SCIENTIFIC MEASUREMENT

CHEM IH: CHAPTER 3

Stating a MeasurementStating a Measurement

In every measurement there is aIn every measurement there is a

Number Number followed by a followed by a

Unit Unit from a measuring devicefrom a measuring device

The number should also be as precise as The number should also be as precise as

the measuring device.the measuring device.

Ex: Reading a MeterstickEx: Reading a Meterstick

. l. l22. . . . I . . . . I. . . . I . . . . I33 . . . .I . . . . I . . . .I . . . . I44. . cm. . cm

First digit (known)First digit (known) = 2 = 2 2.?? cm2.?? cm

Second digit (known)Second digit (known) = 0.7 = 0.7 2.7? cm2.7? cm

Third digit (estimated) between 0.05- 0.07Third digit (estimated) between 0.05- 0.07

Length reportedLength reported == 2.75 cm 2.75 cm

oror 2.74 cm 2.74 cm

oror 2.76 cm2.76 cm

UNITS OF MEASUREMENTUNITS OF MEASUREMENT

Use Use SI unitsSI units — based on the metric — based on the metric systemsystem

Length Length

MassMass

VolumeVolume

TimeTime

TemperatureTemperature

Meter, mMeter, m

Kilogram, kgKilogram, kg

Seconds, sSeconds, s

Celsius degrees, ˚CCelsius degrees, ˚Ckelvins, Kkelvins, K

Liter, LLiter, L

Metric PrefixesMetric Prefixes

Conversion FactorsConversion Factors

Fractions in which the numerator and Fractions in which the numerator and denominator are EQUAL quantities expressed denominator are EQUAL quantities expressed in different unitsin different units

Example: 1 hr. = 60 min

Factors: 1 hr. and 60 min60 min 1 hr.

How many minutes are in 2.5 hours?

Conversion factor

2.5 hr x 2.5 hr x 60 min 60 min = 150 min = 150 min

1 hr1 hr

cancel

By using dimensional analysis / factor-label method, the By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!and the UNITS are calculated as well as the numbers!

Learning Check

How many seconds are in 1.4 days?

Unit plan: days hr min seconds

1.4 days x 24 hr x ___min x ____ s = 1 day hr min

ANSWER: 120,960 s.

Significant Figures (Honors only)Significant Figures (Honors only)

The numbers reported in a The numbers reported in a measurement are limited by the measurement are limited by the measuring toolmeasuring tool

Significant figures in a Significant figures in a measurement include the known measurement include the known digits plus one estimated digitdigits plus one estimated digit

Counting Significant Figures: Counting Significant Figures: Non-Zero Digits (Honors Only)Non-Zero Digits (Honors Only)

RULE 1. All non-zero digits in a measured RULE 1. All non-zero digits in a measured number ARE significant. number ARE significant.

#of Significant Figures

38.15 cm38.15 cm 44

5.6 ft5.6 ft 22

65.6 lb65.6 lb ______

122.55 m122.55 m ___

Counting Significant Figures:Counting Significant Figures:Leading Zeros (Honors Only)Leading Zeros (Honors Only)

RULE 2. Leading zeros in decimal numbers RULE 2. Leading zeros in decimal numbers

are are NOTNOT significant. significant.

#of Significant Figures

0.008 mm0.008 mm 11

0.0156 oz0.0156 oz 33

0.0042 lb0.0042 lb ________

0.000262 mL 0.000262 mL ____

Counting Significant Figures:Counting Significant Figures:Sandwiched Zeros (Honors Only)Sandwiched Zeros (Honors Only)

RULE 3. Zeros between nonzero numbers RULE 3. Zeros between nonzero numbers

ARE significant. (They can not be rounded ARE significant. (They can not be rounded

unless they are on an end of a number.)unless they are on an end of a number.)# of Significant Figures

50.8 mm50.8 mm 33

2001 min2001 min 44

0.702 lb0.702 lb ________

0.00405 m0.00405 m ____

Counting Significant Figures:Counting Significant Figures:Zeros @ the End of a # & to the Right Zeros @ the End of a # & to the Right of a Decimal of a Decimal (Honors Only)(Honors Only)

RULE 4. Trailing zeros at the end of a number RULE 4. Trailing zeros at the end of a number

and to the right of a decimal numbers ARE and to the right of a decimal numbers ARE

significant. significant.

# # of Significant Figures

43.00 m. 43.00 m. 44

200.00 yr200.00 yr 55

1.10 gal1.10 gal ________

0.04500 g 0.04500 g ________

Counting Significant Figures:Counting Significant Figures:Trailing Zeros (Honors Only)Trailing Zeros (Honors Only)

RULE 5. Trailing zeros in numbers without RULE 5. Trailing zeros in numbers without

decimals are NOT significant. They are decimals are NOT significant. They are

only serving as place holders.only serving as place holders.

# of Significant Figures

25,000 in. 25,000 in. 22

200. yr200. yr 33

48,600 gal48,600 gal ________

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

Counting Significant Figures:Counting Significant Figures:Unlimited Sig Figs (Honors Only)Unlimited Sig Figs (Honors Only)

RULE 6. 2 instances in which there are an RULE 6. 2 instances in which there are an

unlimited # of sig figs.unlimited # of sig figs.

a)a)CountingCounting. Ex: 23 people in our classroom. . Ex: 23 people in our classroom.

b)b)Exactly defined quantities.Exactly defined quantities. Ex: 1hr = 60 Ex: 1hr = 60

min.min.

Both are exact values. There is no uncertainty.

Neither of these types of values affect the Neither of these types of values affect the

process of rounding an answerprocess of rounding an answer..

Learning Check (Honors Only)Learning Check (Honors Only)

A. Which answers contain 3 significant A. Which answers contain 3 significant figures?figures?1) 0.47601) 0.4760 2) 0.00476 2) 0.00476 3) 4760 3) 4760

B. All the zeros are significant inB. All the zeros are significant in

1) 0.00307 1) 0.00307 2) 25.300 2) 25.300 3) 2.050 x 3) 2.050 x 101033

C. 534,675 rounded to 3 significant figures isC. 534,675 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

Learning Check Learning Check (Honors Only)(Honors Only)

In which set(s) do both numbers In which set(s) do both numbers contain the contain the samesame number of number of significant figures?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

Significant Numbers in Calculations Significant Numbers in Calculations (Honors Only)(Honors Only)

A calculated answer cannot be more precise A calculated answer cannot be more precise than the measuring tool. than the measuring tool.

A calculated answer must match the A calculated answer must match the least least precise precise measurement.measurement.

Significant figures are needed for final answers Significant figures are needed for final answers fromfrom

1) adding or subtracting1) adding or subtracting

2) multiplying or dividing2) multiplying or dividing If you must round to obtain the right # of sig If you must round to obtain the right # of sig

figs, do so figs, do so after all calcs are completeafter all calcs are complete

Adding and Subtracting (Honors Adding and Subtracting (Honors Only)Only)

The answer has the same number of The answer has the same number of decimal places as the measurement with decimal places as the measurement with the fewest decimal places.the fewest decimal places.

25.25.22 one decimal placeone decimal place

+ 1.+ 1.3434 two decimal placestwo decimal places

26.5426.54

answer 26.5answer 26.5 one decimal placeone decimal place

Learning Check (Honors Only)Learning Check (Honors Only)

In each calculation, round the answer to In each calculation, round the answer to the correct number of significant figures.the correct 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

Multiplying and Dividing (Honors (Honors Only)Only)

Round (or add zeros) to the Round (or add zeros) to the calculated answer until you have calculated answer until you have the same number of significant the same number of significant figures as the measurement with figures as the measurement with the fewest significant figures.the fewest significant figures.

Learning Check (Honors Only)Learning Check (Honors Only)

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) 603) 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

What is Scientific What is Scientific Notation?Notation? Scientific notation is a way of Scientific notation is a way of

expressing really big numbers or expressing really big numbers or really small numbers.really small numbers.

For very large and very small For very large and very small numbers, scientific notation is numbers, scientific notation is more concise.more concise.

Scientific notation consists of Scientific notation consists of two parts:two parts: A number between 1 and 10A number between 1 and 10

A power of 10A power of 10

N x 10N x 10xx

ExamplesExamples

Given: 289,800,000Given: 289,800,000 Use: 2.898 (moved 8 places)Use: 2.898 (moved 8 places) Answer:Answer: 2.898 x 102.898 x 108 8 (how many (how many

sig figs? Honors only)sig figs? Honors only)

Given: 0.000567Given: 0.000567 Use: 5.67 (moved 4 places)Use: 5.67 (moved 4 places) Answer:Answer: 5.67 x 105.67 x 10-4 -4 (How many sig (How many sig

figs? Honors only)figs? Honors only)

MEASURING MASS

A mole is a quantity of things, just as…

1 dozen = 12 things1 gross = 144 things1 mole = 6.02 x 1023

things “Things” usually measured in moles

are atoms, molecules, ions, and formula units

You can measure mass, or volume, or you can count pieces

We measure mass in grams

We measure volume in liters

We count pieces in MOLES

A MOLE… is an amount, defined as the

number of carbon atoms in exactly 12 grams of carbon-12

1 mole = 6.02 x 1023 of the representative particles

Treat it like a very large dozen 6.02 x 1023 is called:

Avogadro’s number

Similar Words for an amount: Pair: 1 pair of shoelaces = 2 shoelaces

Dozen: 1 dozen oranges = 12 oranges

Gross: 1 gross of pencils= 144 pencils

Ream: 1 ream of paper= 500 sheets of paper

What are Representative Particles (“RP”)?

The smallest pieces of a substance:1. For a molecular compound: it is

the molecule.2. For an ionic compound: it is the

formula unit (made of ions)3. For an element: it is the atom

Remember the 7 diatomic elements? (made of molecules)

Practice Counting Particles How many oxygen atoms in the following?1. CaCO3 3 atoms of oxygen2. Al2(SO4)3 12 (4 x 3) atoms of oxygen

How many ions in the following?1. CaCl2

3 total ions (1 Ca2+ ion and 2 Cl1- ions)2. NaOH

2 total ions (1 Na1+ ion and 1 OH1- ion)3. Al2(SO4)3

5 total ions (2 Al3+ + 3 SO4 ions)

CONVERSION FACTOR

MOLES = RPs x ____1 mole___ 6.02 x

1023 RPs

EXAMPLES: ATOMS MOLES

How many moles of B are in 3.15 x 1023 atoms of B? Conversion: 1 mole B = 6.02

x 1023 atoms B(b/c the atom is the RP of

boron)

1 mole B

3.15 x 1023 atoms of B

6.02 x 1023 atoms B

= 0.532 mole

EXAMPLES: MOLES ATOMS

How many atoms of Al are in 1.5 mol of Al? Conversion: 1 mole = 6.02 x 1023

atoms

1.5 mol of Al6.02 x 1023 atoms Al

1 mole Al

= 9.03 x 1023 atoms of Al

CAUTION: Identify RPs Carefully!

See next slide!

EXAMPLES: MOLECULES MOLESHow many atoms of H are there in 3 moles of H2O? (HINT: Are atoms the RP for water?)Conversions:1 mole = 6.02 x 1023 molecules

(b/c molecules are the RP for H2O)

3 moles of H2O 6.02 x 1023 molec H2O

1 mole H2O

2 atoms H

1 H2O molecule

= 3.612 x 1024 atoms H

H2O molecule = 2 atoms of Hydrogen

MOLAR MASSDef: The mass of a mole of representative particles of a substance.

Each element & compound has a molar mass.

MOLAR MASS OF AN ELEMENTDetermined simply by looking at the periodic table

Molar mass (g) = Atomic Mass (amu)

Ca20

40.08

* Thus, 1 mol Ca = 40 g

1 atom of Ca weighs 40.08 amu1 mole of Ca atoms weighs 40.08 grams

MOLAR MASS FOR COMPOUNDS

To calculate the molar mass of a compound, find the number of grams of each element in one mole of the compound

Then add the masses within the compound

Example: H2O

H= 1.01 2 (1.01) + 1 (15.999)= 18.02 g/mol

O= 15.999

SOME PRACTICE PROBLEMS How many atoms of O are in 3.7 mol of

O? 2.2 X 1024 atoms of oxygen

How many atoms of P are in 2.3 mol of P? 1.4 x 1024 atoms of phosphorus

How many atoms of Ca are there in 2.5 moles of CaCl2? 1.5 x 1024 atoms Ca

How many atoms of O are there in 1.7 moles of SO4? 4.1 x 1024 atoms of oxygen

Remember!!!! The molar mass of any substance (in

grams) equals 1 mole This applies to ALL substance: elements,

molecular compounds, ionic compounds Use molar mass to convert between mass

and moles Ex: Mass, in grams, of 6 mol of MgCl2 ?

mass of MgCl2 = 6 mol MgCl2 92.21 g MgCl2 1 mol

MgCl2

= 571.26 g MgCl2

VOLUME AND THE MOLE

Volume varies with changes in temperature & pressure

Gases are predictable, under the same physical conditions

Avogadro’s hypothesis helps explain:equal volume of gases, at the same temp and pressure contains equal number of particles

Ex: helium balloon

Gases vary at different temperatures, makes it hard to measure

Because of variation use STP Standard Temperature and Pressure Temperature = 0° C Pressure = 1 atm (atmosphere) or 101.3

kPal

Molar Volume

At STP:1 mole, 6.02 x 1023 atoms, of any gas has a volume of 22.4 L

1 mole gas = 22.4 L gas

Called Molar Volume Used to convert between # of moles and

vol of a gas @ STP Ex: what is the vol of 1.25 mol of sulfur gas

1.25 mol S 22.4 L = 28.0 L 1 mol

MOLAR MASS FROM DENSITY Different gases have different densities Density of a gas measured in g/L @ a specific

temperature Can use the following formula to solve :

grams = grams X 22.4 Lmole L 1 mole Ex: Density of gaseous compound containing

oxygen and carbon is 1.964 g/ L, what is the molar mass?

grams = 1.964 g X 22.4 L then you solve

mole 1 L 1 mole = 44.o g/mol

Atoms, molecules, etc.

Molarity

Def: the concentration of a solution. How many moles/liter

Can be used to calculate # of moles of a solute

Ex: Household laundry bleach is a dilute aqueous solution of sodium hypochlorite (NaClO). How many moles of solute are present in 1.5 L of 0.70 M NaClO?

Calculating Percent Composition of a Compound Like all percent problems: a part ÷ the

whole1. Find the mass of each of the components

(the elements)2. Next, divide by the total mass of the

compound3. Then X 100 % = percent

Formula:% Composition = Mass of element X 100%

Mass of compound

Method #1: % Comp When Actual Masses are Given

A compound is formed when 9.03 g of Mg combines completely with 3.48 g of N.

What is the percent composition of the compound?1. First add the 2 mass of the 2 compounds to

reach the total mass 9.03 g Mg + 3.48 g N = 12.51 g Mg3N2

1. Find the % of each compound

% Mg= 9.03 g Mg X 100% = 72.2 %12.51 g Mg3N2

% N= 3.48 g N X 100% = 27.8 % 12.51 g Mg3N2

Method 2: % Comp When Only The Formula is Known Can find the percent composition of a

compound using just the molar mass of the compound and the element

% mass=mass of the element 1 mol cmpd X100%

molar mass of the compound Example:

Find the percent of C in CO2

12.01 g C X 100% = 27.3% C

44.01 g CO2

Can find O % by subtracting 27.3% from 100%

Using % Composition Can use % composition as a conversion factor

just like the mole After finding the % comp. of each element in

a cmpd. can assume the total compound = 100g

Example: C= 27.3% 27.3 g C O= 72.7 % 72.7 g O

In 100 g sample of compound there is 27.3 g of C & 72.7 g of O

How much C would be contained in 73 g of CO2?

73 g CO2 27.3 g C = 19.93 g C

100 g CO2

EMPIRICAL FORMULAS Empirical formulas are the

lowest WHOLE number ratios of elements contained in a compound

REMEMBER… Molecular formulas tells the actual

number of of each kind of atom present in a molecule of the compound

Ex:H2O2 HOMolecular Empirical Formula Formula

CO2 CO2

Molecular Empirical For CO2 they are the same

Formula Formula

Formulas for ionic compounds are ALWAYS empirical (the lowest whole number ratio = can not be reduced)

Examples: NaCl MgCl2 Al2(SO4)3 K2CO3

Simplest whole number ratio for NaCl

A formula is not just the ratio of atoms, it is also the ratio of moles

In 1 mole of CO2 there is 1 mole of carbon and 2 moles of oxygen

In one molecule of CO2 there is 1 atom of C and 2 atoms of O

Formulas for molecular compounds MIGHT be empirical (lowest whole number ratio)

Molecular: H2O C6H12O6 C12H22O11

(Correct formula)

Empirical:

(Lowest whole H2O CH2O C12H22O11

number ratio)

CALCULATING EMPIRICAL We can get a ratio from the percent

composition 1.Assume you have a 100 g sample the

percentage become grams (75.1% = 75.1 grams)

2.Convert grams to moles3.Find lowest whole number ratio by

dividing each number of moles by the smallest value

Example calculations Calculate the empirical formula of a

compound composed of 38.67 % C, 16.22 % H, and 45.11 %N

Assume 100 g sample, so 38.67 g C x 1 mol C =

12.0 g C 16.22 g H x 1 mol H =

1.0 g H 45.11 g N x 1 mol N =

14.0 g N *Now divide each value by the smallest value

3.22 mole C

3.22 mole N

16.22 mole H

…Example 1

The ratio is 3.22 mol C = 1 mol C 3.22 mol N 1

mol N The ratio is 16.22 mol H = 5 mol H

3.22 mol N 1 mol N

C1H5N1 which is = CH5N

MORE PRACTICE

A compound is 43.64 % P and 56.36 % O

What is the empirical formula? PO3

Caffeine is 49.48% C, 5.15% H, 28.87% N and 16.49% O

What is its empirical formula?

C4H5N2O

EMPIRICAL TO MOLECULAR

Since the empirical formula is the lowest ratio, the actual molecule would weigh more

Divide the actual molar mass by the empirical formula mass – you get a whole number to increase each coefficient in the empirical formula

EXAMPLE Caffeine has a molar mass of 194 g, what

is its molecular formula?1.Find the mass of the empirical formula,

C4H5N2O

2.Divide the molar mass by the empirical mass:194.0 g/mol =97.1 g/mol

3.Now multiply the entire empirical formula by 2

2(C4H5N2O) =

final molecular formula

2

C8H10N4O2