Measurements in Chemistry Precise measurements are essential in chemistry

Measurements in Chemistry

Precise measurements are essential in chemistry.

Part 1

Recording Data

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..

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

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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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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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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Significant Figures

What is the length of the cylinder?


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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.


Measurement of Volume Using a Buret

1.4

Part 2

Counting Significant Figures


I. Rules for Counting Significant Figures

• Nonzero integers always count as significant figures:

3456 g has 4 sig figs

1.5

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 ___


2. Rules for Counting Significant Figures (continued)

• Leading zeros do not count as significant figures:

0.048 g has 2 sig figs

1.5

Leading ZerosLeading Zeros


0.008 mm0.008 mm ________

0.0156 oz0.0156 oz ________

0.0042 lb0.0042 lb ________

0.000262 mL 0.000262 mL ____


3. Rules for Counting Significant Figures (continued)

• Captive zeros always count as significant figures:

16.07 has 4 sig figs

1.5

Captured ZerosCaptured Zeros


50.8 mm50.8 mm ________

2001 min2001 min ________

0.702 lb0.702 lb ________

0.00405 m0.00405 m ________ ____


4. Rules for Counting Significant Figures

• Trailing zeros are significant only if the number contains a decimal point:

9.300 m has 4 sig figs150 m 2 sig figs

1.5

Trailing ZerosTrailing Zeros


25,000 in. 25,000 in. ________

200. yr200. yr ________

48,600 gal48,600 gal ________

25,005,000 g 25,005,000 g ________

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


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

Part 3

Calculations with Significant Figures

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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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)

Adding and SubtractingAdding and Subtracting

The answer has the same number of The answer has the same number of decimal places decimal places as 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


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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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?)


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

Scientific Notation

• Scientific notation is simply a method for expressing, and working with, very large or very small numbers.

The number 567000 in scientific notation is written as

exponent 5.67 x 105

coefficient base

Practice Problems

• http://www.fordhamprep.org/gcurran/sho/sho/review/rev25a.htm

Do A#3

http://www.fordhamprep.org/gcurran/sho/sho/review/rev25a.htm

http://www.fordhamprep.org/gcurran/sho/sho/review/rev25a.htm

Metric Prefixes http://www.allaboutcircuits.com/vol_5/chpt_1/10.html

http://www.allaboutcircuits.com/vol_5/chpt_1/10.html

Converting Units-Dimensional Analysis Problem: Convert 20 in/s into ft/min Given 12in = 1 ft and 1 min = 60 s

• Step 1. Express what you are given and what units you want .

• Step 2. Insert the required conversion factors to change between units

• Step 3. Cancel units where you can, and solve the math.

• http://www.mathsisfun.com/measure/metric-system.html

Convert 400 ft/ml to mile/L

http://www.mathsisfun.com/measure/metric-system.html

Examples: IMP: You must have the converting factors

• Example 1. A student determines that the density of a certain material is 4.46 kg/cm3. What would be the density of this material in g/L? converting factor 1000 cm3 = 1L

• Example 2. Imagine that water is leaking from a container, at a rate of 1.2 ml/hour. If this rate does not change, how many liters of water will be lost in a week?

Converting factors 1 L = 1000 ml

• Example 3. Change 6.34 km/h to m/s• • Practice the following worksheet a , then do A#4• http://www.fordhamprep.org/gcurran/sho/sho/lessons/lesson24.htm

http://www.fordhamprep.org/gcurran/sho/sho/lessons/lesson24.htm

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Measurements in Chemistry Precise measurements are essential in chemistry