Calculations in Chemistry - Lanka Education and...
Transcript of Calculations in Chemistry - Lanka Education and...
Calculations in Chemistry
Dr. S. Sri Skandaraja
Department of ChemistryUniversity of Kelaniya
CHEM 11111
Graphical presentation of data
Straight line graphs
How variable „y‟ changes as variable „x‟
changes
y = mx + c where m =slope
c= intercept
Tables and graphs are visual representations. They are used to
organise information to show patterns and relationships. A graph
shows this information by representing it as a shape.
line graphs
0
0.5
1
Concentration
Tra
ns
mit
tan
ce
, T
Transmittance decreases
exponentially as concentration
increases
T=10-A =10- ecl
Transmittance and Concentration
Calibration Techniques
1. Calibration Curve Method
2. Standard Additions Method
3. Internal Standard Method
Calibration Curve Method
1. Most convenient when a large number
of similar samples are to be analyzed.
2. Most common technique.
Calibration Curve Procedure
1. Prepare a series of standard solutions
(analyte solutions with known
concentrations).
2. Plot [analyte] vs. Analytical Signal.
3. Use signal for unknown to find [analyte].
Example: Pb in Blood by GFAAS
[Pb] Signal
(ppb) (mAbs)
0.50 3.76
1.50 9.16
2.50 15.03
3.50 20.42
4.50 25.33
5.50 31.87
Example: Pb in Blood by GFAAS
[Pb] Signal
(ppb) (mAbs)
0.50 3.76
1.50 9.16
2.50 15.03
3.50 20.42
4.50 25.33
5.50 31.87
Results of linear regression:
S = mC + b
m = 5.56 mAbs/ppb
b = 0.93 mAbs
Using a Calibration Curve
Prefer calibration with a linear response
- analytical signal proportional to the quantity of analyte
Linear range
- analyte concentration range over which
the response is proportional to
concentration
Dynamic range
- concentration range over which
there is a measurable response
to analyte
Additional analyte does not result in
an increase in response
Impact of “Bad” Data Points
Identification of erroneous data point.
- compare points to the best-fit line
- compare value to duplicate measures
Omit “bad” points using chemometry.
- “bad” data points can skew the best-fit line and
distort the accurate interpretation of data.
Remove “bad” point
Improve fit and
accuracy of m and b
y=0.16x + 0.12 R2=0.53261 y=0.091x + 0.11 R2=0.99518
Limitations in a Calibration Curve
(iv)Limited application of calibration curve to
determine an unknown.
- Limited to linear range of curve
- Limited to range of experimentally determined
response for known
analyte concentrations
Unreliable determination
of analyte concentration
Uncertainty increases further
from experimental points
The product-moment correlation coefficient
The first problem - is the calibration plot linear?
A common method of estimating how well the experimental points fit a straight line is to calculate the product-moment correlation coefficient, r.
This statistic is often referred to simply as the ‘correlation coefficient’
Example
Standard aqueous solutions of fluoresceine are examined spectrophotometrically and yielded the following intensities:
Intensities 2.2 5.0 9.0 12.6 17.3 21.0 24.7
Conc. Pg ml-1 0 2 4 6 8 10 12
Determine r.
All significant figures must be considered
the calibration curve must always be
plotted (on graph paper or a computer
monitor): otherwise a straight-line
relationship might wrongly be
deduced from the calculation of r
•a zero correlation coefficient does not mean that y and x are entirely unrelated; it only means that they are not linearly related.
Misinterpretation of correlation coefficients
Standard Addition In standard addition, known quantities of analyte are
added to the unknown.
From the increase in signal, we deduce how much
analyte was in the original unknown.
This method requires a linear response to analyte.
Standard addition is especially appropriate when the
sample composition is unknown or complex and
affects the analytical signal.
The matrix is everything in the unknown, other than
analyte.
A matrix effect is a change in the analytical signal
caused by anything in the sample other than analyte.
Graph shows a
strong matrix effect
in the analysis of
perchlorate (ClO4-)
by mass
spectrometry.
Hence, the method
of standard
addition is
required.
Consider a standard addition in which a sample
with unknown initial concentration of analyte [X]igives a signal intensity IX.
Then a known concentration of standard, S, is
added to an aliquot of the sample and a signal ISX is
observed for this second solution.
Addition of standard to the unknown changes the
concentration of the original analyte because of
dilution.
Diluted concentration of analyte = [X]f;
Where “f” stands for “final.”
Concentration of standard in the final solution = [S]f. (Bear in mind that the chemical species X and S are the same.)
Signal is directly proportional to analyte
concentration
Concentration of analyte
in initial solution
Concentration of analyte
plus standard in final solution
signal from initial solution
signal from final solution=
Concentration of analyte
in initial solution signal from initial solutionα
Concentration of analyte
plus standard in final solutionsignal from final solutionα
Concentration of analyte
in initial solution
Concentration of analyte
plus standard in final solution
signal from initial solution
signal from final solution=
Vo = initial volume of unknown
VS = added volume of standard with concentration[S]i,
V = Vo + VS = total volume
Serum containing Sodium gave a signal of 4.27 mV in an
atomic emission analysis. Then 5.00 mL of 2.08 M NaCl
were added to 95.0 mL of serum. This spiked serum gave
a signal of 7.98 mV. Find the original concentration of
Sodium in the serum.
Graphical Procedure for Standard
Addition
There are two common methods to perform standard
addition.
If the analysis does not consume solution, we begin with
an unknown solution and measure the analytical signal.
Then, we add a small volume of concentrated standard
and measure the signal again.
We add several more small volumes of standard and
measure the signal after each addition.
Standard should be concentrated so that only small volumes
are added and the sample matrix is not appreciably altered.
Added standards should increase the analytical signal by a
factor of 1.5 to 3.