measurements in chemistry the vodcast for this powerpoint is divided in to 3 parts
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Measurements in Chemistry
The vodcast for this powerpoint is divided in to 3 parts
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Part 1
Recording Data
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Types of Observations and Types of Observations and MeasurementsMeasurements
• We make QUALITATIVE We make QUALITATIVE observations of reactions — observations of reactions — changes in color and physical state.changes in color and physical state.
• We also make QUANTITATIVE We also make QUANTITATIVE MEASUREMENTS, which involve MEASUREMENTS, which involve numbersnumbers..
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Copyright © Houghton Mifflin Company. All rights reserved. Chapter 1 | Slide 4
Nature of Measurement• Measurement – quantitative observation
consisting of two parts:NumberScale (unit)
• Examples:20 grams6.63 6.63 × 10× 10-34-34 joule·seconds
1.3
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Chemistry: An Integrated Approach, 3rd ed., Hill & Petrucci. ©2002 Prentice Hall. All rights reserved
Precision and Accuracy in Measurements• Precision – how closely repeated measurements
approach one another• Accuracy – closeness of measurement to “true”
(accepted) valueDarts are close together, but they
aren’t “bullseyes”.
Darts are close together, and are “bullseyes”.
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Chemistry: An Integrated Approach, 3rd ed., Hill & Petrucci. ©2002 Prentice Hall. All rights reserved
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Precision and Accuracy in Measurements
• In the real world, we never know whether the measurement we make is accurate
• We make repeated measurements, and strive for precision
• We hope (not always correctly) that good precision implies good accuracy
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Chemistry: An Integrated Approach, 3rd ed., Hill & Petrucci. ©2002 Prentice Hall. All rights reserved
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Uncertainty in Measurement
• In recording measurements, the numbers should be written in a way that reflects the precision of the measuring device.
• Significant figures – all known digits, plus the first uncertain (estimated) digit.
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Chemistry: An Integrated Approach, 3rd ed., Hill & Petrucci. ©2002 Prentice Hall. All rights reserved
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Significant Figures
What is the length of the cylinder?
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Chemistry: An Integrated Approach, 3rd ed., Hill & Petrucci. ©2002 Prentice Hall. All rights reserved
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Significant figures• The cylinder is 6.3 cm…plus a little more• The next digit is uncertain; 6.36? 6.37?• We use three significant figures to express
the length of the cylinder.
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Copyright © Houghton Mifflin Company. All rights reserved. Chapter 1 | Slide 10
Measurement of Volume Using a Buret
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Part 2
Counting Significant Figures
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Copyright © Houghton Mifflin Company. All rights reserved. Chapter 1 | Slide 12
Rules for Counting Significant Figures
• Nonzero integers always count as significant figures:
3456 g has 4 sig figs
1.5
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Counting Significant FiguresCounting Significant Figures
Number of Significant Figures
38.15 cm38.15 cm ______5.6 ft5.6 ft ______65.6 lb65.6 lb ______122.55 m122.55 m ___
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Copyright © Houghton Mifflin Company. All rights reserved. Chapter 1 | Slide 14
Rules for Counting Significant Figures (continued)
• Leading zeros do not count as significant figures:
0.048 g has 2 sig figs
1.5
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Leading ZerosLeading Zeros
Number of Significant Figures
0.008 mm0.008 mm ________
0.0156 oz0.0156 oz ________
0.0042 lb0.0042 lb ________
0.000262 mL 0.000262 mL ____
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Copyright © Houghton Mifflin Company. All rights reserved. Chapter 1 | Slide 16
Rules for Counting Significant Figures (continued)
• Captive zeros always count as significant figures:
16.07 has 4 sig figs
1.5
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Captured ZerosCaptured Zeros
Number of Significant Figures
50.8 mm50.8 mm ________
2001 min2001 min ________
0.702 lb0.702 lb ________
0.00405 m0.00405 m ________ ____
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Copyright © Houghton Mifflin Company. All rights reserved. Chapter 1 | Slide 18
Rules for Counting Significant Figures (continued)
• Trailing zeros are significant only if the number contains a decimal point:
9.300 m has 4 sig figs150 m has 2 sig figs
1.5
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Trailing ZerosTrailing Zeros
Number of Significant Figures
25,000 in. 25,000 in. ________
200. yr200. yr ________
48,600 gal48,600 gal ________
25,005,000 g 25,005,000 g ________
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Learning CheckLearning Check
A.A. Which answers contain 3 significant figures? Which answers contain 3 significant figures?1) 0.47601) 0.4760 2) 0.00476 2) 0.00476 3) 4760 3) 4760
B. B. All the zeros are significant in All the zeros are significant in
1) 0.00307 1) 0.00307 2) 25.300 2) 25.300 3) 2.050 x 10 3) 2.050 x 1033
C. C. 534,675 rounded to 3 significant figures is534,675 rounded to 3 significant figures is
1) 535 1) 535 2) 535,000 2) 535,000 3) 5.35 x 10 3) 5.35 x 1055
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Learning CheckLearning Check
In which set(s) do both numbers contain the In which set(s) do both numbers contain the samesame number of significant figures? number of significant figures?
1) 22.0 and 22.00 1) 22.0 and 22.00
2) 400.0 and 40 2) 400.0 and 40
3) 0.000015 and 150,0003) 0.000015 and 150,000
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Chemistry: An Integrated Approach, 3rd ed., Hill & Petrucci. ©2002 Prentice Hall. All rights reserved
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Significant figures are for measurements
• Defined and counting numbers do not have uncertainty.
• 14 people• 1000 m = 1 km• 7 beakers• These are exact numbers.• They have as many figures as are needed.
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Part 3
Calculations with Significant Figures
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Significant Numbers in CalculationsSignificant Numbers in Calculations
A calculated answer cannot be more precise than the A calculated answer cannot be more precise than the measuring tool. measuring tool.
A calculated answer must match the least precise A calculated answer must match the least precise measurement.measurement.
Significant figures are needed for final answers fromSignificant figures are needed for final answers from 1) adding or subtracting1) adding or subtracting
2) multiplying or dividing2) multiplying or dividing
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Chemistry: An Integrated Approach, 3rd ed., Hill & Petrucci. ©2002 Prentice Hall. All rights reserved
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Significant figures in calculated results
• Addition and Subtraction– Use the same number of decimal places in the result
as the data with the fewest decimal places.• 49.146 m + 72.13 m – 9.1434 m = ?
= 112.1326 m (calculator) = 112.13 m (two decimal
places)
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Adding and SubtractingAdding and Subtracting
The answer has the same number of decimal places as The answer has the same number of decimal places as the measurement with the fewest decimal places.the measurement with the fewest decimal places.
25.25.22 one decimal placeone decimal place
+ 1.+ 1.3434 two decimal placestwo decimal places 26.5426.54answer 26.5 answer 26.5 one decimal placeone decimal place
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Learning CheckLearning Check
In each calculation, round the answer to the correct In each calculation, round the answer to the correct number of significant figures.number of significant figures.A. 235.05 + 19.6 + 2.1 = A. 235.05 + 19.6 + 2.1 =
1) 256.751) 256.75 2) 256.8 2) 256.8 3) 2573) 257
B. 58.925 - 18.2B. 58.925 - 18.2==1) 40.7251) 40.725 2) 40.73 2) 40.73 3) 40.73) 40.7
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Chemistry: An Integrated Approach, 3rd ed., Hill & Petrucci. ©2002 Prentice Hall. All rights reserved
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Significant figures in calculated results
• Multiplication and division– Use the same number of significant figures in the
result as the data with the fewest significant figures.• 1.827 m x 0.762 m = 1.392174 m2 (calculator) = 1.39 m2 (three sig.
fig.)
• 453.6 g / 21 people= 21.6 g/person (calculator)= 21.60 g/person (four
sig. fig.)(Question: why didn’t we round to 22 g/person?)
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Learning CheckLearning Check
A. 2.19 X 4.2 = A. 2.19 X 4.2 = 1) 91) 9 2) 9.2 2) 9.2 3) 9.1983) 9.198
B. 4.311 ÷ 0.07 = B. 4.311 ÷ 0.07 = 1)1) 61.5861.58 2) 62 2) 62 3) 60 3) 60
C. C. 2.54 X 0.00282.54 X 0.0028 = = 0.0105 X 0.060 0.0105 X 0.060 1) 11.31) 11.3 2) 112) 11 3) 0.041 3) 0.041
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The End