Expt 4: Determination of Iron by Absorption
Spectrophotometry
Calibration solutions:
Iron(II)ammonium sulfate = ferrous ammonium sulfate
FeSO4(NH4)2SO4·6H2O, M.W. = 392.14 g
Stock 1
0.210 g in 12.5 mL of 0.7 M H2SO4 diluted to 500
mL with deionized water
Stock 2
25.00 mL Stock 1 diluted 10-fold with 5 mL 0.7 M
H2SO4 using deionized water sufficient to make 250
mL total
Why not make stock 2 directly from scratch?
Precision of mass measurement
0.210 g ± 0.1 mg
± 0.1mg
× 100 = ±0.05%
relative error = 210mg
± 0.1mg
relative error = 21mg × 100 = ±0.5%
less error associated with volume error of dilution
Why add the sulfuric acid?
To prevent oxidation of Fe(II) to Fe(III), which in
turn reacts with water eventually to form Fe(OH)3(s)
A matrix modifier!!!
Next step:
To various volumes of stock 2 you add 1 mL
NH2OH·HCl (1.44 M) and 10 mL of sodium acetate
(NaOOCH3) (1.22 M), all diluted to 100 mL
Why NH2OH·HCl?
Hydroxylamine is a reducing agent that helps to
prevent Fe(III) formation.
A matrix modifier!!!
Why sodium acetate?
A pH buffer to maintain solution at pH = 4.8±1
Another matrix modifier!!!
Why maintain pH at roughly 4.8?
Protonation of 1,10-phenanthroline competes with
complexation with Fe(II)
We want:
Fe(H2O)62+ + 3phen → Fe(phen)32+ + 6H2O
Upon addition of third phen, complex turns red. (λmax
= 508 nm)
3 matrix modifiers needed to make the method work.
They prevent deleterious competing reactions (2 to
minimize oxidation of Fe(II) and one to minimize
protonation of 1,10 phenanthroline)
Lab 4 Purposes:
Determine an unknown ferrous concentration (via a
calibration curve) using spectrophotometry data
Understand quantitative relationships between
transmittance, absorption, and concentration
Understand relationships between measurement
errors (random and systematic), sensitivity, and
concentration
Propagation of errors and sensitivity:
Measured →
response
Calculation →
C = f(R)
Concentration
Measurement →
error
ΔR, sR
Propagation of → Concentration
measurement error error
ΔC, sC
Recall propagation of errors in mathematical calculations:
If y = m + n,
s y2 = s m2 + s n2
and, in terms of the standard deviations
s y = sm2 + sn2
a ⋅b
y
=
For
c ,
s 2y y 2 = s 2a a 2 + s b2 b 2 + s c2 c 2
or,
2
2
⎛s ⎞ ⎛s ⎞ ⎛s ⎞
= ⎜ a ⎟ +⎜ b ⎟ +⎜ c ⎟
y
⎝a⎠ ⎝b⎠ ⎝c⎠
sy
For y = log a, sy = 0.434 sa/a
2
Measurement →
error
ΔR, sR
Propagation of → Concentration
measurement error error
ΔC, sC
ΔR = systematic (determinate) response error
ΔC = systematic concentration error
sR = random (indeterminate) response error
sC = random concentration error
Φ = sensitivity, dR/dC (ΔR/ΔC for linear relationships)
In general,
ΔC =
1
1
⋅ ΔR and sC = ⋅ sR
Φ
Φ
The absolute concentration error is directly related to
the response error and inversely related to
sensitivity…
Linear relationships, Φ = constant:
Concentration error is directly related to response
error:
Concentration error is inversely related to sensitivity:
Non-linear relationships: sensitivity is concentration
dependent, therefore absolute concentration error
becomes concentration dependent
e.g., transmittance and absorbance
Beer’s Law:
A = εbC = log (P0/P) = log (1/T) = -log T
ε = molar absorptivity (M-1 cm-1) at specified λ
b = path length (cm) (note, not the intercept)
C = concentration of absorbing species (M)
Slope=εb
A
C (M)
We expect a linear relationship between A and C.
A = -log T or T = 10-A
A = εbC
In practice, we actually measure P and P0 and
calculate A from T. T has a non-linear dependence
on C:
T = 10-εbC
For y = log a, sy = 0.434sa/a
A = -log T, so sA = -0.434sT/T
Let’s look at this graphically…
For a constant uncertainty in transmittance response,
the absolute concentration error is highly dependent
upon concentration:
The rapidly changing sensitivity associated with
transmittance versus concentration at constant error
due to transmittance, sT, leads to a concentration error
that is concentration dependent in the A versus C
plot.
T
C
sA
Slope=εb
A
C (M)
T vs. C – fixed error, variable sensitivity
A vs. C – fixed sensitivity, variable error
Either way leads to:
sC
C
Non-linear increase in absolute concentration
uncertainty with increasing concentration.
What about relative concentration error (RCE)?
i.e. concentration error/concentration, (sC/C)
for a constant sC, RCE ↓ as C ↑
for a transmittance measurement, however, sc ↑ as C↑
leads to a minimum in sc versus C plot
Stray light and wavelength error:
Why we adjust 100% T with pure solvent or a blank
solution:
The blank corrects for loss processes other than
absorbance by the analyte.
The filter after the sample is usually a cut-off filter to
remove long wavelengths (that can arise from second
and higher order diffraction from the grating, these
longer wavelengths constitute stray light.)
Who cares about some stray light?
T
C
We expect a logarithmic relationship between T and
C. T = 10-A = 10-εbC
Note: in lab write up, α = intercept and β = slope
(instead of b = intercept to avoid confusion with path
length)
In practice, from a calibration curve we get
A = α + βC
T = 10-(α + βC)
10-x = e-2.3x, so T = e-2.3(α + βC)
Beer’s Law:
A = εbC = log (P0/P) = log (1/T) = -log T
T = 10-A = 10-εbC
ε = molar absorptivity
b = path length
c = concentration of absorbing species
Slope=εb
A
C (M)
We expect a linear relationship between A and C.
Beer’s law assumes a single ε: