Download 1/30 Lecture

Chem. 31 – 1/30 Lecture
Announcements I
• Wednesday
– Quiz (on homework and material covered in lecture)
– Corrected diagnostic quiz due
• In Lab Wednesday and Thursday – Lab
Procedures Quiz (covers lab lectures,
introductory parts of lab manual, safety lectures,
and lab grading)
• Adding (vacancies – Sect 4 and 6?)
Announcements II
• SacCT
– Now Set up
– Will update grades (assignment grades about 2 weeks
after collected and net grades after each test)
– Homework, quiz and exam keys also will be posted
• Today’s Lecture
– Stoichiometry (last slide)
– Error and Uncertainty (Chapter 3)
• Definitions
• Significant figures
• Accuracy and precision in measurements
Stoichiometry
• Remember: there are two (common) ways
to deliver a known amount (moles) of a
reagent:
– Mass (using formula weight)
– Volume (if molarity is known)
Chapter 3 – Error and Uncertainty
• Error is the difference between measured
value and true value or
error = measured value – true value
• Uncertainty
– Less precise definition
– The range of possible values that, within
some probability, includes the true value
Measures of Uncertainty
• Explicit Uncertainty:
Measurement of CO2 in the air: 399 + 3 ppmv
The + 3 ppm comes from statistics associated
with making multiple measurements (Covered in
Chapter 4)
• Implicit Uncertainty:
Use of significant figures (399 has a different
meaning than 400 and 399.32)
Significant Figures
(review of general chem.)
• Two important quantities to know:
– Number of significant figures
– Place of last significant figure
Example: 13.06
4 significant figures and last place is hundredths
• Learn significant figures rules regarding
zeros
Significant Figures - Review
• Some Examples (give # of digits and place of
last significant digit)
–
–
–
–
21.0
0.030
320
10.010
Significant Figures in Mathematical
Operations
• Addition and Subtraction:
– Place of last significant digit is important
(NOT number of significant figures)
– Place of sum or difference is given by least
well known place in numbers being added or
subtracted
Example: 12.03 + 3 = 15.03 = 15
Hundredths place
ones place
Least well known
Significant Figures in Mathematical
Operations
• Multiplication and Division
– Number of sig figs is important
– Number of sig figs in Product/quotient is
given by the smallest # of sig figs in numbers
being multiplied or divided
Example: 3.2 x 163.02 = 521.664 = 520 = 5.2 x 102
2 places
5 places
Significant Figures in Mathematical
Operations
• Multi-step Calculations
– Follow rules for each step
– Keep track of # of and place of last significant
digits, but retain more sig figs than needed
until final step
Example: (27.31 – 22.4)2.51 = ?
Step 1 (subtraction): (4.91)2.51
Note: 4.91 only has 2 sig figs, more digits listed (and used in next step)
Step 2 multiplication = 12.3241 = 12
Significant Figures
More Rules
• Separate rules for logarithms and powers
(Covering, know for homework, but not tests)
– logarithms: # sig figs in result to the right of decimal
point = # sig figs in operand
example: log(107) = 2.02938 = 2.029
107 = operand
3 sig fig
results need 3 sig figs past
decimal point
– Powers: # sig figs in results = # sig figs in operand
to the right of decimal point
= 2.51 x 10-12 = 3 x 10-12
example: 10-11.6
1 sig fig past decimal point
Significant Figures
More Rules
• When we cover explicit uncertainty, we
get new rules that will supersede rules
just covered! So you get to learn new
rules from scratch again!
Types of Errors
• Systematic Errors
True
Volume
– Always off in one direction
– Examples: using a “stretched” plastic ruler to make
length measurements (true length is always greater
than measured length); reading buret without moving
eye to correct height
• Random Errors
eye
– Equally likely in any direction
– Present in any (continuously varying type)
Meas.
Volume
measurement
– Examples: 1) fluctuation in readings of a balance with
window open, 2) errors in interpolating (reading
between markings) buret readings
Accuracy and Precision
• Accuracy is a measure
of how close a
measured value is to
a true value
• Precision is a measure
of the variability of
measured values
Precise,
but not(Accuracy
accurate
Poor precision
Precise and Accurate
also not great)
Accuracy and Precision
• Accuracy is affected by systematic and
random errors
• Precision is affected mainly by random
errors
• Precision is easier to measure
Accuracy and Precision
• Both imprecise and
inaccurate measurements
can be improved
• Accounting for errors
improves inaccurate
measurements (if shot is
above and right aim low
+ left)
• Averaging improves
imprecise measurements
rough ave of
imprecise shots
aim here
Propagation of Uncertainty
• What does propagation of uncertainty refer to?
• It refers to situations when one or more variables
are measured in order to calculate another
variable
• Examples:
Vinitial
– Calculation of volume delivered by a buret:
Vfinal
Vburet = Vfinal – Vintial
– Note: uncertainty in Vburet can be calculated by
uncertainty in Vinitial and Vfinal or by making multiple
readings to get multiple values of Vburet (and then
using the statistics covered in Chapter 4)
– Calculation of the volume of a rectangular solid:
l
Vobject = l·w·h
– Calculation of the volume of a cube
Vobject = l3
– Calculation of the density of a liquid:
Density = mliquid/Vliquid
• Go to Board to go over examples
h
w