Tutorial 2 - Calibration Methods
Question 1
The following data were obtained when calibrating a calcium ion electrode for the determination
of pCa. A linear relationship between the potential E and pCa is exists in the given
concentration range.
pCa
E / mV
5.00
-53.8
4.00
-27.7
3.00
+2.7
2.00
+31.9
1.00
+65.1
(a) Plot the data and draw a line through the points by hand.
(b) Derive a least-squares expression for the best straight line through the points. Draw this
line on the same graph.
(c) Calculate the standard deviation for the slope of the least-squares line.
(d) Calculate the standard deviation of the intercept of the least-squares line.
(e) Calculate the pCa of a serum solution in which the electrode potential was 20.3 mV.
(f) Calculate the molar calcium ion concentration for the sample described in (e).
Question 2
An unknown sample of Cu 2+ gave an absorbance of 0.262 in an atomic absorption analysis.
Then 1.00 mL of solution containing 100.0 ppm (= 100 g/mL) Cu2+ was mixed with 95.0 mL of
unknown, and the mixture was diluted to 100.0 mL in a volumetric flask. The absorbance of the
new solution was 0.500.
(a) Denoting the initial unknown concentration as [Cu2+]i, write an expression for the final
concentration [Cu2+]f, after dilution. Units of concentration are ppm.
(b) In a similar manner, write the final concentration of added standard Cu 2+, designated as [S]f.
(c) Find [Cu2+]i in the unknown.
Question 3
Eu(III) emits orange light when illuminated with ultraviolet radiation. Certain organic compounds
that bind to Eu(III) are required to enhance the emission. The figure below shows standard
addition experiments in which 10.00 mL of sample and 20.00 mL containing large excess of
organic additive were placed in 50 mL volumetric flasks. Then Eu(III) standards (0, 10.00, or
15.00 mL) were added and the flasks were diluted to 50.0 mL with water. Standards added to
tap water contained 0.152 ng/mL (ppb) of Eu(III), but those added to pond water were 100 times
more concentrated (15.2 ng/mL).
40
35
Pond water
Emission Peak Area
30
25
20
-14.6 mL
15
10
-6.0 mL
Tap water
5
0
-20.0
-15.0
-10.0
-5.0
-5
0.0
5.0
10.0
15.0
20.0
Volume of Added Standard (mL)
(a) From the x-intercepts in the graph, calculate the concentration of Eu(III) (ng/mL) in pond
water and tap water.
(b) In the case of tap water, the emission peak area increases by 4.61 units when 10.00 mL of
0.152 ng/mL standard are added. This response is 4.61 units per 1.52 ng = 3.03 units per
ng of Eu(III). For pond water the response is 12.5 units when 10.00 mL of 15.2 ng/mL
standard is added, or 0.0822 units per ng. How would you explain these observations?
Why was standard addition necessary for this analysis?
Question 4
Students performed an experiment in which each flask contained 25.00 mL of serum, varying
additions of 2.640 M NaCl standard, and a total volume of 50.00 mL
Volumetric Flask
Volume of Standard (mL)
Na+ Atomic Emission Signal
1
0
3.13
2
1.000
5.40
3
2.000
7.89
4
3.000
10.30
5
4.000
12.48
(a) Prepare a standard addition graph and find the concentration of Na + in the serum.
(b) Find the uncertainty in the answer to part (a). (See “Propogation of uncertainty with
calibration curves” in the textbook (pg 100 in 5th ed.))
Question 5
Chloroform is an internal standard in the determination of DDT in a polarographic analysis in
which each compound is reduced at an electrode surface. A mixture containing 0.500 mM
chloroform and 0.800 mM DDT gave signals of 15.3 A for chloroform and 10.1 A for DDT.
10.0 mL of an unknown solution containing DDT was placed in a 100-mL volumetric flask and
10.2 L of chloroform (M = 119.39 g/mol, density = 1.484 g/mL) were added. After diluting to
the mark with solvent, polarographic signals of 29.4 and 8.7 A were observed for the
chloroform and DDT, respectively. Find the concentration of DDT in the unknown.
Additional Questions
Question 6
Mass spectrometric signals for known concentrations of methane in H2 are given in the table
below.
CH4 (Vol %)
0
0.062
0.122
0.245
0.486
0.971
1.921
Signal (mV)
9.1
47.5
95.6
193.8
387.5
812.5
1671.9
(a) Subtract the blank value from all other values. Then use the method of least-squares to find
the slope and intercept. Construct a calibration curve.
(b) Replicate measurements of an unknown gave 152.1, 154.9, 153.9, and 155.1 mV, and a
blank gave 8.2, 9.4, 10.6, and 7.8 mV. Subtract the average blank from the average
unknown to find the average corrected signal for the unknown.
(c) Find the concentration of the unknown and its uncertainty.
Question 7
In a chromatographic analysis, a solution containing 3.47 mM X (analyte) and 1.72 mM S
(internal standard) gave peak areas of 3 473 and 10 222, respectively. Then 1.00 mL of 8.47
mM S was added to 5.00 mL unknown X, and the mixture was diluted to 10.00 mL. This
solution gave peak areas of 5 428 and 4 431 for X and S, respectively.
(a) Calculate the response factor for the analyte.
(b) Find the concentration of S (mM) in the 10.0 mL of mixed solution.
(c) Find the concentration of X (mM) in the 10.0 mL of mixed solution.
(d) Find the concentration of X (mM) in the original unknown.
Question 8
The quantity of substance Y produced radioactively in a fixed time is proportional to the
concentration of catalyst X in the solution. An unknown containing X in a unknown matrix with
an initial volume of 50.0 mL was treated with increments of standard 0.531 M X and the
following results were obtained:
Volume of added X (L)
0
100.0
200.0
300.0
400.0
Counts/min of radioactive Y
1 084
1 844
2 473
3 266
4 010
Prepare a standard addition graph and find the concentration of X in the original unknown.