Making Measurements S Measurements in Life S What

Making Measurements S

Measurements in Life S What are some examples of situations in your life that require making measurements? S Amount of time it takes to do something S Body temperature when you’re sick S Speed of a thrown baseball S Distance between the line of scrimmage and the goal

2 Types of Measurements S There are 2 types of measurements that can be made: S Qualitative S Quantitative S Qualitative: measurements that do NOT involve the use of numbers and concern characteristics of an object. S Quantitative: measurements that involve numbers and must be determined with an apparatus of some sort.

Qualitative or Quantitative? S It is hot outside. Qualitative S Yesterday I ran 3 miles. Quantitative S It was 102° outside this afternoon. Quantitative S The balloon was big and blue. Qualitative S The paper felt soft on my skin. Qualitative S I need 3. 25 mm of string for my project. Quantitative S I am 3 foot 4 inches tall. Quantitative S Wow you’re short!! Qualitative

Don’t Forget… S Why are units just as important in communicating a quantitative measurement as the number is? S A number without a unit is meaningless S Ex: 35 °F is cold and 35 °C is hot

Accuracy vs Precision S Accuracy: refers to how close a measured value is to an accepted value S Precision: refers to how close a series of measurements are to one another

Accuracy vs Precision Ken Sue Jon Trial 1 (g/cm 3) 1. 54 1. 40 1. 70 Trial 2 (g/cm 3) 1. 60 1. 68 1. 69 Ken, because his average is closest to the accepted value. Trial 3 (g/cm 3) 1. 57 1. 45 1. 71 S Who collected the most precise Average (g/cm 3) 1. 57 1. 51 1. 70 Accepted Value = 1. 59 g/cm 3 S Who collected the most accurate data? Jon, because his values varied by the smallest amount (0. 02 g/cm 3.

Scientific Notation Rules 1. The first figure is a number from 1 9. 2. The first figure is followed by a decimal point and then the rest of the figures. 3. Then multiply by the appropriate power of 10.

Scientific Notation v. Given: 289, 800, 000 Use: 2. 898 (moved 8 places) Answer: 2. 898 x 108 v. Given: 0. 000567 Use: 5. 67 (moved 4 places) Answer: 5. 67 x 10 4

Learning Check S Express these numbers in Scientific Notation: 4. 05789 x 105 1) 405789 3. 872 x 10 -3 2) 0. 003 872 3 x 109 3) 3, 000, 000 2 x 10 -8 4) 0. 000 02 5) 0. 478260 4. 7826 x 10 -1

S Convert the following number to scientific notation S 1. ) 0. 000 000 276 S 2. ) 150, 000 S 3. ) Determine if the following set of data is accurate, precise or both. The bug is 2. 59 cm long 3. 58 cm 3. 59 cm 3. 57 cm

Significant Figures S What is the difference between S 75. 00 m. L S 75 m. L S Are they all the same number or are they different?

Significant Figures S How do we read the ruler? S 4. 5515 cm? S 4. 551 cm? S 4. 55 cm? S 4 cm? S We needed a set of rules to decide 1 2 3 4 5

Significant Figure Rules Rule #1: All real numbers (1, 2, 3, 4, etc. ) count as significant figures. S Therefore, you only have to be concerned with the 0 S Whether a 0 is significant or not depends on the location of that 0 in the number

Which zeros count? Rule #2: Zeros at the end of a number without a decimal point don’t count 12400 g (3 sig figs) Rule #3: Zeros after a decimal without a number in front are not significant. 0. 045 g (2 sig figs)

Which zeros count? Rule #4: Zeros between other sig figs do count. 1002 g (4 sig figs) Rule #5: Zeroes at the end of a number after the decimal point do count 45. 8300 g (6 sig figs)

Significant Figures Pacific Ocean S When the decimal is Present, start counting with the first nonzero number on the left. S Keep counting until you fall off Atlantic Ocean S When the decimal is Absent, start counting with the first nonzero number on the right. S Keep counting until you fall off.

Other Information about Sig Figs S Only measurements have sig figs. S A a piece of paper is measured 11. 0 inches tall. S Counted numbers are exact S A dozen is exactly 12 S Being able to locate, and count significant figures is an important skill.

Learning Check A. Which answers contain 3 significant figures? 1) 0. 4760 cm 2) 0. 00476 cm 3) 4760 cm B. All the zeros are significant in 1) 0. 00307 m. L 2) 25. 300 m. L 3) 2. 050 x 103 m. L C. 534, 675 g rounded to 3 significant figures is 1) 535 g 2) 535, 000 g 3) 5. 35 x 105 g

Learning Check In which set(s) do both numbers contain the same number of significant figures? 1) 22. 0 and 22. 00 2) 400. 0 and 40 3) 0. 000015 and 150, 000 NO NO YES- 2 4) 63, 000 and 2. 1 YES- 2 5) 600. 0 and 144 NO 6) 0. 0002 and 2000 YES-1

Rounding rules S Look at the number behind the one you’re rounding. S If it is 0 to 4 don’t change it S If it is 5 to 9 make it one bigger

Rounding S 5. 87192 S Round 2 digits 5. 9 S Round 3 digits 5. 87 S Round 4 digits 5. 872 S 7. 9237439 S Round 1 digits 8 S Round 2 digits 7. 9 S Round 4 digits 7. 924 S Round 5 digits 7. 9237

Learning Check How many sig figs are in the following measurements? 658 g 3 6850. g 4 6850 g 0. 0685 g 0. 006085 g 60. 006085 g 3 3 4 8

Calculations Using Sig Figs Addition/ Subtraction S The least accurate measurement determines the accuracy of the answer. S Keep only as many decimal places as the least accurate measurement. S Ex: 12. 01 + 35. 2 + 6 = 53 Multiplication/ Division S The least precise measurement determines the accuracy of the answer. S Round your answer to the least number of significant figures in any of the factors. S Ex: 1. 35 x 2. 467 = 3. 33

Another Example If 27. 93 m. L of Na. OH is added to 6. 6 m. L of HCL, what is the total volume of your solution? l l First line up the decimal places Then do the adding Find the estimated numbers in the problem This answer must be rounded to the tenths place 27. 96 m. L + 6. 6 m. L 34. 56 m. L 34. 6 m. L

Example: 135 cm x 32 cm = 4320 cm 2 3 S. F. 2 S. F. Round off the answer to 3 4300 cm which is 2 sig figs.

Learning Check 1. 2. 19 m X 4. 2 m = A) 9 m 2 B) 9. 2 m 2 C) 9. 198 m 2 2. 4. 311 cm 2 ÷ 0. 07 cm = A) 61. 58 cm B) 62 cm C) 60 cm 3. (2. 54 m. L X 0. 0028 m. L) = 0. 0105 m. L X 0. 060 m. L A. ) 11. 3 m. L B)11 m. L C) 0. 041 m. L

Percent Error S Percent error is a way for scientists to express how far off a lab value is from the commonly accepted value. S The formula is: S % Error = |Accepted value – Experimental Value| x 100 % Accepted Value

Percent Error S Example 1: S Experimental Value = 1. 24 g S Accepted Value = 1. 30 g S % Error = |Accepted value – Experimental Value| x 100 % Accepted Value S % Error = |1. 30 – 1. 24| x 100 % 1. 30 = 4. 62 %

S How many sig figs are in the following number S 1. ) 45. 00 S 2. ) 4, 500 S 3. ) 0. 04500 S 4. ) 0. 00045

Why do we need common units? S It is important for scientists around the world to be able to communicate with each other! S If we all used a different set of units, communication would be different if not impossible. S Therefore. . .

International System of Units S The common system of units scientists have devised in order to communicate with each other even when they’re from different places is called the Systemme Internationale (International System in French) or SI. S This system has seven base units that are based on an object or event in the physical world.

SI Base Units Quantity SI Base Unit Symbol Time second s Length meter m Mass kilogram kg Temperature Kelvin K Amount of Substance moles mol Electric Current Ampere A Luminous Intensity candela cd

Time S The SI base unit for time is the second, s. S How is this unit officially defined? S The frequency of microwave radiation given off by a cesium 133 atom is the physical standard used to establish the length of a second. S This is why atomic (cesium) clocks are more accurate than the standard clocks and stopwatches we normally used to measure time.

Length S The SI base unit for length is the meter, m. S How is this unit officially defined? S A meter is the distance that light travels through a vacuum in 1/299792458 of a second. S If you need to measure length that is longer than this base unit… you’d measure in kilometers (km). S If you need to measure length that is a shorter distance than the base unit… you’d measure in centimeters (cm) or millimeters (mm).

Mass S Mass is the measure of the amount of matter in a sample. S The SI base unit for mass is the kilogram, kg. S How is this officially defined? S The kilogram is defined by a platinum iridium metal cylinder stored in Sevres, France. A copy is kept at the National Institute of Standards and Technology in Gaithersburg, Maryland.

Mass S What units are you most likely to use to measure mass in lab? S The masses measured in lab are often much smaller than a kg, for those cases we use grams (g) or milligrams (mg)

Temperature S The SI base unit for temperature is the Kelvin, K. S This scale was calibrated so that changing one unit on the Kelvin scale is the same as changing a temperature by one degree Celsius. S Defining temperature points S Celsius: 0° water freezes, 100° water boils S Kelvin: 273 water freezes, 0 all motion stops

Temperature S Why was the Kelvin scale invented/ why is it useful? S We needed an “absolute zero scale” so that we could do calculations without negative numbers. S Convert between Kelvin and Celsius S K = °C + 273 S °C = K – 273 S A third temperature scale that we will not use in the lab is Fahrenheit. S How do you convert between Celsius and this scale? S °F = (1. 8 x °C) + 32 S °C = (°F 32) / 1. 8

History of Temperature Lord Kelvin Anders Celsius

Derived Units S Not all quantities can be measured with base units. S Example: the SI unit for speed is meters per second (m/s). S Notice that this includes 2 base units the meter and the second. S A unit that is defined by a combination of base units is called a derived unit.

Volume S Volume is space occupied by an object. S The derived SI unit for volume is the cubic meter, m 3, which is represented by a cube whose sides are all one meter in length. S This unit is much larger than what will commonly be needed in the lab so a more useful derived unit, the cubic centimeter, cm 3 is used. S The unit cm 3 works well for solid objects with regular dimensions, but not as well for liquids or for solids with irregular shapes. The metric unit for volume is the Liter, L. S What are the conversions between volume units? S 1000 m = 1 L; 1 cm 3 = 1 m. L; (memorize 1 cm 3 1 m. L)

Metric Dimensional Analysis Trick Name/ Symbol Factor King Kilo (K) 1000 or 103 Henry Hecto (H) 100 or 102 Died Deca (D) 10 By base 1 drinking deci (d) 1/10 chocolate centi (c) 1/100 or 1/102 milk milli (m) 1/1000 or 1/103 Micro (µ) 1/1000000 or 1/106 Nano (n) 1/100000 or 1/109

S Mass, distance, time, volume, and quantity (amount) are the ones most common to chemistry. S These measurements each have their own base unit. We want to know/ measure What it’s called Standard system Metric Base Unit Abbreviation How much something weighs Mass Pounds, ounces, tons Gram g How long/short something is Distance Inches, feet, miles Meter m How much space something takes up Volume Pints, gallons, quarts, cups Liter L Time Seconds, minutes, hours Second s Quantity Dozen, gross Mole mol How long something takes How many of something we have

#2 The greater unit gets the 1 Symbol S 950 g = ____ kg 950 g x K 1000 H 100 D 10 b 1 d 1/10 c 1/100 m 1/1000 1 kg 1000 g Factor = 0. 95 kg

The greater unit gets the 1 #1 Symbol K 1000 or 103 H 100 or 102 D 10 C 1 b S 35 m. L = _____ c. L d S TWO prefixes = TWO steps 1/10 C 1/100 or 102 c 35 m. L x 1 L 100 0 m. L x Factor m 1/1000 or 103 μ 1/1000000 or 106 100 c. L 1 L = 3. 5 c. L

The greater unit gets the 1 #8 S 0. 005 kg= _____ dag x 103 g 1 kg x Factor K 1000 or 103 H 100 or 102 D 10 b CC 1 1/10 d S TWO prefixes = TWO steps 0. 005 kg Symbol c 1/100 or 102 m 1/1000 or 103 μ C 1/1000000 or 106 μg 1 g = 5 x 106 μg

Exit Ticket S Perform the following metric conversion S 180 ns to ks S 77. 2 cm 3 to L S Round the following number to 3 sig figs S 45674

Extra Dimensional Analysis

Dimensional Analysis S Many problems in chemistry do not have a simple formula that you can plug the data into and get the answer. Instead, solving a chemistry problem requires planning, much like taking a trip. You must determine where you are going (what you are solving for) and how you are going to get there (what do you need to know to solve the problem).

Dimensional Analysis S In chemistry most data is in the form of a measurement. A measure contains two parts the number and the UNIT! S Many problems involve converting measurements from one unit (or dimension) to another. These units help you to plan the solution to the problem you are trying to solve. The technique of converting between units is called DIMENSIONAL ANALYSIS.

Dimensional Analysis S When you use dimensional analysis to solve chemistry problems you will keep track of the units involved in the calculations you use. When you multiply or divide numbers with units you also multiply or divide the units. You cancel units the same way that you cancel the numerators and denominators of fractions. S A conversion factor is a relationship between different units of measure.

Dimensional Analysis S Give an example of a conversion factor and show 3 ways of writing it. S Inches and feet S Minutes and seconds

Dimensional Analysis 1. Write the given. 2. Set up your conversion factor your units will cancel out. 3. Multiply by factors on the top and divide by factors on the bottom. S Be sure your units are cancelling out and that the unit you’re left with is the desired unit.

Dimensional Analysis S How many inches are equal to 4. 5 feet? S How many steps? 1 (12 in = 1 ft) 4. 50 ft x 12 in 1 ft = 54 in

Dimensional Analysis S How many dollars are in 140 dimes? S How many steps? 1 (1 dollar = 10 dimes) 140 dimes x 1 dollar 10 dimes = 14 dollars

Dimensional Analysis S Pistachio nuts cost $6. 00 per pound. How many pounds of nuts can be bought for $20. 00? S How many steps? 1 (1 pound = $6. 00) 20 dollars x 1 pound 6 dollars = 3. 33 pounds

Dimensional Analysis S How much does 4. 15 pounds of pistachio nuts cost? S How many steps? 1 (1 pound = $6. 00) 4. 15 pounds x 6 dollars 1 pound = 24. 90 dollars