Download Measurements, Sig Figs and Graphing

4/9/2010
Measurements, Sig Figs
and Graphing
Chem 1A Laboratory #1
Chemists as Control Freaks
• Precision:
Accurate Measurements g Knowledge
Knowledge g Power
 How close together
• Accuracy:
 How close to the true value
• Error: What really happens
Accuracy = Precision
There is always uncertainty
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About those errors
• Systematic errors:
 Consistent error in the same direction
due to a bias in the data collection – like an
improperly calibrated balance
• Random errors:
That can’t be right!!!
 Unpredictable fluctuations in a
measurement
 Occur in different directions from the true
value
Understanding uncertainty:
Significant Figures
• All laboratory measurements have uncertainty
associated with the last digit of the value.
8.24 or 8.25 cm?
52.26 or 52.27 mL?
• We have to keep track of the uncertainty to know how
accurate and reliable our results are.
• We identify the number of significant figures or digits in
each measurements and use simple rules for tracking
“sig figs” in our calculations
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Our Uncertain Equipment
For measuring volume:
• Graduated containers:




Cylinders
Beakers
Burets
Pipets
• Volumetric containers
 Pipets
 Flasks
• Calibration temperature; accuracy
• To Contain (TC) vs To Deliver (TD)
Reading volumes
Graduated Cylinders
Burets
Reading what goes into it
Reading what went out of it
0.00 mL --1
Meniscus
1.42 mL
3.67 mL
1
Uncertain digit
2
3
--4
5
6
7
0
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Recording measurements
• Recording a measurement with the correct number of
significant figures is necessary to show the precision of
the measuring device correctly.
• Unless stated otherwise, the uncertainty in a number is
taken to be ± one unit in the estimated digit.
• What are the measurements with correct # of sig figs?
10 mL graduated cylinder
50 mL buret
Ruler: in and cm
100 mL
graduated cylinder
Working with measurements
Key Steps:
1. Record the measurements carefully.
2. Repeat the measurement to increase its reliability, then
calculate the average or mean as the “best value”
3. Establish the probable limits of uncertainty


Precision Range = Highest Value – Lowest Value
Accuracy: Deviation from true value
• Accuracy is often reported as percent error:
 Percent Error = Experimental Value – Accepted Value x 100%
Accepted value
• Keep track of significant figures. Do not write a reading
of 50.00 mL as 50 mL or as 50.000 on your worksheet.
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Estimating the Last Digit
• For instruments marked with a
scale, you get the last digit by
estimating between the marks.
52.5 mL
• Mentally divide the space into 10
equal spaces, then estimate what
100 mL graduated cylinder
the last digit should be.
• The total number of digits in a
measurement, including the last
6.31 mL
estimate are called the significant
figures or “sig figs”
• The last digit is just our best
estimate of the true value. It tells 10 mL graduated cylinder
us that the actual value is
Both of these measurements
between 6.30 and 6.32 mL
have 3 sig figs
Significant Figures
• The non-placeholding digits in a
reported measurement are called
significant figures.
 Some zeros in a written number are
only there to help you locate the
decimal point.
• Significant figures tell us the range
of values to expect for repeated
measurements.
 The more significant figures there are
in a measurement, the smaller the
range of values. Therefore, the
measurement is more precise.
12.3 cm
has 3 significant figures
and its range is
12.2 to 12.4 cm.
12.30 cm
has 4 significant figures
and its range is
12.29 to 12.31 cm.
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Zeros & Significant Figures
• All non-zero digits are significant.
 1.5 has 2 significant figures.
• Interior zeros are significant.
 1.05 has 3 significant figures.
• Trailing zeros after a decimal point are significant.
 1.050 has 4 significant figures.
• Leading zeros are NOT significant.
 0.001050 has 4 significant figures
• Zeros at the end of a number without a written
decimal point are ambiguous and should be avoided
by using scientific notation.
 150,000 is ambiguous
How Many Sig Figs?
• How many significant figures are in each of the
following numbers?




3.15 x 1016
0.007510
10200.
150.108
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Significant Figures Review
• When multiplying or dividing measurements with
significant figures, the result has the same number of
significant figures as the measurement with the fewest
number of significant figures.
5.02 × 89,665 × 0.10 = 45.0118 = 45
3 SFs
5 SFs
2 SFs 2 SFs.
• When adding or subtracting measurements with
significant figures, the result has the same number of
decimal places as the measurement with the fewest
number of decimal places.
5.74 + 0.823 +
2.651 = 9.214 = 9.21
2 dec. pl.
3 dec. pl. 3 dec. pl.
2 dec. pl.
Multiplication/Division with
Addition/Subtraction
• When doing different math operations on
measurements, identify the significant figures for any
intermediate answer, then do the remaining steps.
Round only at the end for Mastering Chemistry problems.
• Follow the standard order of operations.
Please Excuse My Dear Aunt Sally.
n
3.489
3.489
4 sig figs
-
(5.67 – 2.3) =
2 dp
1 dp
3.37
=
12
2 sig figs
2 sig figs
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Sig Figs and Logarithms
• The logarithm (or log) of a number to a given base is the
power or exponent to which the base must be raised in
order to produce that number.
 If x=10y; y = log 10 (x)
 For example: the log 10 of 100 is 2, because 2 is the power
to which 10 must be raised to get 100: 102 = 100, so
log10100 = 2.
• Characteristic and mantissa of a logarithm
 Characteristic = number on left of decimal= power of 10
 Mantissa = number on right of decimal g # of sig figs
• Log (3.000) = 0.4774
• Log (3.00) = 0.477
4 sig figs
3 sig figs
• Antilogs: # of sig figs still comes from mantissa
• Antilog (5.89) = 105.89 = 7.8 x 105
2 sig figs
Exact Numbers vs. Measurements
• Sometimes you can determine an exact value for a
quality of an object.
 Often by counting.
• Pennies in a pile.
 Sometimes by definition
• There are exactly 1000 meters in 1 kilometer.
• There exactly 2.54 cm/in
 From integer values in equations.
• In the equation for radius of a circle (r=d/2), the 2 is exact
 Exact or exactly implies an infinite number of sig figs
 If we use an exact number in a calculation, we don’t
consider it when we determine the number of sig figs
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Your Mission in lab Today
• Test your measuring skills; pay attention to accuracy of the
equipment and record measurements with correct # of sig figs
• Each bench top will be given an identifying number (1 – 8, write it
down) and will have the following equipment set up:

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
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100 mL volumetric flask filled to the mark with water
10 mL volumetric pipet
5 mL graduated pipet
250 mL beaker partially filled with water
100 mL graduated cylinder partially filled with water
10 mL graduated cylinder partially filled with water
50 mL buret partially filled with water
• Examine each piece of equipment and fill out Data Table I,
including units. Write neatly!!
• Part B: Each person must individually record the volume of
water in each piece of equipment in the spaces provided. Do not
change any of the volumes of water.
Your Continuing Mission
• Part C: Compare your measurements in Part B with the
other people at your bench top and answer the
questions
• Part D: Using the data provided and graph paper, make
a graph (by hand) of total mass of water plus beaker (yaxis) versus total volume (x-axis) of water in the beaker
following graphing rules given in Appendix A. Plan your
axes so you can extrapolate the y-intercept.
• Perform the calculations and answer the questions
based on your graph.
• Complete follow-up questions before leaving lab
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Handy Things to Know
• Range: Highest value –Lowest value
 Provides estimate of precision
• Accuracy:
Experimental Value – Accepted Value x 100%
Accepted Value
• Estimated uncertainty:
± 1 unit of estimated digit
• If volumetric glassware is not marked with the
uncertainty, estimate ± 0.2 mL for volumetric
flasks and ± 0.02 mL for a volumetric pipet.
 Why such a big difference?
 What does that ± 0.02 mL mean for a 20 mL pipet?
For Next Week
• Tuesday:
 Safety Quiz – must pass with 85% or better
 Completed Measurements assignment due at beginning
of lab
 No PreLab, but review Nomenclature Worksheet ; we will
work on it in class.
• Thursday:
 Completed PreLab for Density of 7-Up lab due at
beginning of lab period
 Nomenclature Worksheet will be due at beginning of lab
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