Unit 2. Measurement This lesson is 8 days long

Do Now In your own words, what do you think is the difference between Accuracy and Precision? https://www.youtube.com/watch?v=hRAFPdDppzs

Accuracy vs. Precision Accuracy - how close a measurement is to the accepted value

Accuracy vs. Precision Precision - how close a series of measurements are to each other

ACCURATE = CORRECT PRECISE = CONSISTENT

Percent Error Equation The accuracy of an individual value can be compared with the correct or accepted value by calculating the percent error. Percent Error Equation experimental - accepted value x 100 accepted value

Percent Error Example: Measuring the boiling point of H2O Thermometer reads – 99.1OC You know it should read – 100OC experimental - accepted value x 100 accepted value

% error = |99.1oC – 100.0oC| x 100% 100oC = 0.9o C x 100% 100o C = 0.009 x 100% = 0.9%

Not All Errors are equal… You fly from NY to San Francisco You are an eye surgeon Your plane is blown off course by 3cm Your scalpel misses the mark by 3cm They sound equal … but are they?

Objectives: Describe the difference between a qualitative and a quantitative measurement. Describe the difference between accuracy and precision. Write a number in scientific notation. State the appropriate units for measuring length, volume, mass, density, temperature and time in the metric system.. Calculate the percent error in a measurement. Calculate density given the mass and volume, the mass given the density and volume, and the volume given the density and mass.

Units of Measurement

Do Now: Name the equipment and briefly describe the purpose of each. A. B. C. D. E. https://www.youtube.com/watch?v=_A3JxpMU63s

Measurements represent quantities. A quantity is something that has magnitude, size or amount. All measurements are a number plus a unit (grams, teaspoon, liters).

A. Number vs. Quantity Number + Unit! … Always!

B. SI Units Length l meter m Mass m kilogram kg Time t second s Temp T Quantity Symbol Base Unit Abbrev. Length l meter m Mass m kilogram kg Time t second s Temp T kelvin K Amount n mole mol

Do Now What are the SI units for…. Length: ______________ Mass: _______________ Temperature: ____________

B. SI Units Prefix Symbol Factor mega- M 106 kilo- k 103 BASE UNIT --- 100 deci- d 10-1 centi- c 10-2 milli- m 10-3 micro- μ 10-6 nano- n 10-9 pico- p 10-12

SI Prefix Conversions 1) 20 cm = ______________ m 2) 0.032 L = ______________ mL 3) 45 μm = ______________ m

Do Now 1) .87 cm = ______________ μ m 2) 62.3 L = ______________ hL 3) 0.98 μm = ______________ nm

Do Now 1. 4.5nm = ___________ cm 2. 0.568hg = ____________ mg 3. 0.986 cL = _________ μL

Derived SI Units Many SI units are combinations of the quantities shown earlier. Combinations of SI units form derived units. Derived units are produced by multiplying or dividing standard units.

Scientific Notation https://www.youtube.com/watch?v=AWof6knvQwE

Let’s Try These 1.0 x 101 = ______________ 2.0 x 102 = ______________

Scientific Notation https://www.youtube.com/watch?v=AWof6knvQwE

A Problem worked out 23,415 = ____________________ 2.3415 X 10,000 If you go to the …. Right = negative number in exponent Left = positive number in exponent

Do Now A. 124 = _____________________________ B.  0.000000000 043 = _________________ C. 93,000,00 = ________________________ D.  3.6 × 1012 = ______________________

What is this called? How do you use it? List the steps! https://www.youtube.com/watch?v=QtnPiKSKKtI

Do Now A. 3290 = _____________________________ B.  0.000000689 = _________________ C. 76,500,000 = ________________________ D.  4.5 × 10-9 = ______________________

M V D = C. Derived Units cont… Density: ratio between mass and volume kg/m3 or g/mL or g/cm3 does not depend on size of sample D = M V

Volume Volume is the amount of space occupied by an object. length x width x height Expressed as cubic centimeter (cm3) or cubic meter (m3). When measuring liquid volumes in the laboratory a chemist typically uses milliliters (mL) 1 mL = 1 cm3

How do you calculate density? You need the measure Mass and Volume Mass - Obtain by weighing the mass of an object by using a balance and then determine the volume.

How do you calculate density? Solids - the volume can be a little difficult since it’s not a perfect shape. If the object is a regular solid, like a cube, you can measure its three dimensions and calculate the volume. Volume = length x width x height

Volume continued … If the object is an irregular solid, like a rock, determining the volume is more difficult. Archimedes’ Principle – states that the volume of a solid is equal to the volume of water it displaces. Put some water in a graduated cylinder and read the volume. Next, put the object in the graduated cylinder and read the volume again. The difference in volume of the graduated cylinder is the volume of the object.

Volume Displacement 25 mL A solid displaces a matching volume of water when the solid is placed in water. 35mL 25 mL

Learning Check What is the density (g/mL) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL? 1) 0.2 g/mL 2) 6 g/mL 3) 252 g/mL

PROBLEM: Mercury (Hg) has a density of 13. 6 g/cm3 PROBLEM: Mercury (Hg) has a density of 13.6 g/cm3. What is the mass of 95 mL of Hg in grams?

Do Now: 1. What is the equation for density. 2 Do Now: 1. What is the equation for density? 2. What is Archimedes’ Principle ?

PROBLEM: Mercury (Hg) has a density of 13. 6 g/cm3 PROBLEM: Mercury (Hg) has a density of 13.6 g/cm3. What is the mass of 95 mL of Hg? First, note that 1 cm3 = 1 mL Strategy Use density to calc. mass (g) from volume. Density = Mass Volume

PROBLEM: Mercury (Hg) has a density of 13. 6 g/cm3 PROBLEM: Mercury (Hg) has a density of 13.6 g/cm3. What is the mass of 95 cm of Hg? 3 Density = Mass Volume 13.6g/cm3= Mass (g)3 95 cm 3

Do NOW- What units do we use for….. A. Volume B. Mass C. Density *** List all that apply*** What’s the equation for density?

Learning Check Osmium is a very dense metal. What is its density in g/cm3 if 50.00 g of the metal occupies a volume of 2.22cm3? 1) 2.25 g/cm3 2) 22.5 g/cm3 3) 111 g/cm3

Solution Placing the mass and volume of the osmium metal into the density setup, we obtain D = mass = 50.00 g = volume 2.22 cm3 = 22.522522 g/cm3 = 22.5 g/cm3

Learning Check The density of octane, a component of gasoline, is 0.702 g/mL. What is the mass, in kg, of 875 mL of octane? 1) 0.614 kg 2) 614 kg 3) 1.25 kg

Learning Check The density of octane, a component of gasoline, is 0.702 g/mL. What is the mass, in kg, of 875 mL of octane? 1) 0.614 kg

Problem-Solving Steps 1. Analyze 2. Plan 3. Compute 4. Evaluate

D. Density V = 825 cm3 D = 13.6 g/cm3 M = ? GIVEN: WORK: An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass. GIVEN: V = 825 cm3 D = 13.6 g/cm3 M = ? WORK:

D. Density An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass. GIVEN: V = 825 cm3 D = 13.6 g/cm3 M = ? WORK: M = DV M = (13.6g/cm3)(825cm3) M = 11,200 g

Do Now: D = 0.87 g/mL V = ? M = 25 g GIVEN: WORK: A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? M = 25 g WORK:

D. Density D = 0.87 g/mL V = M V = ? M = 25 g V = 25 g 0.87 g/mL A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? M = 25 g WORK: V = M D V = 25 g 0.87 g/mL V = 29 mL

III. Unit Conversions

A. SI Prefix Conversions 1. Find the difference between the exponents of the two prefixes. 2. Move the decimal that many places. To the left or right?

A. SI Prefix Conversions Symbol Factor mega- M 106 kilo- k 103 BASE UNIT --- 100 deci- d 10-1 move left move right centi- c 10-2 milli- m 10-3 micro- μ 10-6 nano- n 10-9 pico- p 10-12

A. SI Prefix Conversions 1) 20 cm = ______________ m 2) 0.032 L = _____________ mL 3) 45 μm = ______________ nm 4) 805 dm = ______________ km

A. SI Prefix Conversions 0.2 1) 20 cm = ______________ m 2) 0.032 L = ______________ mL 3) 45 μm = ______________ nm 4) 805 dm = ______________ km 32 45,000 0.0805 C. Johannesson

DO NOW A golden-colored cube is handed to you. The person wants you to buy it for $100, saying that is a gold nugget. You pull out your old geology text and look up gold in the mineral table, and read that its density is 19.3 g/cm3. You measure the cube and find that it is 2 cm on each side, and weighs 40 g. What is its density? Is it gold? Should you buy it?

Conversion Factors Conversion Factors Conversion factor – a ratio derived from the equality between two different units that can be used to convert from one unit to the other. Example: the conversion between quarters and dollars: 4 quarters 1 dollar 1 dollar or 4 quarters

Conversion Factors Conversion Factors Example: Determine the number of quarters in 12 dollars? Number of quarters = 12 dollars x conversion factor ? Quarters = 12 dollars x 4 quarters = 48 quarters 1 dollar

Learning Check 1. Liters and mL 2. Hours and minutes Write conversion factors that relate each of the following pairs of units: 1. Liters and mL 2. Hours and minutes 3. Meters and kilometers

B. Dimensional Analysis The “Factor-Label” Method Units, or “labels” are canceled, or “factored” out to make your calculations easier

Do Now How many hours are in 2.3 years? *use dimensional analysis to solve this problem*

B. Dimensional Analysis Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

Learning Check a) 2440 cm b) 244 cm c) 24.4 cm 1) A rattlesnake is 2.44 m long. How long is the snake in cm? a) 2440 cm b) 244 cm c) 24.4 cm 2.44 m x 100 cm = 244 cm (b) 1 m

B. Dimensional Analysis 2) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? 8.0 cm 1 in 2.54 cm = 3.2 in

B. Dimensional Analysis 3) A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire? 1.3 m 100 cm 1 m 1 piece 1.5 cm = 86 pieces

Do Now How many meters are 372.4 inches? *use dimensional analysis to solve this problem*

Quantitative vs. Qualitative Data Quantitative data is information about quantities; that is, information that can be measured and written down with numbers.  Ex. Qualitative data is descriptive data that cannot be quantified.

Identify the following as quantitative or qualitative 1. The book is red. 2. The apple has a mass of 2.34 g. 3. The temperature of the room is 412K. 4. There are 4 blue desks in the front of the room. 6. The apple smells rotten.