Chem. 31 – 2/2 Lecture
Announcements
• Due Wednesday
– Turn in corrected diagnostic quiz
– HW Set 1.1 – just additional problem
• Quiz on Wednesday (covering Ch. 1)
• Today’s Lecture
– Stoichiometry
– Titrations
– Start to Ch. 3
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)
• Titrations = A practical way of using
stoichiometry with precise measure of
added volume
Titrations
Definitions
• Titrant:
– Reagent solution added
out of buret (concentration
usually known)
titrant
• Analyte solution:
– Solution containing analyte
• Equivalence Point:
– point where ratio of moles
of titrant to moles of
analyte is equal to the
stoichiometric ratio
analyte
solution
for: Al3+ + 3C2O42- → Al(C2O4)33- n(Al3+)/n(C2O42-) = 3/1 at equivalence pt.
Titrations
Practical Requirements
• The equilibrium constant must be large
– Precision of titration will depend on size of K
and concentration of analyte
– Typically K ~ 106 is marginal, K > 1010 is
better
• The reaction must be fast
• It must be possible to “observe” the
equivalence point
– observed equivalence point = end point
Titrations
Other Definitions
• Standardization vs. Analyte
Titrations
– To accurately determine an
analyte’s concentration, the
titrant concentration must be
well known
– This can be done by preparing
a primary standard (high purity
standard)
– Alternatively, the titrant
concentration can be
determined in a
standardization titration (e.g.
vs. a known standard)
• Rationale:
– many solutions can not be
prepared accurately from
available standards
• Example:
– determination of [H2O2] by
titration with MnO4– neither compound is very
stable so no primary
standard
– instead, [MnO4-]
determined by titration
with H2C2O4 (made from
primary standard) in
standardization titration
– then, H2O2 titrated using
standardized MnO4-
Titrations
Other Definitions
• Direct vs. Back Titration
– In a direct titration, the titrant added slowly
to the analyte until reaching an end point
– In a back titration, a reagent is added to the
analyte in excess, and then the excess
reagent (beyond what was needed to react) is
titrated to an end point
– Often done to get sharper endpoint
Titrations
Back Titration Example
Titration to determine moles of Na2CO3 in a sample:
First, direct titration: Na2CO3 + 2HCl → H2CO3 +
NaCl (we will do following AA lab)
HCl
Direct Titration Plot
not that sharp
14.00
12.00
pH
10.00
Na2CO3
8.00
6.00
4.00
2.00
0.00
0
5
10
15
20
25
V(HCl)
30
35
40
45
50
Titrations
Back Titration Example
HCl
Titration to determine moles of Na2CO3 in a sample:
Now, via back titration: excess HCl added to sample
Na2CO3 + HCl → NaCl + H2CO3 +heat → NaCl + H2O + CO2(g)
After heating only NaCl and excess HCl left
Excess HCl titrated with NaOH to NaCl + H2O
Na2CO3
Direct Titration Plot
Very Sharp
14
12
pH
10
8
Excess HCl
6
4
2
0
0
5
10
15
V(HCl)
20
25
30
NaOH
Titrations
What Makes a Titration Sharp?
-Log[analyte]
uncertainties in
log[analyte]
[reactant]
at eq. point
V(eq. pt.)
V(titrant)
small uncertainty
in V results
NON-SHARP TITRATION
-Log[analyte]
• A sharp titration has a
large slope (absolute
value)
• Slope at endpoint
seen in plot of log[analyte] vs.
V(titrant)
• With a sharp titration,
errors or uncertainties
in V(equivalence
point) are small
SHARP TITRATION
V(titrant)
larger unc. in V
Titrations
Some Questions
1.
2.
3.
List two requirements for a titration to be functional.
In a back titration, what is actually being titrated? (a)
analyte b) reagent added c) excess reagent d)
secondary reagent)
Why might one want to standardize a prepared
solution of 0.1 M NaOH rather than prepare it to
exactly 0.100 M? NaOH is a hygroscopic solid that
also absorbs CO2.
Titrations
Back Titration Example
Sulfur dioxide (SO2) in air can be analyzed by trapping in
excess aqueous NaOH (see 1). With addition of
excess H2O2, it is converted to H2SO4 (see 2), using up
additional OH- (see 3).
1. SO2 (g) + OH- (aq) → HSO32. HSO3- + H2O2(aq) → HSO4- + H2O
3. HSO4- + OH- (aq) → SO42- + H2O
208 L of air is trapped in 5.00 mL of1.00 M NaOH. After
excess H2O2 is added to complete steps 1 to 3
(above), the remaining NaOH requires 21.0 mL of
0.0710 M HCl. What is the SO2 concentration in
mmol/L?
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