Chapter 2a Measurements and Calculations. Chapter 2 Table of Contents Return to TOC 2.1 Scientific...

Chapter 2a

Measurements and Calculations

Chapter 2

Table of Contents

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2.1 Scientific Notation

2.2 Units

2.3 Measurements of Length, Volume, and Mass

2.4 Uncertainty in Measurement

2.5 Significant Figures

Section 2.1

Scientific Notation

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Measurement

• Quantitative observation.• Has 2 parts – number

and unit. Number tells

comparison. Unit tells scale.

Section 2.1

Scientific Notation

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• Technique used to express very large or very small numbers.

• Expresses a number as a product of a number between 1 and 10 and the appropriate power of 10.

Section 2.1

Scientific Notation

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Using Scientific Notation

• Any number can be represented as the product of a number between 1 and 10 and a power of 10 (either positive or negative).

• The power of 10 depends on the number of places the decimal point is moved and in which direction.

Section 2.1

Scientific Notation

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• The number of places the decimal point is moved determines the power of 10. The direction of the move determines whether the power of 10 is positive or negative.

Section 2.1

Scientific Notation

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• If the decimal point is moved to the left, the power of 10 is positive.

345 = 3.45 × 102 very large number

• If the decimal point is moved to the right, the power of 10 is negative.

0.0671 = 6.71 × 10–2 very small numberIn Webassign homework use format:

345 = 3.45e020.0671 = 6.71e-02

Section 2.1

Scientific Notation

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Concept Check

Which of the following correctly expresses 7,882 in scientific notation?

a) 7.882 × 104

b) 788.2 × 103

c) 7.882 × 103

d) 7.882 × 10–3

Section 2.1

Scientific Notation

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Concept Check

Which of the following correctly expresses 0.0000496 in scientific notation?

a) 4.96 × 10–5

b) 4.96 × 10–6

c) 4.96 × 10–7

d) 496 × 107

Section 2.1

Scientific Notation

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Precision vs. Accuracy

good precision poor precision

good precisionpoor accuracy good accuracy

good accuracy

Section 2.1

Scientific Notation

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Measurement Accuracy

How long is this line?

There is no such thing as a totally accurate measurement!

Section 2.2

Units

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• Quantitative observation consisting of two parts. number scale (unit)

Nature of Measurement

Measurement

• Examples 20 grams 6.63 × 10–34 joule·seconds

If a CHP asks you what do you have and you answer I have 3 kilos, you may go to jail. You should have said I have 3 kg of doughnuts for my chemistry instructor.

Section 2.1

Scientific Notation

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Length Mass Volume Time

meter gram Liter second

SI

Sys

tem Km=1000m Kg=1000g KL=1000L 1min=60sec

100cm=1m 1000mg=1 g 1000mL=1L 60min=1hr

1000mm=1m

Bri

tish

12in=1ft 16oz=1 lb 4qt=1gal (same)

3ft=1yd 2000 lb=1 ton 2pts=1qt

5280ft=1mile

Foot pound gallon second

lll

Measurement in Chemistry

http://www.kickstarter.com/projects/52746223/the-state-of-the-unit-the-kilogram-documentary-fil

Section 2.1

Scientific Notation

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2.54 cm = 1 in

1.06 qt = 1 L

454 g = 1 lb

1 (cm)3 = 1 cc = 1 ml = 1 gwater

Conversion between British and SI Units

Section 2.2

Units

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• Prefixes are used to change the size of the unit.

Prefixes Used in the SI System

Section 2.3

Measurements of Length, Volume, and Mass

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• Fundamental SI unit of length is the meter.

Length

Section 2.3


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Volume

• Measure of the amount of 3-D space occupied by a substance.

• SI unit = cubic meter (m3)

• Commonly measure solid volume in cm3.

• 1 mL = 1 cm3

• 1 L = 1 dm3

Section 2.3


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Mass

• Measure of the amount of matter present in an object.

• SI unit = kilogram (kg)• 1 kg = 2.2046 lbs• 1 lb = 453.59 g

Section 2.3


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Copyright © Cengage Learning. All rights reserved

Concept Check

Choose the statement(s) that contain improper use(s) of commonly used units (doesn’t make sense)?

A gallon of milk is equal to about 4 L of milk. A 200-lb man has a mass of about 90 kg. A basketball player has a height of 7 m tall. A nickel is 6.5 cm thick.

Section 2.4

Uncertainty in Measurement

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• A digit that must be estimated is called uncertain.

• A measurement always has some degree of uncertainty.

• Record the certain digits and the first uncertain digit (the estimated number).

Section 2.4


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Measurement of Length Using a Ruler

• The length of the pin occurs at about 2.85 cm. Certain digits: 2.85 Uncertain digit: 2.85

Estimate between smallest division!

Section 2.4


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Significant Figures

• Numbers that measure or contribute to our accuracy.• The more significant figures we have the more accurate

our measurement.• Significant figures are determined by our measurement

device or technique.

Section 2.4


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Rules of Determining the Number of Significant Figures

1. All non-zero digits are significant.

203 = 3 sig figs 1.003 = 4 sig figs 1,030.2 = 5 sig figs

2. All zeros between non-zero digits are significant.

234 = 3 sig figs 1.333 = 4 sig figs 1,234.2 = 5 sig figs

Section 2.4


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3. All zeros to the right of the decimal and to the right of the last non-zero digit are significant.

0.0200 = 3 sig figs 0.1220 = 4 sig figs 0.000000012210 = 5 sig figs

4. All zeros to the left of the first non-zero digit are NOT significant.

2.30 = 3 sig figs 1.000 = 4 sig figs 3.4500 = 5 sig figs

Section 2.4


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5. Zeros to the right of the first non-zero digit and to the left of the decimal may or may not be significant. They must be written in scientific notation.

2300 = 2.3 x 103 or 2.30 x 103 or 2.300 x 103

2 sig figs 3 sig figs 4 sig figs

Section 2.4


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6. Some numbers have infinite significant figures or are exact numbers.

233 people 14 cats (unless in biology lab)

7 cars on the highway 36 schools in town

Section 2.4


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How many significant figures are in each of the following?

1) 23.34

2) 21.003

4 significant figures

4 significant figures3) .0003030

4) 210

5) 200 students

6) 3000

5 significant figures

2 or 3 significant figures

infinite significant figures

1, 2, 3, or 4 significant figures

Section 2.4


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Chapter 2b

Measurements and Calculations

Section 2.4


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2.5 Significant Figures

2.6 Problem Solving and Dimensional Analysis

2.7 Temperature Conversions: An Approach to Problem Solving

2.8 Density

Section 2.4


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Using Significant Figures in Calculations

Addition and Subtraction1. Line up the decimals.

2. Add or subtract.

3. Round off to first full column.

23.345 +14.5 + 0.523 = ?

23.345 14.5+ 0.523 38.368 = 38.4 or three significant figures

Section 2.4


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Using Significant Figures in Calculations

Multiplication and Division

1. Do the multiplication or division.

2. Round answer off to the same number of significant figures as the least number in the data.

(23.345)(14.5)(0.523) = ? 177.0368075

= 177 or three significant figures

Section 2.5

Significant Figures

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1. If the digit to be removed is less than 5, the preceding digit stays the same. 5.64 rounds to 5.6 (if final result to 2 sig figs)

Rules for Rounding Off

Section 2.5

Significant Figures

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1. If the digit to be removed is equal to or greater than 5, the preceding digit is increased by 1. 5.64 rounds to 5.6 (if final result to 2 sig figs) 3.861 rounds to 3.9 (if final result to 2 sig figs)


Section 2.5

Significant Figures

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2. In a series of calculations, do within the parenthesis first and determine the significant figures and use that answer to calculate and find the significant figures after the multiplication and/or division.


Section 2.5

Significant Figures

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Concept Check

You have water in each graduated cylinder shown. You then add both samples to a beaker (assume that all of the liquid is transferred).

How would you write the number describing the total volume?

3.08 mL

What limits the precision of the total volume?

2.80 1st graduated cylinder

+ .280 2ndgraduated cylinder

3.080 or 3.08 ml

Section 2.6

Problem Solving and Dimensional Analysis

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Example #1

• To convert from one unit to another, use the equivalence statement that relates the two units.

1 ft = 12 in

The two unit factors are:

A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent?

1 ft 12 in and

12 in 1 ft

Section 2.6


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• Choose the appropriate conversion factor by looking at the direction of the required change (make sure the unwanted units cancel).

Example #1


6.8 ft12 in

1 ft

in

Section 2.6


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• Multiply the quantity to be converted by the conversion factor to give the quantity with the desired units.

• Correct sig figs? Does my answer make sense?

Example #1


6.8 ft12 in

1 ft

82 in

Section 2.6


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Example #2

An iron sample has a mass of 4.50 lb. What is the mass of this sample in grams?

(1 kg = 2.2046 lbs; 1 kg = 1000 g)

4.50 lbs1 kg

2.2046 lbs

1000 g

1 kg 3= 2.04 10 g

454 gOR 4.50 lbs x -------------- = 2043g = 2.04x103 g 1 lb

Section 2.6


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Concept Check

What data would you need to estimate the money you would spend on gasoline to drive your car from New York to Los Angeles? Provide estimates of values and a sample calculation.

Sample Answer:

Distance between New York and Los Angeles: 2500 miles

Average gas mileage: 25 miles per gallon

Average cost of gasoline: $3.25 per gallon

1 gal $3.252500 mi = $325

25 mi 1 gal = $(3.3x102)

Section 2.7

Temperature Conversions: An Approach to Problem Solving

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• Fahrenheit• Celsius• Kelvin

Three Systems for Measuring Temperature

Gabriel Fahrenheit

Lord Kelvin

Section 2.7


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The Three Major Temperature Scales

F = 1.8C + 32C = (F-32)/1.8K = C + 273

What is 35oC in oF? 95 oF

What is 90oF in oC? 32oC

What is 100K in oC? -173oC

Section 2.7


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Exercise

The normal body temperature for a dog is approximately 102oF. What is this equivalent to on the Kelvin temperature scale?

a) 373 K

b) 312 K

c) 289 K

d) 202 KC = (F-32)/1.8 = (102-32)/1.80 = 38.9oC

K = C + 273 = 38.9 + 273 = 312 K

Section 2.7


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Exercise

At what temperature does C = F?

Section 2.7


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• Since °C equals °F, they both should be the same value (designated as variable x).

• Use one of the conversion equations such as:

• Substitute in the value of x for both T°C and T°F. Solve for x.

Solution

FC

32

1.80

TT

Section 2.7


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Solution

FC

32

1.80

TT

32

1.80

xx

So –40°C = –40°F

40 x

1.80x = x -32 0.80x = -32

x = -32/0.80

Section 2.8

Density

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• Mass of substance per unit volume of the substance.

• Common units are g/cm3 or g/mL.

massDensity =

volume

Section 2.8

Density

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Measuring the Volume of a Solid Object by Water Displacement

Section 2.8

Density

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Example #1

massDensity =

volume

3

17.8 gDensity =

2.35 cm

Density = 37.57 g/cm

A certain mineral has a mass of 17.8 g and a volume of 2.35 cm3. What is the density of this mineral?

Section 2.8

Density

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Example #2

massDensity =

volume

What is the mass of a 49.6 mL sample of a liquid, which has a density of 0.85 g/mL?

0.85 g/mL = 49.6 mL

x

mass = = 42 gx

49.6 mL 0.85 g/mL = 42 mL

OR

g

Section 2.8

Density

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Exercise

If an object has a mass of 243.8 g and occupies a volume of 0.125 L, what is the density of this object in g/cm3?

a) 0.513

b) 1.95

c) 30.5

d) 1950

3

3cm

cm

243.8 g 1L 1mL = 1.95g/

0.125 L 1000mL 1

Section 2.8

Density

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Using Density as a Conversion Factor

How many lbs of sugar is in 945 gallons of 60.0 Brix (% sugar) orange concentrate if the density of the concentrate is 1.2854 g/mL?

945 gal 4 qt1 gal

1 L

1.06qt

1000 mL 1 L

1.2854 gT

1 mL60.0 gS

100 gT

1 lbs

454gS

= 6057.865514lbs = 6.06 x 103 lbs sugar

lbs of what? Coffee? Cocaine?

Section 2.8

Density

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Using Density as a Conversion Factor Using the Formula

How many lbs of sugar is in 256 L of 60.0 Brix (% sugar) orange concentrate if the density of the concentrate is 1.2854 g/mL?

DV = M

= 3.29 x 105 gT (1.2854 g/mL)(256,000 mL) = 329062.4 gT

Solve for Mass MD = V

3.29 x 105 gT 1 lbT

454 gT

60.0 lbsS

100 lbsT

= 434.8017621 lbsS

= 4.35 x 102 lbsS

= 435 lbsS

Section 2.8

Density

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Concept Check

Copper has a density of 8.96 g/cm3. If 75.0 g of copper is added to 50.0 mL of water in a graduated cylinder, to what volume reading will the water level in the cylinder rise?

a) 8.4 mL

b) 41.6 mL

c) 58.4 mL

d) 83.7 mL

3

3

cm

cm

1 1mL75.0g = 8.37mL Cu

8.96g 1

8.37 mL Cu + 50.0 mL water = 58.4 mL

Chapter 2a Measurements and Calculations. Chapter 2 Table of Contents Return to TOC 2.1 Scientific...

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