Chemistry Lectures

7/29/2019 Chemistry Lectures

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Measurement, Uncertainty,

& Sig Figs


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2

Fast is fine, but accuracy is everything.

- Wyatt Earp


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Measuring - Practice

What is

the

volume?

36.3


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Dimensional Analysis - Practice

Examples


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Scientific Notation

If your calculator displays scientific notation as:1.2 E10

please write it as:

1.2 1010


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Scientific Notation


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Scientific Notation - Examples

Convert into standard notation :

A B


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Scientific Notation - Examples

Convert into scientific notation:

A B


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Scientific Notation:

Operations Examples Examples:

A


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B


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C


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13/37

Definition vs Measurement

Circumference of moon

= 10,921 km

1 meter = 100 cm

Definition: relationship

determined by convention

1 m = 100.000000000cm

Measurement: an estimation

limited by experimental error

= 10,921.???? km

complete certainty uncertainty


14/37

Measurements are always accompanied by a finite amount of error.

reflect limitations in the techniques used to make them.

always contain an element ofuncertainty.

must be reported in such a way that reflects appropriate

units of measure and level of uncertainty.

As technology/skill improves, amount of associated

error decreases (but never disappears completely).

13.45 0.01 m


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Measurement Reminders

Always read a measuring device to themaximum number of digits possible.

Uncertainty last digit of a measurementis estimated.

Always include the units with ameasurement.


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Measurement Error

Two sources Limitations in the sensitivity of instruments used

Imperfections in measurement techniques used

Two classes

systematic error

random error


17/37

Systematic vs Random Error

Systematic Error Random Error

results from imperfections in

equipment/technique

results from limitations in

equipment/technique


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Accuracy vs. Precision

Accuracy Closeness of a measurement to

the true or standard value of that quantity

Precision Degree of exactness in ameasurement; Degree to which individual

measurements of the same quantity agree


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Systematic vs Random Error II

Systematic Error Random Error

leads to results that are

precise but not accurate

leads to results that may

be accurate, on the

average, but not precise


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Reducing Error

Systematic errors can be reduced by increasing care and patience while measuring

increasing accuracy of measuring tools

Random errors can be reduced by

averaging the results of many measurements of

the same quantity

increasing precision of measuring tools


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Accurate v Precise Chart

Inaccurate(systematic error)

Accurate

Imprecise(random error)

Precise


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Rank these

rulers in

order ofincreasing

precision.

B < D < A = E < C


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Measurement Reminders II

FAIL

You are only allowed to estimate one level of

precision beyond the markings on a measuring tool

4.5 5.0

4.82

4.82 cm

H t d t t


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How many students are at

Westview right now?


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Significant Figures (Sig Figs)

Precision (exactness) of a measurement is

represented by number ofsignificant figures

those digits in a measurement that are known

with certainty plus the first digit that is

estimated results can not appear more accurate than the

equipment/technique used to make

measurements


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Significant Figures Are

All non-zero digits

111 m

All zeros between non-zero digits

captured zeros

101 m

All zeros to the right of a non-zero digit in a

decimal measurement

100. m

100.0 m

1000.0 m

{ 3 SFs}

{ 3 SFs}

{ 3 SFs}

{ 4 SFs}

{ 5 SFs}


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Significant Figures Are NOT

Zeros to the left of the first non-zero

leading zeros

0.45 g

0.0045 g

0.0450 g

All zeros to the right of last non-zero digit in a

non-decimal measurement

trailing zeros

100 g

1010 g

{ 2 SFs}

{ 2 SFs}

{ 3 SFs}

{ 1 SFs}

{ 3 SFs}


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All non-zero digits

10

100

120 123

12340

10000

1 sf

1 sf

2 sf 3 sf

4 sf

1 sf


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All zeros between non-zeros

103

1004

10305

1004007

3 sf

4 sf

5 sf

7 sf


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All zeros to right of a non-zero in

a decimal measurement

0.10

0.1030

0.100400

0.010040

10.0

1000.

2 sf

4 sf

6 sf

5 sf

3 sf

4 sf


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Scientific Notation & Sig Figs

Decimal part of scientific notationonly represents significant digits!

4 SFs 4 SFs

2 SFs 2 SFs


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Exact Numbers

Exact numbers have an unlimited number ofsignificant figures

1 km = 1000 m = 1000. m = 1000.00000000 m

Coefficients (and mole ratios) are exact numbers Constants are not necessarily exact!

Avogadros Number (6.022 1023 mol1) is a

measurement

4 SFs


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Why bother?

5.740.823

+ 2.651

9.214

5.74 m0.823 m

+ 2.651 m

9.214 m FAIL

?

uncertain!

2 SF right of

decimal

Answer must have same # of SF right of decimal as themeasurement with fewest SF right of decimal!

9.21 m

Win

3 SF right of

decimal

3 SF right of

decimal


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Significant Figures Rules

RULES for calculating (based on answer not beingmore precise than least precise component):

Add/subtract: answer has same # of s.f. to right

of decimal as measurement with fewest # of s.f.to right of decimal.

Multiply/divide: answer has same # of s.f. as

measurement with fewest # of s.f.

Round off calculation results to achieve appropriate

# of s.f.


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Significant Figures for Chem 1-2

Just round-off your answer to

two decimal places


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Rules For Rounding

If digit after last s.f. is

0 4: round DOWN

6 9: round UP

5 :

30.2

30.3

30.23

30.26

???round UPIn science, rounding off 5s is actually a bit complicated,

but typical calculators always round 5s up

30.330.25

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