ 8.4 mL

Section 3.3 International System of Units The International System of Units (SI) is a revised version of the metric system. Le Systéme International d’Unités It was adopted by international agreement in 1960.

Base Units There are seven SI base units. From these base units, all other SI units are derived.

Derived Units Derived units are made from a combination of base units. Examples include: m3 = Volume g/cm3 = Density Pa = Pressure

Prefixes Used in the Metric System

Units of Length 1 km = 1000 m Meter (m) is base unit 1 dm = 1/10 m 1 dm = 0.1 m 1 cm = 1/100 m 1 cm = 0.01 m 1 mm = 1/1000 m 1 mm = 0.001 m 1 μm= 1/1 000 000 m 1 μm = 0.000 001 m 1 nm = 1/1 000 000 000 m 1 nm = 0.000 000 001 m

Examples Convert the following lengths: 25 m to cm 1.67 mm to m 2,300 mm to km 4.5 x 109 nm to cm

Units of Volume The space occupied by any sample of matter is called its volume. Length x width x height = volume 1m x 1m x 1m = 1 m3 Other useful volume units include: Liter (L) Milliliter (mL) Cubic centimeter (cm3)

Examples Convert the following volumes: 35 mL to L 2300 m3 to cm3 15 mL to cm3 25 cm3 to mm3

Units of Mass Mass is how much matter an object has Mass base unit – kilogram (kg) Weight is dependent on gravity Weight – force on object due to gravity An astronaut’s weight on the moon is 1/6th of the weight on Earth. His/her mass is the same no matter where they are!

Examples Convert the following masses: 0.075 kg to grams 1,200 g to kg 73.5 mg to cg 3.50 x 108 μg to g

Section 3.4 Density Density – amount of mass in a given volume Mass per unit volume Common Units g/cm3 kg/m3 g/mL

Example A copper penny has a mass of 3.1 g and a volume of 0.35 cm3. What is the density of copper?

Example The density of silver at 20 ˚C is 10.5 g/cm3. What is the volume of a 68 g bar of silver?

Example Find the mass of an object that has a density of 3.50 g/cm3 and a volume of 1.0 cm3.

Specific Gravity Specific gravity – is a comparison of the density of a substance with the density of a reference substance, usually at the same temperature. Usually compared to water Measured with hydrometer

Section 3.5 Temperature Temperature is a measurement directly proportional to the average kinetic energy of particles. It determines the direction of heat transfer. When two objects of different temperatures are in contact, heat moves from the object at the higher temperature to the object at lower temperature. Almost all substances expand when they get hot and contract when the temperature decreases, or gets cold.

Temperature Scales Fahrenheit Celsius Kelvin H2O Freezes at 32 ˚F and Boils at 212 ˚F Celsius H2O Freezes at 0 ˚C and Boils at 100 ˚C Kelvin H2O Freezes at 273 K and Boils at 373 K

Converting Temperature Scales K = ºC + 273.15 ºC = K – 273.15 ºC = 5/9 (ºF – 32) ºF = 9/5 ºC + 32

Temperature Absolute zero – the lowest possible theoretical temperature Not reachable All particles stop moving Strange things happen

Examples Convert 45 ˚C to K Convert 55 ˚F to ˚C Convert 82 ˚F to K

Chapter Recap 3.1 – The Importance of Measurement Qualitative measurements: are not numerical Quantitative: numerical measurements Scientific Notation: 5 x 103 3.2 – Uncertainty in Measurements Precision: consistency Accuracy: closeness to actual value Error: difference between measurement and actual value 3.3 – International System of Units Length: base unit is meter (m) volume: derived unit - cubic meters (m3) mass: base unit is kilogram (kg) 3.4 – Density Density: amount of matter in a certain amount of space D=m/V 3.5 – Temperature Temperature: is proportional to the average kinetic energy of particles Celsius: metric scale Kelvin: SI scale and also absolute scale