Eleanor Calibration Curves_emw

Eleanor Calibration Curves_emw - Calibra'on
Curves
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Unformatted text preview: Calibra'on
Curves
 Eleanor
Waxman
 28
and
30
September
2011
 Eleanor.waxman@colorado.edu
 Plan
 1.  Regular
Calibra'on
Curves
(Wed)
 2.  Standard
Addi'on
(Wed/Fri)
 3.  If
'me,
in
class
analysis
example
(Fri)
 •  Please
bring
your
computer.
 •  To
prep
for
this,
please
download
“Data
for
 Friday,
30
September.xlsx”
or
“Data
for
Friday,
30
 September_xlscompa'ble.xls”
and
have
it
 loaded.
 What
is
a
calibra'on
curve?
 •  A
plot
of
instrument
response
versus
analyte
concentra'on.
 Absorbance
(arbitrary
units)
 Sample
Calibra2on
Curve
 0.58
 0.48
 0.38
 0.28
 0.18
 0.08
 ‐0.02
 y
=
0.9948x
‐
0.0214
 R²
=
0.9981
 0
 0.2
 0.4
 0.6
 Concentra2on
(M)
 0.8
 How
do
you
make
one?
 For
this
example,
let’s
add
food
coloring
to
50
mL
of
water.
 Standard:

Solu'on
with
known
amount
of
analyte
 Blanks
 •  Blank:

Solu'on
with
all
reagents
and
solvents,
 but
no
analyte.


 –  In
the
previous
example,
it
would
be
the
same
 type
of
water
used
to
make
the
standards.
 Blank
 Standards
 Discussion
Ques'on
1
 •  What
would
be
an
appropriate
blank
for
 studying
proteins
in
a
carbonate
buffer?
 •  Next
semester,
there’s
a
lab
looking
at
 tartrazine
(yellow
dye)
in
Mountain
Dew.

 What
would
be
an
appropriate
blank?
 How
do
you
make
one?
 Drops
Added
 Absorbance
(532
nm)
 0
 0.01
 10
 0.18
 20
 0.41
 30
 0.60
 40
 0.79
 50
 1
 Absorbance
versus
Drops
Added
 Absorbance
 1
 0.8
 0.6
 0.4
 0.2
 0
 0
 10
 20
 30
 40
 Drops
of
Food
Coloring
Added
 50
 How
do
you
make
one?
 Drops
Added
 Absorbance
(532
nm)
 0
 0.01
 1
 0.02
 2
 ‐0.01
 3
 0.01
 5
 0.11
 10
 0.18
 15
 0.29
 20
 0.41
 25
 0.52
 30
 0.60
 35
 0.71
 40
 0.79
 45
 0.92
 50
 1
 55
 0.98
 60
 0.99
 This
is
a
scafer
plot
of
the
data.
 Absorbance
of
Green
Food
Coloring
at
532
nm
 1.2
 Absorp2on
(unitless)
 1
 0.8
 0.6
 0.4
 0.2
 0
 0
 ‐0.2
 10
 20
 30
 40
 Drops
Added
 50
 60
 70
 Clicker
Ques'on
1
 Which
region(s)
would
you
use
to
calculate

 your
calibra'on
curve?
 Absorbance
of
Green
Food
Coloring
at
 532
nm
 Absorp2on
(unitless)
 1.2
 A:

A
 B:

B
 C:

C
 D:

A
and
B
 E:

A,
B,
and
C
 C
 1
 0.8
 B
 0.6
 0.4
 0.2
 A
 0
 0
 ‐0.2
 10
 20
 30
 40
 Drops
Added
 50
 60
 70
 Clicker
Ques'on
1
Analysis
 Which
region(s)
would
you
use
to
calculate

 your
calibra'on
curve?
 Absorbance
of
Green
Food
Coloring
at
 532
nm
 Absorp2on
(unitless)
 1.2
 C
 1
 0.8
 B
 0.6
 0.4
 0.2
 A
 0
 0
 ‐0.2
 10
 20
 30
 40
 Drops
Added
 50
 60
 70
 B
is
the
only
 linear
region.

 This
is
the
only
 part
we
can
 easily
fit
a
line
 to.
 Clicker
Ques'on
2
 What
is
going
on
in
Region
A?
 A:

Instrumental
noise
 Absorbance
of
Green
Food
Coloring
at
 532
nm
 Absorp2on
(unitless)
 1.2
 B:

Below
the
detec'on
 limit
 C
 1
 0.8
 0.6
 0.4
 0.2
 C:

Student
messed
up
 their
measurements
 B
 A
 D:

Spectrometer
broke.
 0
 0
 ‐0.2
 10
 20
 30
 40
 Drops
Added
 50
 60
 70
 E:

Spectrometer
is
 saturated
 Clicker
Ques'on
2
Analysis
 What
is
going
on
in
Region
A?
 Absorbance
of
Green
Food
Coloring
at
 532
nm
 Absorp2on
(unitless)
 1.2
 This
sec'on
is
below
the
 spectrometer’s
detec'on
 limit.


 C
 1
 0.8
 B
 0.6
 0.4
 0.2
 It
is
the
smallest
quan'ty
 that
is
“significantly
 different”
from
the
blank.
 A
 0
 0
 ‐0.2
 10
 20
 30
 40
 Drops
Added
 50
 60
 70
 D.L.
=
blank
+
3σ
 Clicker
Ques'on
3
 What
is
going
on
in
Region
C?
 A:

Instrumental
noise
 Absorbance
of
Green
Food
Coloring
at
 532
nm
 Absorp2on
(unitless)
 1.2
 B:

Below
the
detec'on
 limit
 C
 1
 0.8
 0.6
 0.4
 0.2
 C:

Student
messed
up
 their
measurements
 B
 A
 D:

Spectrometer
broke.
 0
 0
 ‐0.2
 10
 20
 30
 40
 Drops
Added
 50
 60
 70
 E:

Spectrometer
is
 saturated
 Clicker
Ques'on
3
Analysis
 What
is
going
on
in
Region
C?
 The
spectrometer
is
 saturated.

The
 concentra'on
is
outside
 of
the
linear
range,
and
it
 can’t
measure
any
higher
 concentra'ons.
 Absorbance
of
Green
Food
Coloring
at
 532
nm
 Absorp2on
(unitless)
 1.2
 C
 1
 0.8
 B
 0.6
 0.4
 0.2
 A
 0
 0
 ‐0.2
 10
 20
 30
 40
 Drops
Added
 50
 60
 70
 This
is
equivalent
to
those
 white
areas
in
photos,
 where
the
camera
is
 saturated.
 Discussion
Ques'on
2
 What
would
you
do
if
you
needed
to
measure
a
 point
in
region
A
or
C?
 Absorbance
of
Green
Food
Coloring
at
 532
nm
 Absorp2on
(unitless)
 1.2
 C
 1
 0.8
 B
 0.6
 0.4
 0.2
 A
 0
 0
 ‐0.2
 10
 20
 30
 40
 Drops
Added
 50
 60
 70
 Trendlines
 Absorbance
of
Green
Food
Coloring
at
532
nm
 Absorp2on
(unitless)
 1.2
 y
=
0.0201x
+
0.0014
 R²
=
0.9985
 1
 0.8
 0.6
 0.4
 0.2
 0
 0
 10
 20
 30
 Drops
Added
 40
 50
 60
 Discussion
Ques'on
3
 Absorp2on
(unitless)
 Absorbance
of
Green
Food
Coloring
at
532
nm
 1.2
 y
=
0.0201x
+
0.0014
 R²
=
0.9985
 1
 0.8
 0.6
 0.4
 0.2
 0
 0
 10
 20
 30
 40
 50
 Drops
Added
 What
does
the
y‐intercept
mean?
 60
 Clicker
Ques'on
4
 How
many
drops
of
food
coloring
corresponds

 to
an
absorp'on
of
0.55?
 A:

25
 Absorbance
of
Green
Food
Coloring
at
532
nm
 Absorp2on
(unitless)
 1.2
 B:

30
 1
 0.8
 C:

13
 0.6
 D:

27
 0.4
 0.2
 E:

I
need
coffee
 0
 0
 10
 20
 30
 Drops
Added
 40
 50
 60
 Clicker
Ques'on
4
Analysis
 How
many
drops
of
food
coloring
corresponds

 to
an
absorp'on
of
0.55?
 A:

25
 Absorp2on
(unitless)
 Absorbance
of
Green
Food
Coloring
at
532
nm
 B:

30
 1.2
 1
 0.8
 C:

13
 0.6
 0.4
 D:

27
 0.2
 0
 0
 10
 20
 30
 Drops
Added
 40
 50
 60
 E:

I
need
coffee
 Clicker
Ques'on
5
 How
many
drops
of
food
coloring
does
an
absorp'on
 of
0.372
correspond
to?
 A:

18.577
 Absorp2on
(unitless)
 Absorbance
of
Green
Food
Coloring
at
532
nm
 1.2
 1
 B:

0.0075
 y
=
0.0201x
+
0.0014
 R²
=
0.9985
 0.8
 0.6
 C:

18.43
 0.4
 0.2
 D:

0.0089
 0
 0
 10
 20
 30
 Drops
Added
 40
 50
 60
 E:

I
need
coffee
 Clicker
Ques'on
5
Analysis
 How
many
drops
of
food
coloring
does
an
absorp'on
 of
0.372
correspond
to?
 Plug
and
chug
with
the
equa'on:
 0.372
=
0.0201x
+
0.0014
 (0.372‐0.0014)
=
0.0201x
 x
=
(0.372‐0.0014)/0.0201
=
18.43
 A:

18.577
 B:

0.0075
 C:

18.43
 D:

0.0089
 E:

I
need
coffee
 Want
to
minimize
the
 ver'cal
devia'ons
 between
the
points
and
 the
line!

 Linear equation: y = mx + b & each point is (xi, yi) Deviation at each point: di = yi – y = yi – (mxi+b) Square the deviations to make them all positive: di2 = (yi-mxi+b)2 Find m and b values that minimize the sum of these squared vertical deviations! Luckily, Excel can calculate this for us! (Example on Friday) R2
Values
 •  Pearson’s
R:

A
measure
of
how
correlated
x
 and
y
are.
 •  For
a
calibra'on
curve,
look
for
R2
>
0.995
 Source:

Wikipedia
 R2
Values
 •  

 Real
Calibra'on
Curves
 y=89244 x-1.0028×106 R2 = 0.693758 y=50565x -5.7304×105 R2 = 0.921725 An
anomalous
point
can
make
a
big
difference!


 Is
there
a
reason
to
get
rid
of
it?

 What
do
you
think
of
these
curves?

 Standard
Addi'on
 Recall
for
a
normal
calibra'on
curve:
 Blank
 Standards
 Unknown
 For
a
standard
addi'on
curve:
 U
 Unknown
 U
+
5μL
 U
+
10μL
 U
+
15μL
 U
+
20μL
 Unknown
+
increasing
amounts
of
a
concentrated
standard
 Why
bother
with
standard
addi'on?
 •  Matrix
effects
and
interferences!
 –  Did
you
know
that
pH
meters
are
sensi've
to
Na+
ions
 as
well
as
H+?

If
you
measure
the
pH
of
a
 concentrated
Na+
salt
solu'on,
the
pH
meter
reads
 too
many
H+.
 –  In
atomic
absorp'on,
you
vaporize
a
solu'on
and
 measure
the
absorp'on
of
a
specific
metal.

For
Ca+2,
 SO4‐2
and
PO4‐3
interfere
by
crea'ng
non‐vola'le
salts
 so
the
AA
will
read
too
few
Ca+2.
 –  If
you
are
using
a
complicated
environmental
sample,
 you
don’t
know
if
there’s
an
interference
you
don’t
 know
about!
 Clicker
Ques'on
6
 You
have
a
mass‐less,
opaque
bag
(that
came
from
the
same
physics
 closet
as
mass‐less,
fric'on‐less
pulleys)
with
an
unknown
number
of
 M&Ms
inside.
 Mass
of
unknown
number
of
M&Ms:

50
g
 You
add
5
M&Ms
to
the
bag.
 Mass
of
unknown
number
of
M&Ms
+
5:

55
g.
 How
many
M&Ms
were
in
the
bag
originally?
 A.

50
 B.

51
 C.

55
 D.

60
 E.

45
 Clicker
Ques'on
6
Analysis
 You
have
a
mass‐less,
opaque
bag
(that
came
from
the
same
physics
 closet
as
mass‐less,
fric'on‐less
pulleys)
with
an
unknown
number
of
 M&Ms
inside.
 Mass
of
unknown
number
of
M&Ms:

50
g
 You
add
5
M&Ms
to
the
bag.
 Mass
of
unknown
number
of
M&Ms
+
5:

55
g.
 How
many
M&Ms
were
in
the
bag
originally?
 A.

50
 B.

51
 C.

55
 D.

60
 E.

45
 Clicker
Ques'on
7
 You
have
digested
a
soil
sample
with
an
unknown
lead
 concentra'on
in
nitric
acid
and
have
a
100.0
mL
solu'on.

You
 measure
the
response
by
atomic
absorp'on
to
be
0.5879.

 You
add
0.1
mL
of
a
500
μg/mL
Pb
solu'on
to
the
soil
sample
 and
measure
the
response
to
be
0.7816.

What’s
the
 concentra'on
of
Pb
in
the
original
sample?
 A.

0.001516
μg/mL
 B.

0.3757
μg/mL
 C.

1.516
μg/mL
 D.

15.16
μg/mL
 E.

1516
μg/mL
 Clicker
Ques'on
7
Analysis
 You
have
digested
a
soil
sample
with
an
unknown
lead concentra'on
in
nitric
acid
and
have
a
100.0
mL
solu'on.

You
 measure
the
response
by
atomic
absorp'on
to
be
0.5879.

 You
add
0.1
mL
of
a
500
μg/mL
Pb
solu'on
to
the
soil
sample
 and
measure
the
response
to
be
0.7816.

What’s
the
 concentra'on
of
Pb
in
the
original
sample?
 A.

0.001516
μg/mL
 B.

0.3757
μg/mL
 C.

1.516
μg/mL
 D.

15.16
μg/mL
 E.

1516
μg/mL
 For
mul'ple
data
points…
 •  The
previous
calcula'on
used
the
response
of
the
 unknown
+
standard
based
on
the
diluted
 concentra'on
of
the
standard.
 •  If
we
make
solu'ons
with
different
amounts
of
 standard,
then
we
can
make
a
calibra'on
curve!
 •  Assump'on
for
calcula'on:

Signalspiked
=
Signalunk
 +
Signalspike.

Mostly
valid
because
of
the
small
 amount
of
dilu'on,
but
can
correct
signal
by
 mul'plying
by
Vi/Vf,
or
100.0
mL/100.1
mL
 Standard
Addi'on
Example
 •  Add
0.279
M
ascorbic
acid
to
50.0
mL
orange
 juice,
measure
with
electrochemistry.
 Vol.
Standard
added

(Vs),
mL
 Signal
(IS+X),
μA
 0.000
 1.78
 0.050
 2.00
 0.250
 2.81
 0.400
 3.35
 0.550
 3.88
 0.700
 4.37
 0.850
 4.86
 1.000
 5.33
 1.150
 5.82
 Standard
Addi'on
Example
 •  Add
0.279
M
ascorbic
acid
to
50.0
mL
orange
 juice,
measure
with
electrochemistry.
 Vol.
Standard
added

(Vs),
mL
 Signal
(IS+X),
μA
 Si*Vs/V0
 0.000
 1.78
 0.000
 0.050
 2.00
 0.279
 0.250
 2.81
 1.395
 0.400
 3.35
 2.232
 0.550
 3.88
 3.069
 0.700
 4.37
 3.906
 0.850
 4.86
 4.743
 1.000
 5.33
 5.580
 1.150
 5.82
 6.417
 Standard
Addi'on
Example
 •  Add
0.279
M
ascorbic
acid
to
50.0
mL
orange
 juice,
measure
with
electrochemistry.
 Vol.
Standard
added

(Vs),
mL
 Signal
(IS+X),
μA
 Si*Vs/V0
 IS+X*Vf/V0
 0.000
 1.78
 0.000
 1.780
 0.050
 2.00
 0.279
 2.002
 0.250
 2.81
 1.395
 2.824
 0.400
 3.35
 2.232
 3.377
 0.550
 3.88
 3.069
 3.923
 0.700
 4.37
 3.906
 4.431
 0.850
 4.86
 4.743
 4.943
 1.000
 5.33
 5.580
 5.437
 1.150
 5.82
 6.417
 5.954
 Clicker
Ques'on
8
 •  What’s
the
concentra'on
of
ascorbic
acid
in
 the
orange
juice?
 Corrected
response
vs
Ascorbic
Acid
 6
 IS+X*Vf/V0
 B:

.1208
M
 y
=
0.6463x
+
1.8687
 R²
=
0.99833
 5
 4
 A:

1.208
M
 C:

12.08
M
 3
 2
 D:

2.891
M
 1
 0
 0
 2
 4
 Si*Vs/V0
 6
 E:

0.2191
M
 Clicker
Ques'on
8
 •  What’s
the
concentra'on
of
ascorbic
acid
in
 the
orange
juice?
 Corrected
response
vs
Ascorbic
Acid
 6
 IS+X*Vf/V0
 B:

.1208
M
 y
=
0.6463x
+
1.8687
 R²
=
0.99833
 5
 4
 A:

1.208
M
 C:

12.08
M
 3
 2
 D:

2.891
M
 1
 0
 0
 2
 4
 Si*Vs/V0
 6
 E:

0.2191
M
 Discussion
Ques'on
4

 Pick
your
favorite
point
from
the
table
and
 calculate
the
ascorbic
acid
concentra'on
from
 that.

How
does
that
compare
to
2.891
M?
 Vol.
Standard
added

(Vs),
mL
 Signal
(IS+X),
μA
 Si*Vs/V0
 IS+X*Vf/V0
 0.000
 1.78
 0.000
 1.780
 2.00
 0.279
 2.002
 2.81
 1.395
 2.824
 3.35
 2.232
 3.377
 0.550
 3.88
 3.069
 3.923
 0.700
 4.37
 3.906
 4.431
 0.850
 4.86
 4.743
 4.943
 1.000
 5.33
 5.580
 5.437
 1.150
 5.82
 6.417
 5.954
 0.050
 0.250
 0.400
 Concentra'on
of
 standard:

0.279
M
 Vol.
of
orange
 juice:

50.0
mL
 ...
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This note was uploaded on 11/16/2011 for the course CHEM 4171 at Colorado.

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