Expt 4: Determination of Iron by Absorption Spectrophotometry Calibration solutions: Iron(II)ammonium sulfate = ferrous ammonium sulfate FeSO 4 (NH 4 ) 2 SO 4 6H 2 O, M.W. = 392.14 g Stock 1 0.210 g in 12.5 ml of 0.7 M H 2 SO 4 diluted to 500 ml with deionized water Stock 2 25.00 ml Stock 1 diluted 10-fold with 5 ml 0.7 M H 2 SO 4 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 relative error = ± 0.1mg 210mg 100 = ± 0.05% ± 0.1mg relative error = 100 = ± 0.5% 21mg 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 NH 2 OH HCl (1.44 M) and 10 ml of sodium acetate (NaOOCH 3 ) (1.22 M), all diluted to 100 ml Why NH 2 OH 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(H 2 O) 6 2+ + 3phen Fe(phen) 3 2+ + 6H 2 O Upon addition of third phen, complex turns red. (λ max = 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 Calculation Concentration response C = f(r) Measurement error ΔR, s R Propagation of Concentration measurement error error ΔC, s C Recall propagation of errors in mathematical calculations: If y = m + n, 2 2 s = s + y m s 2 n and, in terms of the standard deviations s = s + s y 2 m 2 n For or, a b y = c, s 2 2 2 2 2 2 y y = s a a + s b b + s 2 c c 2 s y y = s a a 2 + s b b 2 + s c c 2 For y = log a, s y = 0.434 s a /a
Measurement error ΔR, s R Propagation of Concentration measurement error error ΔC, s C ΔR = systematic (determinate) response error ΔC = systematic concentration error s R = random (indeterminate) response error s C = random concentration error Φ = sensitivity, dr/dc (ΔR/ΔC for linear relationships) In general, 1 ΔC = ΔR Φ and s C = 1 Φ s R 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 (P 0 /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) A Slope=εb 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 P 0 and calculate A from T. T has a non-linear dependence on C: T = 10 -εbc For y = log a, s y = 0.434s a /a A = -log T, so s A = -0.434s T /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, s T, leads to a concentration error that is concentration dependent in the A versus C plot.
T C s A A Slope=εb C (M)
T vs. C fixed error, variable sensitivity A vs. C fixed sensitivity, variable error Either way leads to: s C C Non-linear increase in absolute concentration uncertainty with increasing concentration.
What about relative concentration error (RCE)? i.e. concentration error/concentration, (s C /C) for a constant s C, RCE as C for a transmittance measurement, however, s c as C leads to a minimum in s c 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 -(α + βc) T = 10 10 -x = e -2.3x -2.3(α + βc), so T = e
Beer s Law: A = εbc = log (P 0 /P) = log (1/T) = -log T T = 10 -A = 10 -εbc ε = molar absorptivity b = path length c = concentration of absorbing species A Slope=εb C (M) We expect a linear relationship between A and C.
Beer s law assumes a single ε: