Topic 11: Measurement and Data
Processing
Honors Chemistry
Mrs. Peters
Fall 2014
What is Chemistry?
Chemistry is the study of the composition of
matter and the changes that matter undergoes.
• What is matter?
– Anything that takes up space and has mass
• What is change?
– To make into a different form
Scientific Process
Steps to Scientific Process:
1.Observations: Use your senses to obtain information
directly
2.Problem: propose a question based on your
observations
3.Hypothesis: Propose an explanation of your problem
(If…, then… statement)
Scientific Process
Steps to Scientific Process:
4. Experiment: Materials list and procedure to test your
hypothesis
5. Results: Collection of experiment’s data and analysis of
data
6. Conclusion: statements about what your experiment
found based on the data collected
Measurement in Chemistry
• Use the International System of Units (SI)
– Aka: the metric system
Quantity
Unit
Symbol
Length
meter
m
Volume
liter
L
Mass
gram
g
Temperature
Degree Celcius
oC
Density
Grams per cubic cm or
grams per milliliter
g/cm3 or g/mL
Metrics for Honors Chemistry
Scientific Units and Devices
Device
Unit
Measurement
Balance
Gram
mass
Graduated
cylinder
Liter
volume
Meter Stick
Meter
Length or
distance
Thermometer
Celsius
temperature
Clock
Second
Time
Measurement in Chemistry
Devices to use for taking measurements:
– Balance – mass, usually in grams
– Ruler – length, usually in cm or mm
– Thermometer: temperature, usually in oC
– Graduated cylinder: volume, usually in mL
11.1 Uncertainty and errors in
measurements
EI: All measurement has a limit of precision and
accuracy, and this must be taken into account
when evaluating experimental results.
NOS: Making quantitative measurements with
replicated to ensure reliability – precision,
accuracy, systematic, and random errors must
be interpreted through replication
U1 & U2. Types of Data
Qualitative Data
• Non-numerical data
• Usually observations
made during an
experiment
• Use your senses, with
exception to taste
EX: color, texture, smell,
luster, temperature
Quantitative Data
• Numerical data
• Measurements
collected during the
experiment
EX: 5.64 g, 9.25mm
A & S 8. Distinguish between precision
and accuracy
• Precision: how close several experimental
measurements of the same quantity are to each
other
• Accuracy: how close a measured value is to the
actual value
A & S 8. Precision and Accuracy
Low
accuracy,
low precision
Low
accuracy,
high
precision
High
accuracy, low
precision
High
accuracy,
high
precision
A & S 7. Calculating Error
• Error: the difference between the accepted
value and the experimental value
– Accepted value: the correct value based on
reliable resources
– Experimental value: value measured in the lab
Error = experimental value - accepted value
A & S 7. Calculating Percent
Error
• Percent Error: the relative error, shows the
magnitude of the error
Percent Error = I error I x 100
accepted value
Metrics for Honors Chemistry
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•
•
•
•
•
•
•
•
Metric Prefixes M K H D _ d c m_ _ m
Mega (M) 106
Kilo (K) 103
Hecta (H) 102
Deca (D) 101
ORIGIN: meter, liter, gram
deci (d) 10-1
centi (c) 10-2
milli (m) 10-3
micro (m) 10-6
U 2. Sig Figs
Significant Figures (sig figs): the digits in a
measurement up to and including the first
uncertain digit
• Ex: 62 cm3 = 2 sig figs; 100.00 g = 5 sig figs
U 2. Sig Figs
Rules for Counting Sig Figs
1.
Every nonzero digit represented in a measurement is
significant.
24.7 m has 3 sig figs
0.4587 has 4 sig figs
134.798 has ? sig figs
0.6668 has ? sig figs
U 2. Sig Figs
Rules for Counting Sig Figs
2.
Zeros appearing between non zero digits are significant.
70.03 has 4 sig figs
0. 96501 has 5 sig figs
40.30609 has ? sig figs
0.306201 has ? sig figs
U 2. Sig Figs
Rules for Counting Sig Figs
3. Zeros ending a number to the right of the decimal point are
significant
23.80 has 4 sig figs
0.130700 has 6 sig figs
1,006.00 has ? sig figs
0.34090 has ? sig figs
U 2. Sig Figs
Rules for Counting Sig Figs
4. Zeros starting a number or ending the number to the left of the
decimal point are not counted as significant
16000 has 2 sig figs
0.0002709 has 4 sig figs
870,600 has ? sig figs
0.0450 has ? sig figs
U 2. Sig Figs
General Rule for Counting Sig Figs
Start on the left with the first nonzero digit.
End with the last nonzero digit OR with the last
zero that ends the number to the right of the
decimal point
U 2. Sig Figs
Sig Fig Practice
In your notes: copy the problem and write the
number of sig figs for each number
1. 34.6 g
2. 56.78 g
3. 4.00670 g
4. 0.000450 g
5. 300.45 g
U 2. Sig Figs
Sig Fig Calculations
1. Adding/Subtracting: the number of decimal places is
important, answer should have same number of
decimal places as the smallest number of decimal places
7.10 g + 3.10 g = 10.20 g
22.36 g – 15.16 g = 7.20 g
U 2. Sig Figs
Sig Fig Calculations
1. Adding/Subtracting:
3.45 g + 3.6 g =
78.645 g – 5.46 g =
U 2. Sig Figs
Sig Fig Calculations
2. Multiplying/Dividing: the number of sig figs is
important, the number with the least number of sig figs
determines sig figs in the answer.
0.125kg x 7.2 oC x 4.18kJ kg-1 oC-1= 3.762 kJ round to 3.8 kJ
7.55 m x 0.34 m =
U 2. Sig Figs
Sig Fig Calculations Practice
In your notes: copy the problems and solve.
1. 4.67 g + 3.4 g =
2. 59.74 ml – 45.689 ml =
3. 34.57 g x 23.4 g =
4. 256.8 g / 5.36 g =
U 2. Scientific Notation
• Scientific Notation is useful for very small and
very large numbers.
• 0.00000450 is written as 4.50 x 10-6
• 770000000 is written as 7.7 x 108
U 2. Scientific Notation
To Convert into Scientific Notation:
•move the decimal point so only 1 non-zero digit is
to the left of the decimal point.
•if you move the decimal point to the left, the
power of 10 will be positive (the number is the
number of spaces moved)
•if you move the decimal point to the right, the
power of 10 will be negative.
U 2. Scientific Notation
Scientific Notation Practice
3,600 = 3.6 x 103
0.000 075 2 = 7.52 x 10-5
5,732,873.912 = ?
0.124 04 = ?
U 2. Scientific Notation
To Convert out of Scientific Notation:
•if the power of 10 is positive move the decimal
point to the right the power number of places
•if the power of 10 is negative move the decimal
point to the left the power number of places.
U 2. Scientific Notation
Scientific Notation:
8.1 x 10-5 = 0.000081
1.2 x 108 = 120000000
9.342 780 23 x 104 = ?
3.704 x 10-6 = ?
U 2. Scientific Notation
Scientific Notation Calculations
Addition/ Subtraction: exponents must be the
same, adjust each number to the same
exponent, then add or subtract as usual.
U 2. Scientific Notation
Scientific Notation Calculations
Ex: 5.40 x 103 + 6.0 x 102 =
convert 6.0x 102 to 0.60 x 103
5.40x 103 + 0.60x 103 = 6.00x 103
U 2. Scientific Notation
Scientific Notation Calculations
Multiplication: multiply the coefficients, then
add the exponents.
(3.0x 104) x (2.0 x 102) = 6.0 x 106
U 2. Scientific Notation
Scientific Notation Calculations
Division: divide the coefficients, then subtract
the exponents.
(3.0 x 104) / (2.0 x 102) = 1.5 x 102
U 2. Density
Density: The ratio of the mass of an object
to its volume
Density = Mass
Volume
units = g/cm3 (solid & liquid) or g/L (gases)
U 2. Density
Ex: a piece of lead has a volume of 10.0 cm3
and a mass of 114 g, what is it’s density?
114g/ 10.0cm3 = 11.4 g/cm3
11.1 Uncertainty and Error in
Measurement
• Measurement is important in chemistry.
• Many different measurement apparatus are
used, some are more appropriate than others.
11.1 Uncertainty and Error in
Measurement
• Example: You want to measure 25 cm3 (25 ml)
of water, what can you use?
– Beaker, volumetric flask, graduated cylinder,
pipette, buret, or a balance
– All of these can be used, but will have different
levels of uncertainty. Which will be the best?
A & S 1. Systematic Errors
• Systematic Error: occur as a
result of poor experimental
design or procedure.
– Cannot be reduced by
repeating experiment
– Can be reduced by careful
experimental design
A & S 1. Systematic Errors
• Systematic Error Example:
measuring the volume of water
using the top of the meniscus
rather than the bottom
• Measurement will be off every
time, repeated trials will not
change the error
A & S 1. Random Error
• Random Error: imprecision of measurements, leads to
value being above or below the “true” value.
• Causes:
–
–
–
–
Readability of measuring instrument
Effects of changes in surroundings (temperature, air currents)
Insufficient data
Observer misinterpreting the reading
• Can be reduced by repeating measurements
A & S 1: Random and Systematic Error
Systematic and Random Error Example
Random: estimating the mass of Magnesium ribbon rather than
measuring it several times (then report average and uncertainty)
0.1234 g, 0.1232 g, 0.1235 g, 0.1234 g, 0.1235 g, 0.1236 g
Avg Mass= 0.1234 + 0.0002 g
A & S 1: Random and Systematic Error
Systematic and Random Error Example
Systematic: The balance was zeroed incorrectly with each
measurement, all previous measurements are off by 0.0002 g
0.1236 g, 0.1234 g, 0.1237 g, 0.1236 g, 0.1237 g, 0.1238g
Avg Mass = 0.1236
A & S 8. Distinguish between precision and
accuracy in evaluating results
Precision: how close several experimental
measurements of the same quantity are to each
other
– how many sig figs are in the measurement.
– Smaller random error = greater precision
A & S 8. Distinguish between precision and
accuracy in evaluating results
Accuracy: how close a measured value is to the
correct value
– Smaller systematic error = greater accuracy
• Example: masses of Mg had same precision, 1st
set was more accurate.
U 5. Reduction of Random Error
• Random errors can be reduced by
– Use more precise measuring equipment
– Repeat trials and measurements (at least 3,
usually more)
A & S 2. Uncertainty Range (±)
• Random uncertainty can be estimated as half
of the smallest division on a scale
• Always state uncertainty as a ± number
A & S 2. Uncertainty Range (±)
• Example:
– A graduated cylinder has increments of 1 mL
– The uncertainty or random error is
1mL / 2 = ± 0.5 mL
A & S 2. Uncertainty Range (±)
Uncertainty of Electronic Devises
On an electronic devices the last digit is rounded up
or down by the instrument and will have a random
error of ± the last digit.
Example:
–Our balances measure ± 0.01 g
–Digital Thermometers measure ± 0.1 oC
State uncertainties as absolute and
percentage uncertainties
• Absolute uncertainty
– The uncertainty of the apparatus
– Most instruments will provide the uncertainty
– If it is not given, the uncertainty is half of a
measurement
– Ex: a glass thermometer measures in 1oC
increments, uncertainty is ±0.5oC; absolute
uncertainty is 0.5oC
State uncertainties as absolute and
percentage uncertainties
• Percentage uncertainty
= (absolute uncertainty/measured value) x 100%
Determine the uncertainties in results
Calculate uncertainty
Using a 50cm3 (mL) pipette, measure 25.0cm3.
The pipette uncertainty is ± 0.1cm3.
What is the absolute uncertainty?
0.1cm3
What is the percent uncertainty?
0.1/25.0 x 100= 0.4%
Determine the uncertainties in results
Calculate uncertainty
Using a 150 mL (cm3) beaker, measure 75.0 ml
(cm3). The beaker uncertainty is ± 5 ml (cm3).
What is the absolute uncertainty?
5 ml (cm3)
What is the percent uncertainty?
5/75.0 x 100= 6.66%  7%
Determine the uncertainties in
results
Percent error = I error l
accepted
x 100
If percent error is greater than uncertainty, then
systematic errors are a problem
Random error is estimated by uncertainty, if
smaller than percent error, then systematic
errors are causing inaccurate data.
Determine the uncertainties in
results
Error Propagation: If the measurement is added
or subtracted, then absolute uncertainty in
multiple measurements is added together.
Determine the uncertainties in
results
Example:
If you are trying to find the temperature of a
reaction, find the uncertainty of the initial
temperature and the uncertainty of the final
temperature and add the absolute
uncertainty values together.
Determine the uncertainties in
results
Example: Find the change in temperature
Initial Temp: 22.1 ± 0 .1oC
Final Temp: 43.0 ± 0.1oC
Change in temp: 43.1-22.1 = 20.9
Uncertainty: 0.1 + 0.1 = 0.2
Final Answer: Change in Temp is 20.9 ± 0.2 oC
Determine the uncertainties
in results
Error Propagation: If the measurement requires
multiplying or dividing: percent uncertainty in
multiple measurements is added together.
Determine the uncertainties
in results
Example:
If you are trying to find the density of an object,
find the uncertainty of the mass, the
uncertainty of the volume, you add the
percent uncertainty for each to get the
uncertainty of the density.
Determine the uncertainties
in results
Example: Find the Density given:
Mass: 25.45 ± 0.01 g and Volume: 10.3 ± 0.05
mL
Density: 25.45/10.3 = 2.47 g/mL
% uncertainty Mass: (0.01/25.45) x 100 = 0.04%
% uncertainty Volume: (0.05/10.3) x 100 = .5%
0.04 + .5 = .54%
Final Answer: Density is 2.47 ± .54%
Determine the uncertainty in
results
Uncertainty in Results (Error Propagation)
1. Calculate the uncertainty
a. From the smallest division (on a graduated cylinder or
glassware)
b. From the last significant figure in a measurement (a
balance or digital thermometer)
c. From data provided by the manufacturer (printed on the
apparatus)
2. Calculate the percent error
3. Comment on the error
a. Is the uncertainty greater or less than the % error?
b. Is the error random or systematic? Explain.
11.2 Graphing
EI: Graphs are a visual representation of trends
in data.
NOS: The idea of correlation – can be tested in
experiments whose results can be displayed
graphically.
U 1. Graphical Techniques
Why do are graphs used?
• Graphs are an effective means of
communicating the effect of the independent
variable on a dependent variable, and can
lead to determination of physical quantities.
U1. Graphical Techniques
Example Graph
– show the relationship
between the independent
variable and the
dependent variable
Dependent
• Graphs are used to
present and analyze data.
Independent
U2. Sketched graphs
Example Graph
– Have labeled, but unscaled
axes
– Used to show qualitative
trends
• Variables that are
proportional or inversely
proportional
Dependent
• Sketched graphs:
Independent
U3. Drawn Graphs
Graphs MUST have:
• A title
• Label axes with
quantities and units
Mass (g)
Candle Mass After Burning
Time (min.)
U3, A &S 1. Drawn Graphs
Graphs MUST have:
• Use available space as
effectively as possible
• Use sensible linear
scales- NO uneven jumps
• Plot ALL points correctly
Mass (g)
Candle Mass After Burning
Time (min.)
A&S 3. Best Fit Lines
– drawn smoothly and
clearly
– Do not have to go
through all the points,
but do show the overall
trend
Temperature (oC)
Best Fit Lines should be
Time (sec)
A & S 4 Physical quantities from graphs
• Find the gradient (slope) and the intercept
• Use y = m x + b for a straight line
•
•
•
•
y= dependent variable
x = independent variable
m= the gradient (slope)
b = the intercept on the vertical (y) axis
A & S 4 Physical quantities from graphs
• Ex: to find the slope (m), find 2 data points
(2,5) and (4, 10)
m= (y2-y1) = (10-5) = 5 = 2.5
(x2-x1)
(4-2) 2
A & S 2. Interpretation of Graphs
Dependent
Variables:
Independent- the cause,
plotted on the
horizontal axis (x-axis)
AKA: Manipulated
Example Graph
Independent
A & S 2 Interpretation of Graphs
Dependent
Variables:
Dependent- the effect,
plotted on the the
vertical axis (y-axis)
AKA: Responding
Example Graph
Independent
A & S 2. Interpretation of Graphs
Interpolation:
determining an
unknown value using
data points within the
values already
measured
A & S 2. Interpretation of Graphs
Extrapolation: when a line
has to be extended
beyond the range of the
measurements of the
graph to determine
other values
– Absolute zero can be
found by extrapolating
the line to lower
temperatures.