Foundations of College Chemistry, 1 - PowerPoint Presentation

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Foundations of College Chemistry, 1 - PPT Presentation

5 th Ed Morris Hein Susan Arena and Cary Willard amp Schultz Careful and accurate measurements o f ingredients are important both when c ooking and in the chemistry laboratory 2 Standards for ID: 741128

reserved amp sons rights amp reserved rights sons wiley john 2016 significant figures copyright measurement unit units number mass

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Slide1

Foundations of College Chemistry, 15th Ed.

Morris Hein, Susan Arena, and Cary Willard & Schultz

Careful and accurate measurementsof ingredients are important both whencooking and in the chemistry laboratory!

2 Standards for Measurement with Tables

2.1 Scientific Notation2.2 Measurement and Uncertainty

2.3 Significant Figures

A. Rounding Off Numbers2.4 Significant Figures in Calculations A. Addition or Subtraction

Multiplication or Division

2.5

The Metric System A. Measurement of Length B. Measurement of Mass C. Measurement of Volume2.6 Dimensional Analysis: A Problem Solving Method2.7 Percent2.8 Measurement of Temperature2.9 Density

Chapter Outline

Scientific Notation: A way to write very large or smallnumbers (measurements) in a compact form.

2.468 x 108

Number written from 1-10

Raised to a power (-/+ or fractional)

Move the decimal point in the original number so that it is located after the first nonzero digit.

Multiply this number by 10 raised to the number of places the decimal point was moved.

Exponent sign indicates which direction the decimal was moved. Method for Writing a Number in Scientific Notation2.1 Scientific NotationCopyright © 2016 John Wiley & Sons, Inc. All rights reserved.Slide4

Write 0.000423 in scientific notation.Place the decimal between the 4 and 2.

4.23The decimal was moved

4 places so the exponent should be a 4. 4.23 x 10

-4

The decimal was moved to the

right

What is the correct scientific notation for the number 353,000 (to 3 significant figures)?

a. 35.3 x 104

b. 3.53 x 105c. 0.353 x 106d. 3.53 x 10

-5

e. 3.5 x 105

Scientific Notation Practice

Measurement: A quantitative observation. Examples: 1 cup, 3 eggs, 5 molecules, etc.

Measurements are expressed by a numerical value and

2. a unit of the measurement. Example: 50 kilometers

Numerical Value

Unit

A measurement always requires a unit.

21.2 ºCUncertainty exists in the last digit of the measurement because this portion of the numerical value is estimated.

The other two digits are certain. These digits would not change in readings made by one person to another.

Every measurement made with an instrument requires estimation. Numerical values obtained from measurements

re never exact values.

Measurement and Uncertainty

Some degree of uncertainty exists in all measurements.By convention, a measurement typically includes all

certain digits plus one digit that is estimated. Because of this level of uncertainty, any measurement

is expressed by a limited number of digits.These digits are called significant figures.

Recorded as 22.0 °C (3 significant figures with uncertainty in the last digit)Recorded as 22.11 °

C (4 significant figures with uncertainty in the last digit)

Because all measurements involve uncertainty, we must be careful to use the correct number of significant figures in calculations.

Ex. 12 inches are always in 1 foot Exact numbers have no uncertainty.

3. Zeroes are significant when: a. They are in between non zero digits Ex. 75.04 has 4 significant figures (7,5,0 and 4)b. They are at the end of a number after a decimal point.

Ex. 32.410 has five significant figures (3,2,4,1 and 0) Slide12

Zeroes are not significant when:a. They appear before the first nonzero digit.

Ex. 0.00321 has three significant figures (3,2 and 1)

They appear at the end of a number without a decimal point. Ex. 6920 has three significant figures (6,9 and 2)

When in doubt if zeroes are significant,

use scientific notation!

Rules for Counting Significant Figures

How many significant figures are in the following measurements?

3.2 inches2 significant figures25.0 grams

3 significant figures103 peopleExact number (∞ number of sig figs)

0.003 kilometers

1 significant figure

Let’s Practice!

With a calculator, answers are often expressed with moredigits than the proper number of significant figures.

These extra digits are omitted from the reported number,and the value of the last digit is determined by rounding off.

1. < 5, the digit retained does not change. Ex. 53.

2305

= 53.2 (other digits dropped)

digit retained2. ≥ 5, the digit retained is increased by one. Ex. 11.789 = 11.8 (other digits dropped) digit rounded up to 8 Rules for Rounding OffIf the first digit after the number that will be retained is:Rounding Off NumbersCopyright © 2016 John Wiley & Sons, Inc. All rights reserved.Slide15

Round off the following numbers to the given number of significant figures.

79.137 (four)79.140.04345 (three)

0.0435136.2 (three)136

0.1790 (two)

0.18

Let’s Practice!

The results of a calculation are only as precise as the least precise measurement.

Calculations Involving Multiplication or DivisionThe significant figures of the answer are based on the

measurement with the least number of significant figures. Example79.2 x 1.1 = 87.12

The answer should contain

two

significant figures,

Round the following calculation to the correct number of significant figures.

a. 4.9b. 4.87

4.84.872e. 5.0

(12.18)(5.2)

= 4.872

The results of a calculation are only as precise as the least precise measurement.

Calculations Involving Addition or SubtractionThe significant figures of the answer are based on the

precision of the least precise measurement.Example Add 136.23, 79, and 31.7.

136.23

Round the following calculation to the correct number of significant figures.

a. 129.57b. 129.6

130129.5129142.57 - 13.0

142.57

13.0

Round the following calculation to the correct number of significant figures.

a. 0.69109b. 0.70

c. 0.693d. 0.6912.18

5.2

6.98

-The numerator must be rounded to the tenths place.12.18 - 5.210.17.010.1= 0.693069

Final answer is now rounded to 2 significant figures.

Let’s Practice!

How many significant figures should the answer to the following calculation contain?

a. 1

b. 2c. 3d. 4

1.6

Metric or International System (SI):Standard system of measurements for mass, length,

time and other physical quantities.

Based on standard units that change based on factors of 10.Prefixes are used to indicate multiples of 10.

This makes the metric system a decimal system.

Quantity

Unit Name

AbbreviationLengthMetermMassKilogramkgTemperatureKelvinK

Time

Second

Amount of Substance

Mole

mol

Electric current

Ampere

2.5

The Metric System

Meter (m): standard unit of length of the metric system.

Definition: the distance light travels in a vacuum during 1/299,792,458 of a second.

Common Length Relationships:

1 meter (m) = 100 centimeters (cm)

1 kilometer (km) = 1000 meters

Relationship Between the Metric and English System:

7/24/2017 4:48 PM

How to solve a problems just using units

A. You must write the following steps in

order to get full credit.

1. Write what you know.

2. Write what you don’t know.

3. Write a plan on how to get from the known to the unknown. 4. Write the conversion(s) you are going to use.Slide26

7/24/2017 4:48 PM

How to solve a problems just using units

A. You must write the following steps in

order to get full credit.

5. Complete the table

a. Draw a table based on the below: 1 column for known 1 column for each conversion 1 column for the unknown Every table has 2 rows

Slide27

7/24/2017 4:48 PM

How to solve a problems just using units

A. You must write the following steps in

order to get full credit.

5. Complete the table

Known_Unit

(Given)

Unknown_Units

Conversion (Answer)

Unknown_Unit

(Answer)

Known_Units

Conversion (Given)Slide28

7/24/2017 4:48 PM

How to solve a problems just using units

6. How do you know what goes on top in the conversion column?

The units you start with go on the bottom. The units you end with go on the top.

Known_Unit

(Given)

Unknown_Units

Conversion (Answer)

Unknown_Unit

(Answer)

Known_Units

Conversion (Given)Slide29

7/24/2017 4:48 PM

How to solve a problems just using units

7. The first column is always what you start with.

8. The last column is always what you need to end with.

Known_Unit

(Given)

Unknown_Units

Conversion (Answer)

Unknown_Unit

(Answer)

Known_Units

Conversion (Given)Slide30

7/24/2017 4:48 PM

How to solve a problems just using units

9. Notice the red units drop out,

Z*X/Z = X

and you are left with the answer.

Known_Unit

(Given)

Unknown_Units

Conversion (Answer)

Unknown_Unit

(Answer)

Known_Units

Conversion (Given)Slide31

7/24/2017 4:48 PM

How to solve a problems just using units

10. IE: How many inches are in X feet?

Known: X feet

?: inches

Plan: feet  inches Conversion: 1_ft = 12_inSlide32

7/24/2017 4:48 PM

How to solve a problems just using units

10: How many inches are in X feet?

Known:

X feet

?: inches Plan: feet 

inches

Conversion:

1_ft

12_in

X feet

12 inches

inches

1 feetSlide33

7/24/2017 4:48 PM

How to solve a problems just using units

10: How many inches are in X feet?

The vertical lines mean multiplication

The horizontal lines mean division

Since its either multiplication or division there is no order of operations!

X feet

12 inches

(X *

12) inches

1 feetSlide34

Conversion factor: A ratio of equivalent quantities.

Dimensional analysis: converts one unit of measure to

another by using conversion factors.Example: 1 km = 1000 m

Conversion factor:

1 km

1000 m

or1 km1000 mConversion factors can always be written two ways. Both ratios are equivalent quantities and will equal 1.

2.6 Dimensional Analysis:

A Problem Solving Method

Any unit can be converted to another unit bymultiplying the quantity by a conversion factor.

Unit

1 x conversion factor = Unit2Example

A conversion factor must cancel the

original unit

and

leave behind only the new (desired) unit.The original unit must be in the denominator and new unitmust be in the numerator to cancel correctly.1 km1000 m

= 0.002

Units are treated like numbers and can cancel.

Dimensional Analysis:

A Problem Solving MethodSlide36

Many chemical principles or problems are illustrated mathematically.

A systematic method to solve these types of

numerical problems is key.Our approach: the

dimensional analysis method

Create

solution maps

to solve problems. Overall outline for a calculation/conversionprogressing from known to desired quantities.Copyright © 2016 John Wiley & Sons, Inc. All rights reserved.Dimensional Analysis:A Problem Solving MethodSlide37

Convert 215 centimeters to meters.

Solution Map:

known quantitydesired quantity

100 cm= 2.15 m215 cmx

Convert 125 meters to kilometers.

Solution Map:

1000 m

= 0.125

125 m

nown quantity

desired quantity

Dimensional Analysis:

A Problem Solving PracticeSlide38

a. 30,000b. 300,000

c. 300d. 3000

Solution Map:1,000,000 μm

1 m

= 30,000

m0.03 mxHow many micrometers are in 0.03 meters?known quantity

desired quantity

Let’s Practice!

Some problems require a series of conversions to get to the desired unit.

Each arrow in the solution map corresponds to

the use of a conversion factor.Example

Convert from days to seconds.

Solution Map:

24 hours

1 day60 minutes1 hour

= 8.64 x 10

sec

1 day

60 seconds

1 minute

days

hours minutes seconds

Dimensional Analysis:

A Problem Solving Method

How many feet are in 250 centimeters? Solution Map:

1 inch

2.54 cm

1 foot

12 inches

= 8.20

ft250 cmMetric to English Conversionsxx

inches

Dimensional Analysis:

A Problem Solving Practice

2.54 cmHow many meters are in 5 yards?

Solution Map:

3 feet 1

yard

12 inches

1 foot

= 4.57 m5 yardsMetric to English Conversions

a. 9.14

b. 457

c. 45.7

d. 4.57

1 inch

100 cm

1 m

yards

feet inches cm m

Let’s Practice!

How many cm3 are in a box that measures 2.20 x 4.00 x 6.00 inches?

Solution Map:

2.54 cm 1 in

= 865 cm

52.8 in

3Metric to English Conversionsx2.20 in x 4.00 in x 6.00 in3(in

cm)

= 52.8 in

Let’s Practice!

Mass: amount of matter in an object

Mass is measured on a balance. Weight: effect of gravity on an object.

Mass is independent of location, but weight is not. Weight is measured on a scale, which measures force against a spring.

Mass is the standard measurement of the metric system.

The SI unit of mass is the kilogram.

(The gram is too small a unit of mass to be the standard unit.)

1 kilogram (kg) is the mass of a Pt-Ir cylinder standard.

Metric to English ConversionsMetric Units of Mass

Convert 343 grams to kilograms.Solution Map:

1 kg

1000 g

= 0.343 kg

343 g

Use the new conversion factor:1 kg1000 gor1000 g1 kg

Let’s Practice!

a. 120b. 1.2 x 104

c. 1200d. 1.2

How many centigrams are in 0.12 kilograms?Solution Map:

1000 g

= 1.2 x 104 cg0.12 kgx 100 cg1

Let’s Practice!

Volume: the amount of space occupied by matter.

The SI unit of volume is the cubic meter (m3)

The metric volume more typically used is the liter (L) or milliliter (mL).

liter is a cubic decimeter of water (1 kg) at 4 °C.

Volume can be measured with several laboratory devices.

Common Volume Relationships 1 L = 1000 mL = 1000 cm

31 mL = 1 cm31 L = 1.057 quarts (

qt)Convert 0.345 liters to milliliters.

1000 mL

= 345 mL0.345 LxVolume ProblemSolution Map:

Measurement of Volume

How many milliliters are in a cube with sides measuring 13.1 inches each?

2.54 cm1 in.

= 33.3 cm

13.1 in.

Solution Map:

a. 3690b. 3.69c. 369d. 3.69 x 104 Determine the volume of the cube:Volume = (33.3 cm)

x (33.3 cm) x

(33.3 cm

)

3.69 x

1 mL

1 cm

= 3.69 x 10

cm cm

Convert from inches to cm:

= 3.69 x

Convert to the proper units:

Let’s Practice!

Percent can be defined as

parts per 100 x parts = x where x equals percent 100 total parts 100

If we do not have 100 parts then you must convert to parts per 100

Use the formula

percent = parts x 100% total partsSlide51

Solve for percent

Use the formula percent = parts x 100% total parts

What is the total number flowers? 25 + 33 + 22 = 75 total

Percent red flowers =

25 red

x 100% = 33% 75 totalSlide52

Use the formula mass percent =

mass part x 100% mass total

Since the same units cancel out any mass units can be used in the formulaSlide53

Use the formula mass percent = mass part x 100%

mass total14%O 7.64%Ni

65%O 35%Ni

35%

65%Ni53%O 47%NiTotal mass = 14.00g + 7.64g = 21.64g%Ni = 14.00gNi x 100% = 65%Ni 21.64g total%O = 7.64gO x 100% = 35%O

21.64g total

The total of the masses should equal 100%Slide54

Thermal energy: A form of energy involving the motion of small particles of matter.

Temperature: measure of the intensity of thermal energy

of a system (i.e. how hot or cold). Heat: flow of energy due to a temperature difference.

Heat flows from regions of higher to lower temperature.

The SI unit of temperature is the Kelvin (K).

Temperature is measured using a thermometer.

Temperature can be expressed in 3 commonly used scales.Celsius (°C), Fahrenheit (°F), and Kelvin (K).

Celsius and Fahrenheit are both measured in degrees, but the scales are different.

The Fahrenheit scale has a range of 180° between freezing and boiling.

C°FKFreezing Point0 °C32 °F273.15 KBoiling Point100 °C212 °F

373.15 K

The lowest temperature possible on the Kelvin scale

is absolute zero (-

273.15 °C

Different Temperature Scales

Mathematical Relationships Between Temperature ScalesConvert 723 °

C to temperature in both K and °F.°F = 9/5(

723) + 32 = 1333 °F K = 723 + 273.15 = 996 K

Temperature Problem

Solution Map:

K = °C + 273.15

°F = 9/5(°C) + 32 °C K

°C

°F

Converting Between Temperature Scales

What is the temperature if 98.6 °F is converted to °C?

Solution Map:

a. 37b. 371c. 210

d. 175

98.6 = 9/5

(

Density (d): the ratio of the mass of a substance to the volume occupied by that mass.

Density is a physical

property of a substance. The units of density are generally expressed as g/mL org/cm3 for solids and liquids and g/L for gases.

The volume of a liquid changes as a function of temp,

so density must be specified for a given temperature.

Ex.

The density of H2O at 4 ºC is 1.0 g/mL while the density is 0.97 g/mL at 80 ºC. d =volumemass

2.9

Density

Specific gravity (sp gr): ratio of the density of a substance

to the density of another substance (usually H2O at 4 ºC).

An important measurement of proper kidney function is the kidney’s ability to concentrate urine as measured by specific gravity.

What is the SG of a sample of urine with a density of 1.031g/mL?

Specific Gravity =

density of sample_____ density of water at 4oCSolve Specific Gravity = 1.031g/mL 1.000g/mL= 1.031Slide61

Calculate the density of a substance if 323 g occupy a volume of 53.0 mL.

323 g

53.0 mL= 6.09 g/mL

Solution:

d =

volume

The density of gold is 19.3 g/mL.

What is the volume of 25.0 g of gold? Solution Map:

Use density as a conversion factor! 1 mL

19.3 g

= 1.30 mL

25.0 g

What is the mass of 1.50 mL of ethyl alcohol?(d = 0.789 g/mL at 4 ºC)

Solution Map:

a. 1.90 gb. 1.18 gc. 0.526 g

2.32 g

1.50 g

0.789 g

1 mL= 1.18 g1.50 mLxmL

Let’s Practice!

Write decimal numbers in scientific notation.2.1 Scientific Notation

Explain the significance of uncertainty in measurements i

n chemistry and how significant figures are used to indicate a measurement. 2.2 Measurement and Uncertainty

Determine the number of significant figures in a given

easurement and round measurements to a specific number

Apply the rules for significant figures in calculationsinvolving addition, subtraction, multiplication, and division.

2.4 Significant Figures in CalculationsName the units for mass, length, and volume in the metric

system and convert from one unit to another.2.5 The Metric SystemUse dimensional analysis to solve problems

involving unit conversions.

2.6 Dimensional Analysis: A Problem Solving Method

Learning Objectives

Convert measurements among the Fahrenheit, Celsius and Kelvin temperature scales.

2.8 Measurement of TemperatureSolve problems involving density.

2.7 Percent

Solve problems involving percent.

Foundations of College Chemistry, 1 - PowerPoint Presentation

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