Measurement & Data
Processing
IB Chem
• Objective: demonstrate knowledge of
measurement & data processing.
• Warm up: Explain the difference between
accuracy and precision.
Challenge…
• Hemoglobin (C2952H4664O832S8Fe4) is the oxygen
carrier in blood.
• Calculate its molar mass.
An average adult has about 5.0 liters of blood.
Every milliliter of blood has approximately 5.0 x
109 erythrocytes, or red blood cells, and every
red blood cell has about 2 x 108 hemoglobin
molecules.
• Calculate the mass of hemoglobin molecules in
grams in an average adult.
Significant Figures
• The certain (known) digits and one
estimated digit of each measurement are
significant.
• Remember! Every time you make a
measurement, you record all of the certain
digits and one estimated digit.
200.54 g
Significant Figures
5508 has 4
sig figs
1.
Non-zeros are always significant.
Rules for Sig Figs
2.
Zeros between non-zeros are significant.
3.
All final zeros to the right of the decimal are
significant. (estimated value)
67.80 has 4
sig figs
4.
Placeholder zeros are NOT significant.
– Zeros preceding significant digits.
– Zeros following significant digits without
a decimal point.
Significant Figures
Sample Problem:
17.20
4.137
+ 26.6
47.937
(.01)
(.001)
(.1)
Correct Answer: 47.9
Significant Figures
Sample Problem:
14.3
1.0200
x 0.005
0.07293
(3 sig figs)
(5 sig figs)
(1 sig fig)
Correct Answer:
0.07
Scientific Notation
In chemistry, we work with very large and
very small numbers.
Number of particles in a mole =
602200000000000000000000
Mass of an electron =
0.000000000000000000000000000000911kg
Scientific
Notation
1.
2.
3.
4.
Identify the significant
digits
Write out the
significant digits as a
number greater than
1 but less than 10
602200000000000000000000
There are 4 sig figs in this
number
6.022 is < 1 and > 10
The decimal was moved 23
places
Count the number of
places you had to
move the decimal to
complete step 1
6.022 x 1023
Write this number of
decimal places as an
exponent to 10
When the decimal place is
moved to the left, the exponent
is positive.
Things you already know
Types of Uncertainty/Error
• Random:
• Systematic
Error introduced
Error introduced
has an equal
will always be too
probability of being
high or too low.
too high or too low
50/50 chance
Ex: Air bubbles in
Ex: Door open on
thermometer
analytical balance
Using equipment
• Analogue
+/- Half of the
smallest division
• Digital
+/- The smallest
scale division
Uncertainty
• Absolute
± half of the
smallest division
• Percent
Absolute uncertainty
divided by the
measurement x 100
Always include units
35.0 ± 0.5 cm3
0.5/35.0 *100 = 1.4%
Uncertainties in Calculations
Addition/Subtraction
Add absolute uncertainties
+
23.0 ± 0.1 cm3
34.0 ± 0.5 cm3
57.0 ± 0.6 cm3
Uncertainties in Calculations
Multiplication/Division
1. Multiply or divide
measured numbers
3.0 ± 0.1 cm3
x 4.0 ± 0.5 cm3
12
2. Convert absolute
uncertainties into
percents
0.1/3.0 * 100 = 3%
0.5/4.0 * 100 = 10%
(remember to use multiplication/
division sig fig rules)
3. Add percents
12 cm3 ± 13%
4. Convert back to
absolute
13% = 100 * x/12.0
12 ± 1.6 cm3
Percent error
A measure of how close the experimental
value is to the accepted/known value
Not to be confused with percent uncertainty…
(accepted value – experimental value)
X 100
accepted value
Equipment/technique uncertainty
compared to literature values
• If % uncertainty > % error, the experimental value fits
within the uncertainty range and is acceptable; the
differences in the experimental and literature values is
due to random errors
• If % uncertainty < % error, the experimental value
does not fit within the uncertainty range and is
unacceptable; the differences in the experimental and
literature values is due to systematic errors
Equipment/technique uncertainty
compared to literature values
•
Example: % uncertainty is 20 g +/- 5% < % error is
10%
This indicates the data should fall between 19 and 21
grams. The error of 10% falls outside of this. Meaning the
accepted or literature values are outside of this range
produced.
This must be due to systematic error and is
UNACCEPTABLE!
Accuracy vs. Precision
Accuracy vs. Precision
Accuracy measures how close a
measured value comes to a
predetermined target value (the
set volume on your pipettor).
accurate
precise
accurate
not precise
Reproducibility (precision)
measures how close repeated
values are to one another. These
concepts can be visualized using
these cartoon (idealized) bulls-eye
diagrams. Notice that accuracy
and precision can vary
independently, so they can be
evaluated independently, as well.
Test yourself on identifying if these
examples are precise, accurate,
neither, or a mix
not accurate
precise
not accurate
not precise
Graphing video
Graphing
• Always include:
– Title
– Axis titles with units
– A best fit line
– Identification of outliers
– Consistent scales – no uneven jumps
Always make the graph as large as
possible…maximize axis usage and
paper usage
Extrapolation & Interpolation
• Extrapolation- Extending the graph to
determine an unknown value outside
the range of measured values
• Interpolation- Determining an unknown
value within the limits of the measured
values
Challenge…
• Hemoglobin (C2952H4664O832S8Fe4) is the oxygen
carrier in blood.
• Calculate its molar mass.
An average adult has about 5.0 liters of blood.
Every milliliter of blood has approximately 5.0 x
109 erythrocytes, or red blood cells, and every
red blood cell has about 2 x 108 hemoglobin
molecules.
• Calculate the mass of hemoglobin molecules in
grams in an average adult.
• Objective: demonstrate knowledge of
measurement & data processing.
• Warm up: Explain the difference between
accuracy and precision.