# Measurement 100 mL Graduated Cylinder Units of Measuring Volume

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Measurement 100 mL Graduated Cylinder Units of Measuring Volume
Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors Accuracy vs. Precision Accuracy Precision Resolution SI units for Measuring Length Comparison of English and SI Units Reporting Measurements Measuring a Pin Practice Measuring

Measurement 100 mL Graduated Cylinder Units of Measuring Volume
Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors Accuracy vs. Precision Accuracy Precision Resolution SI units for Measuring Length Comparison of English and SI Units Reporting Measurements Measuring a Pin Practice Measuring

100 mL Graduated Cylinder Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 119

Instruments for Measuring Volume

Units of Measuring Volume
1 L = mL 1 qt = 946 mL UNITS OF MEASURING VOLUME A measurement has two parts: a number and a unit. Note: NO NAKED NUMBERS Timberlake, Chemistry 7th Edition, page 3

10 8 6 10 mL line of sight too high reading too high proper line of sight reading correct line of sight too low reading too low graduated cylinder

Units for Measuring Mass
Mass – amount of substance present. Does not change when going to the moon. Mass is measured on a pan balance. Weight – related to gravity. Your weight is about 1/6 on the moon and 2.36X on Jupiter. As gravity increases your weight increases. Pull of gravity on jet fighter planes – make your arms and legs very heavy and g-forces increase. Weight is measured on a scale. 1 kg = lb Timberlake, Chemistry 7th Edition, page 3

Units for Measuring Mass
1 kg (1000 g) 1 lb 1 lb 0.20 lb Christopherson Scales Made in Normal, Illinois USA 1 kg = lb

Quantities of Mass Giga- Mega- Kilo- base milli- micro- nano- pico-
Earth’s atmosphere to 2500 km 1018 g Quantities of Mass 1015 g 1012 g Ocean liner Giga- Mega- Kilo- base milli- micro- nano- pico- femto- atomo- 109 g Indian elephant 106 g Average human 103 g 1.0 liter of water 100 g 10-3 g 10-6 g Grain of table salt 10-9 g 10-12 g 10-15 g 10-18 g Typical protein 10-21 g Uranium atom 10-24 g Water molecule Kelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 25

Factor Name Symbol Factor Name Symbol
decimeter dm decameter dam centimeter cm hectometer hm millimeter mm kilometer km micrometer mm megameter Mm nanometer nm gigameter Gm picometer pm terameter Tm femtometer fm petameter Pm attometer am exameter Em zeptometer zm zettameter Zm yoctometer ym yottameter Ym

Scientific Notation: Powers of Ten
Rules for writing numbers in scientific notation: Write all significant figures but only the significant figures. Place the decimal point after the first digit, making the number have a value between 1 and 10. Use the correct power of ten to place the decimal point properly, as indicated below.         a)  Positive exponents push the decimal point to the right.  The number becomes larger.              It is multiplied by the power of 10.         b)  Negative exponents push the decimal point to the left.  The number becomes smaller.              It is divided by the power of 10.         c)  10o  =  1                     Examples:    3400  =  3.20 x 103                  =  1.20 x 10-2 Nice visual display of Powers of Ten (a view from outer space to the inside of an atom) viewed by powers of 10!

Multiples of bytes as defined by IEC 60027-2
SI prefix Binary prefixes Name Symbol Multiple kilobyte kB 103 (or 210) kibibyte KiB 210 megabyte MB 106 (or 220) mebibyte MiB 220 gigabyte GB 109 (or 230) gibibyte GiB 230 terabyte TB 1012 (or 240) tebibyte TiB 240 petabyte PB 1015 (or 250) pebibyte PiB 250 exabyte EB 1018 (or 260) exbibyte EiB 260 zettabyte ZB 1021 (or 270) yottabyte YB 1024 (or 280) A yottabyte (derived from the SI prefix )

Metric Article Metric Article (questions) Metric Article (questions)
Keys

SI-US Conversion Factors
Relationship Conversion Factors Length 2.54 cm 1 in 1 in 2.54 cm 2.54 cm = 1 in. and 39.4 in 1 m 1 m 39.4 in. 1 m = 39.4 in. and Volume 946 mL 1 qt 1 qt 946 mL 946 mL = 1 qt and 1.06 qt 1 L 1 L 1.06 qt and Dominoes Activity 1 L = 1.06 qt Mass 454 g 1 lb 1 lb 454 g 454 g = 1 lb and 2.20 lb 1 kg 1 kg 2.20 lb 1 kg = 2.20 lb and

Accuracy vs. Precision Systematic errors: reduce accuracy
Scientists repeat experiments many times to increase their accuracy. Good accuracy Good precision Poor accuracy Good precision Poor accuracy Poor precision Systematic errors: reduce accuracy Random errors: reduce precision (instrument) (person)

Accuracy vs. Precision Random errors: reduce precision
Scientists repeat experiments many times to increase their accuracy. Good accuracy Good precision Poor accuracy Good precision Poor accuracy Poor precision Random errors: reduce precision Systematic errors: reduce accuracy

Precision Accuracy check by check by using a repeating
Precision Accuracy reproducibility check by repeating measurements poor precision results from poor technique correctness check by using a different method poor accuracy results from procedural or equipment flaws.

Types of errors Systematic Random Instrument not ‘zeroed’ properly
Reagents made at wrong concentration Random Temperature in room varies ‘wildly’ Person running test is not properly trained

Errors Systematic Random Errors in a single direction (high or low)
Can be corrected by proper calibration or running controls and blanks. Random Errors in any direction. Can’t be corrected. Can only be accounted for by using statistics. Systematic error is when you get the same mistake every time you perform a measurement, and random error is when the mistake varies randomly. It’s much easier to compensate for systematic error than for random error.

Accuracy Precision Resolution
time offset [arbitrary units] not accurate, not precise accurate, not precise not accurate, precise accurate and precise accurate, low resolution -2 -3 -1 1 2 3 subsequent samples

Accuracy Precision Resolution
not accurate, not precise accurate, not precise not accurate, precise accurate and precise accurate, low resolution -2 -3 -1 1 2 3 time offset [arbitrary units] subsequent samples

Standard Deviation The standard deviation, SD, is a precision estimate based on the area score:               where xi is the i-th measurement   x is the average measurement N is the number of measurements. One standard deviation away from the mean in either direction on the horizontal axis (the red area on the above graph) accounts for somewhere around 68 percent of the people in this group. Two standard deviations away from the mean (the red and green areas) account for roughly 95 percent of the people. And three standard deviations (the red, green and blue areas) account for about 99 percent of the people. The more practical way to compute it... In Microsoft Excel, type the following code into the cell where you want the Standard Deviation result, using the "unbiased," or "n-1" method: =STDEV(A1:Z99) (substitute the cell name of the first value in your dataset for A1, and the cell name of the last value for Z99.) y One standard deviation away from the mean in either direction on the horizontal axis (the red area on the graph) accounts for around 68 percent of the people in this group. Two standard deviations away from the mean (the red and green areas) account for roughly 95 percent of the people. Three standard deviations (the red, green and blue areas) account for about 99 percent of the people. x

SI Prefixes kilo- 1000 deci- 1/10 centi- 1/100 milli- 1/1000
Also know… 1 mL = 1 cm3 and 1 L = 1 dm3

SI System for Measuring Length
The SI Units for Measuring Length Unit Symbol Meter Equivalent _______________________________________________________________________ kilometer km ,000 m or 103 m meter m m or 100 m decimeter dm m or 10-1 m centimeter cm m or 10-2 m millimeter mm m or 10-3 m micrometer mm m or 10-6 m nanometer nm m or 10-9 m Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 118

Comparison of English and SI Units
1 inch 2.54 cm 1 inch = 2.54 cm Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 119

Reporting Measurements
Using significant figures Report what is known with certainty Add ONE digit of uncertainty (estimation) By adding additional numbers to a measurement – you do not make it more precise. The instrument determines how precise it can make a measurement. Remember, you can only add ONE digit of uncertainty to a measurement. Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46

Measuring a Pin Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 122

Practice Measuring cm 1 2 3 4 5 4.5 cm cm 1 2 3 4 5 4.54 cm cm 1 2 3 4
1 2 3 4 5 4.5 cm cm 1 2 3 4 5 4.54 cm PRACTICE MEASURING Estimate one digit of uncertainty. a) 4.5 cm b) * 4.55 cm c) 3.0 cm *4.550 cm is INCORRECT while 4.52 cm or 4.58 cm are CORRECT (although the estimate is poor) By adding additional numbers to a measurement – you do not make it more precise. The instrument determines how precise it can make a measurement. Remember, you can only add ONE digit of uncertainty to a measurement. In applying the rules for significant figures, many students lose sight of the fact that the concept of significant figures comes from estimations in measurement. The last digit in a measurement is an estimation. How could the measurement be affected by the use of several different rulers to measure the red wire? (Different rulers could yield different readings depending on their precision.) Why is it important to use the same measuring instrument throughout an experiment? (Using the same instrument reduces the discrepancies due to manufacturing defects.) cm 1 2 3 4 5 3.0 cm Timberlake, Chemistry 7th Edition, page 7

Implied Range of Uncertainty
5 6 4 3 Implied range of uncertainty in a measurement reported as 5 cm. 5 6 4 3 Implied range of uncertainty in a measurement reported as 5.0 cm. When the plus-or-minus notation is not used to describe the uncertainty in a measurement, a scientist assumes that the measurement has an implied range, as illustrated above. The part of each scale between the arrows shows the range for each reported measurement. 5 6 4 3 Implied range of uncertainty in a measurement reported as 5.00 cm. Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 32

20 ? 1.50 x 101 mL 15 mL ? 15.0 mL A student reads a graduated cylinder that is marked at mL, as shown in the illustration. Is this correct? NO Express the correct reading using scientific notation mL or 1.50 x101 mL 10

Reading a Vernier A Vernier allows a precise reading of some value.
In the figure to the left, the Vernier moves up and down to measure a position on the scale. This could be part of a barometer which reads atmospheric pressure. The "pointer" is the line on the vernier labeled "0". Thus the measured position is almost exactly 756 in whatever units the scale is calibrated in. If you look closely you will see that the distance between the divisions on the vernier are not the same as the divisions on the scale. The 0 line on the vernier lines up at 756 on the scale, but the 10 line on the vernier lines up at 765 on the scale. Thus the distance between the divisions on the vernier are 90% of the distance between the divisions on the scale. 756

A Vernier allows a precise reading of some value. In the figure to the left, the Vernier moves up and down to measure a position on the scale. This could be part of a barometer which reads atmospheric pressure. The "pointer" is the line on the vernier labeled "0". Thus the measured position is almost exactly 756 in whatever units the scale is calibrated in. If you look closely you will see that the distance between the divisions on the vernier are not the same as the divisions on the scale. The 0 line on the vernier lines up at 756 on the scale, but the 10 line on the vernier lines up at 765 on the scale. Thus the distance between the divisions on the vernier are 90% of the distance between the divisions on the scale. 770 5 10 Vernier 760 Scale 756 Image courtesy: 750

750 740 760 If we do another reading with the vernier at a different position, the pointer, the line marked 0, may not line up exactly with one of the lines on the scale. Here the "pointer" lines up at approximately on the scale. If you look you will see that only one line on the vernier lines up exactly with one of the lines on the scale, the 5 line. This means that our first guess was correct: the reading is 5 10 741.9 What is the reading now?

750 740 760 If we do another reading with the vernier at a different position, the pointer, the line marked 0, may not line up exactly with one of the lines on the scale. Here the "pointer" lines up at approximately on the scale. If you look you will see that only one line on the vernier lines up exactly with one of the lines on the scale, the 5 line. This means that our first guess was correct: the reading is 5 10 756.0 What is the reading now?

750 740 760 5 10 Here is a final example, with the vernier at yet another position. The pointer points to a value that is obviously greater than and also less than Looking for divisions on the vernier that match a division on the scale, the 8 line matches fairly closely. So the reading is about In fact, the 8 line on the vernier appears to be a little bit above the corresponding line on the scale. The 8 line on the vernier is clearly somewhat below the corresponding line of the scale. So with sharp eyes one might report this reading as ± 0.02. This "reading error" of ± 0.02 is probably the correct error of precision to specify for all measurements done with this apparatus.

How to Read a Thermometer (Celcius)
10 10 100 5 5 5 50 4.0 oC 8.3 oC 64 oC 3.5 oC

Record the Temperature (Celcius)
60oC 6oC 50oC 5oC 25oC 100oC 100oC 40oC 4oC 20oC 80oC 80oC 30oC 3oC 15oC 60oC 60oC 20oC 2oC 10oC 40oC 40oC 10oC 1oC 5oC 20oC 20oC 0oC 0oC 0oC 0oC 0oC A 30.0oC B 3.00oC C 19.0oC D 48oC E 60.oC

Measurements Metric (SI) units Prefixes Uncertainty Conversion factors
Length Mass Volume Conversion factors Significant figures Density Problem solving with conversion factors Timberlake, Chemistry 7th Edition, page 40

MEASUREMENT Using Measurements
Courtesy Christy Johannesson

Accuracy vs. Precision ACCURATE = Correct PRECISE = Consistent
Accuracy - how close a measurement is to the accepted value Precision - how close a series of measurements are to each other ACCURATE = Correct PRECISE = Consistent Courtesy Christy Johannesson

Percent Error Indicates accuracy of a measurement your value
accepted value Courtesy Christy Johannesson

Percent Error % error = 2.9 %
A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL. % error = 2.9 % Courtesy Christy Johannesson

Significant Figures Indicate precision of a measurement.
Recording Sig Figs Sig figs in a measurement include the known digits plus a final estimated digit 2.35 cm Courtesy Christy Johannesson

Significant Figures Counting Sig Figs (Table 2-5, p.47)
Count all numbers EXCEPT: Leading zeros Trailing zeros without a decimal point -- 2,500 Courtesy Christy Johannesson

Counting Sig Fig Examples
Significant Figures Counting Sig Fig Examples 4 sig figs 3 sig figs 3. 5,280 3. 5,280 3 sig figs 2 sig figs Courtesy Christy Johannesson

Significant Figures (13.91g/cm3)(23.3cm3) = 324.103g 324 g
Calculating with Sig Figs Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm3)(23.3cm3) = g 4 SF 3 SF 3 SF 324 g Courtesy Christy Johannesson

Significant Figures 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL
Calculating with Sig Figs (con’t) Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer. 3.75 mL mL 7.85 mL 3.75 mL mL 7.85 mL 224 g + 130 g 354 g 224 g + 130 g 354 g  7.9 mL  350 g Courtesy Christy Johannesson

Significant Figures Calculating with Sig Figs (con’t)
Exact Numbers do not limit the # of sig figs in the answer. Counting numbers: 12 students Exact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm Courtesy Christy Johannesson

Significant Figures Practice Problems 5. (15.30 g) ÷ (6.4 mL)
4 SF 2 SF = g/mL  2.4 g/mL 2 SF g g  18.1 g 18.06 g Courtesy Christy Johannesson

Scientific Notation 65,000 kg  6.5 × 104 kg
Converting into scientific notation: Move decimal until there’s 1 digit to its left. Places moved = exponent. Large # (>1)  positive exponent Small # (<1)  negative exponent Only include sig. figs. Courtesy Christy Johannesson

Scientific Notation Practice Problems 7. 2,400,000 g 8. 0.00256 kg
9. 7  10-5 km  104 mm 2.4  106 g 2.56  10-3 kg km 62,000 mm Courtesy Christy Johannesson

Scientific Notation Calculating with scientific notation
(5.44 × 107 g) ÷ (8.1 × 104 mol) = Type on your calculator: EXP EE EXP EE ENTER EXE 5.44 7 8.1 ÷ 4 = = 670 g/mol = 6.7 × 102 g/mol Courtesy Christy Johannesson

Proportions Direct Proportion Inverse Proportion y x y x
Courtesy Christy Johannesson

Reviewing Concepts Measurement
Why do scientists use scientific notation? What system of units do scientists use for measurements? How does the precision of measurements affect the precision of scientific calculations? List the SI units for mass, length, and temperature. Prentice Hall Physical Science Concepts in Action (Wysession, Frank, Yancopoulos) 2004 pg 20 Why do scientists use scientific notation? Scientific notation makes very large or very small numbers easier to work with. What system of units do scientists use for measurements? Scientists use a set of measuring units called SI. How does the precision of measurements affect the precision of scientific calculations? The precision of a calculation is limited by the least precise measurement used in the calculation.

Rules for Counting Significant Figures
1. Nonzero integers always count as significant figures. 2. Zeros: There are three classes of zeroes. Leading zeroes precede all the nonzero digits and DO NOT count as significant figures. Example: has ____ significant figures. Captive zeroes are zeroes between nonzero numbers. These always count as significant figures. Example: has ____ significant figures. Trailing zeroes are zeroes at the right end of the number. Trailing zeroes are only significant if the number contains a decimal point. Example: x 102 has ____ significant figures. Trailing zeroes are not significant if the number does not contain a decimal point. Example: 100 has ____ significant figure. Exact numbers, which can arise from counting or definitions such as 1 in = 2.54 cm, never limit the number of significant figures in a calculation. 2 4 3 1 Ohn-Sabatello, Morlan, Knoespel, Fast Track to a 5 Preparing for the AP Chemistry Examination 2006, page 53

Significant figures: Rules for zeros
Leading zeros are not significant. Leading zero 0.421 – three significant figures Captive zeros are significant. Captive zero 4012 – four significant figures Trailing zeros are significant. Trailing zero 114.20 – five significant figures

Significant Digits Significant Digits Significant Digits Keys

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