Transcript accepted value

Unit 1: Introduction to Chemistry
Measurement and Significant
Figures
Precision and Accuracy
What is the difference between precision and
accuracy in your measurements?
• Accuracy refers to how close you are to the true
value. It can be improved by making better
measurements.
• Precision refers to how close several
measurements are to each other, or how many
significant digits are allowed in a measurement.
It can be improved by repeating the
measurements, or by using a better instrument.
Precision and Measurements
• Why must reported values show the
correct number of “significant digits?”
Because your measurement will only be
as good as the instrument you use!
• Precision is limited by the gradations -or
markings -on your instrument.
• We can typically estimate
to one-tenth of a gradation
mark when using graduated
instruments in chemistry.
Try it!
Measurement Practice
Not accurate
(avg. is falsely accurate),
not precise
BEAKER
47 +/- 1 mL
Not accurate
but is precise
CYLINDER
36.5 +/- 0.1 mL
Accurate
and precise
BURET
20.38 +/- 0.01 mL
How good are your measurements?
Any 1.6
measurement
• For example, if you are
meters
1.57865467 m?
will have some
tall, we know that you
are
exactly
degree of uncertainty
ONE meter tall (not 0associated
or 2) but
the
with
it….
second digit is an estimate, and
contains some uncertainty (it could
be 0.58 rounded up, or 0.62 rounded
down…)
• Scientific measurements are rounded
off so that the last digit is the only
one that is uncertain. Preceding digits
are known with certainty, and
unnecessary digits are not included.
What is meant by “significant figures”?
• What is the difference between the measurements
25.00 mL and 25 mL?
• The first measurement is known more precisely
and contains more significant figures –it could be
25.01 or 24.99, whereas the second measurement
lies between 24 and 26.
• The number of significant figures tells us how well
we know a measurement, and depends on how
good the instrument used to measure it was.
• The known numbers PLUS the last uncertain
number in a measurement are significant.
20.15 mL
three
certain
digits
one
uncertain
digit
four significant digits!
six sig figs
Middle zeros always count.
0.0700600
Beginning zeros never count.
Ending zeros count IF a decimal
point is anywhere in the number.
round to least # of decimal places
round to least # of significant digits
Examples of each rule:
• Any non-zero number is ALWAYS significant.
example: 762 has 3, and 2500 has 2
• Zeros: (a) beginning zeros are not significant, they are just
place holders. Ex: 006471 has 4, and 0.00284 has 3
(b) Middle zeros between nonzeros are significant. Ex: 1.008
has 4 and 12046 has 5
(c) Ending zeros are significant ONLY if the number contains a
decimal point. Ex: 1.0 x102 has 2, and 3000. has 4
Note: Exact numbers are numbers that are determined by
counting (not measurement), or by definition are assumed to have
an infinite number of significant figures.
example: 1 minute equals 60 seconds
15 students are in class today
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Lets Practice (notes):
(4) How many sig figs are in each?
a) 2.07 mLthree
b) 0.057010 g five
c) 0.0026700 m five
d) 19.0550 kg six
e) 3500 V two
f) 1809000 L four
More Practice:
How many sig figs are in each?
• 4.5090 five
• 0.00607 three
• 6.7 x103 two
• 200. three
• 250 two
• 698,000.1 seven
• 2.0000 x106 five
Converting to Sci. Not.
•The following rule can be used to convert numbers into scientific
notation:
The exponent in scientific notation is equal to the number of
times the decimal point must be moved to produce a number
between 1 and 10.
•Example: In 1990 the population of Chicago was 6,070,000. To
convert this number to scientific notation we move the decimal
point to the left six times.
6,070,000 = 6.07 x 106
•To convert numbers smaller than 1 into scientific notation, we
have to move the decimal point to the right. The decimal point in
0.000985, for example, must be moved to the right four times.
0.000985 = 9.85 x 10-4
Scientific Notation
• The primary reason for converting numbers into
scientific notation is to make calculations with
unusually large or small numbers less
cumbersome.
• Because zeros are no longer used to set the
decimal point, all of the digits in a number in
scientific notation are significant, as shown by
the following examples:
• 2.4 x 1022 has 2 significant figures
9.80 x 10-4 has 3 significant figures
1.055 x 10-22 has 4 significant figures
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Lets Practice (Notes):
(5)Convert to scientific (6) Convert to std. not:
notation:
a) 5.68 x105 568,000
-3
2.25
x10
a) 0.00225
b) 4.1 x10-3 0.0041
3
3.3402
x10
b) 3340.2
c) 1.1 x10-2 0.011
0
5.6
x10
4,000
c) 5.6
d) 4 E 3
-3
2.0
x10
d) 0.0020
e) 1.10 E -2 0.0110
e) 602,000,000,000,
23
6.02
x10
000,000,000,000
More Practice Problems
• Convert the following numbers into sci. notation:
(a) 0.004694 (b) 19.8 (c) 4,679,000
ANSWER: (a) 4.694 x 10-3
(b) 1.98 x 101
(c) 4.679 x 106
NOTES DAY 2
How is density calculated?
• Density is defined as the mass per unit
volume of a substance.
• Equation:
Ex: How many mL are occupied by 112 g of a
liquid with a density of 0.97 g/mL?
What does temperature
measure?
A thermometer bulb’s view
of a hot liquid…
Temperature
is a measure
of the
average
kinetic
energy of
molecules.
How do we convert between
temperature scales?
°C(9/5) + 32
K - 273
Addition and Subtraction Using
Significant Figures
• The answer must have the same number of
decimal places as the least precise
measurement used in the calculation.
• For example, consider the sum
12.11
18.0
+ 1.013
31.123
Final answer must match
leftmost decimal place of
combined measurements
• The answer is 31.1 since 18.0 only has one
decimal place.
Multiplication and division using sig.
figs.
• The number of significant figures in the
answer is the same as the least precise
measurement (lowest number of sig. figs.)
used in the calculation.
• For example, consider the calculation
4.56 x 1.4 = 6.38
• The correct answer is 6.4 (it should only
have two sig figs since 1.4 has only two)
Notes: Get a calculator!
(5) 3.052 m + 2.10 m - 0.75 m = 4.40 m
(6) 6.15 m x 4.026 m = 24.8 m2
(7) (13.7 g + 0.03 g)  8.2 mL = 1.7 g/mL
13.7 g
More practice:
four
three
two
6.384 6.4
two
31.123
31.1
three
three
35.2 x 5.4
190.08
190
1.90 x 102
How do we know if our results
are GOOD?
• One way to tell how “far off you are” is to
compare your results to the “true” or “accepted”
value.
• To determine the percent error of your results,
use the following formula:
% Error = accepted value – (YOUR) measured value x 100%
accepted value
% Error calculation
% Error = accepted value – meas. value x 100%
accepted value
• What is the percent error of a measurement that is
2.51 cm if the accepted value is 2.54 cm?
• ANSWER: (2.54 – 2.51) x 100% = 0.03 x 100%
2.54
2.54
= 1.18% = 1% error
Activity: Find the density of Zn metal and calculate your
% error when compared to known density.
Use sig figs in measurements and calculations.
NOTES DAY 3
What is this map showing???
Common Unit Conversions
60
2.54
12
5,280
60
454
4.18
1
1,000
We will often need to convert from one
unit to another when solving problems in
chemistry. These “conversion factors”
allow us to change the unit without
changing the value of the measurement.
Review: metric unit prefixes
The metric system (a.k.a. SI system) is based on powers of ten and Greek prefixes.
Prefix
Giga
Mega
kilo
Deca
deci
centi
milli
micro
nano
Symbol
G
M
k
D
d
c
m
μ
n
Factor
109
106
103
101
Numerically
1 000 000 000
1 000 000
1 000
10
Name
billion
million
thousand
ten
10-1
10-2
10-3
10-6
10-9
0.1
0.01
0.001
0.000 001
0.000 000 001
tenth
hundredth
thousandth
millionth
billionth
Dimensional Analysis
• The best way to convert between units is by a
method called dimensional analysis (a.k.a.
factor-label method).
• Always remember this:
• For example, consider a pin measuring 2.85 cm
in length. Given that one inch is equal to 2.54
cm, what is its length in inches?
• ? in = 2.85 cm x
1 in
= 1.12 in
2.54 cm
Some Examples:
• Convert 50.0 mL to liters:
Linking conversion factors
• How many seconds are in two years?
More examples
• A Japanese car is advertised as having a gas
mileage of 15 km/L. Convert this rating to
mi/gal. (Given conversion factors 1 mi = 1.609
km, 1L=1.06 qt and 4 qt = 1 gal)
• ANSWER:
15 km x 1mi x 1 L x 4 qt = 35.18 mi/gal
L
1.609 km 1.06 qt 1 gal
With correct sig figs this rounds to 35 mi/gal
Tips for using the method…
• In math you use numbers, in chemistry we use
quantities. A quantity is described by a number and a
unit.
• 100 is a number: 100 Kg is a quantity (notice that in
chemistry we give meaning to the numbers). In
science we solve a lot of the "math" by watching the
units of the quantities NO NAKED NUMBERS!
• There are two main rules to solving science
problems with the factor-label method:
• 1. Always carry along your units with any
measurement you use. Cancel units when
appropriate.
• 2. You need to form the appropriate labeled ratios ,
(which means conversion factors have equal
numerators and denominators).
Conversions (notes)
1. How many ms are in 45 min?
2. How many in3 are in 86.3 cm3?
3. How fast is 65 mi/h in ft/sec?
4. How many cm3 are in 7.5 gal?
5. How many lb/ft2 are in 75 g/cm2?
6. How many km are in 1500 mm?
Extra Credit
Gas prices from Italy trip
summer 2014. Can you
convert the advertised
values to dollars per
gallon? What conversion
factors will you need?
How do these prices
compare to American
prices?
THE END
More Unit Conversion Practice
• A pencil is 7.00 inches long. How long is it
in cm?
• ANSWER: 17.8 cm
• A student has entered a 10.0 km race.
How long is this in miles?
• ANSWER: 6.22 mi
• The speed limit on many highways in the
U.S. is 55 mi/hr. What is this in km/hr?
• ANSWER: 89 km/hr
Exponent Review
• Some of the basics of exponential mathematics
are given below:
– Any number raised to the zero power is equal to 1.
ex: 10 = 1 and 100= 1
– Any number raised to the first power is equal to itself.
ex: 11 = 1 and 101 = 10
– Any number raised to the nth power is equal to the
product of that number times itself n-1 times.
ex: 22 = 2 x 2 = 4 and 105 = 10 x 10 x 10 x 10
x 10 = 100,000
– Dividing by a number raised to an exponent is the
same as multiplying by that number raised to an
exponent of the opposite sign.
ex: 5 ÷ 102 = 5 x 10-2 = 0.05