Chemistry Lectures
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Transcript of 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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Scientific Notation:
Operations Examples Examples:
B
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Scientific Notation:
Operations Examples Examples:
C
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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
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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
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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