Kurtis Malecha
Working with: David Green
Dr. Thoemke
Formal Lab Report
7. December 2011
2+
FeSCN Equilibrium, Revisited (Again) 
Introduction:
In the realm of kinetics, one is concerned with “how fast” something occurs; however,
the question of “how much” of reactants and products A, B, and C will be in equilibrium with
one another after time is also important. When two or more chemicals are in equilibrium with
one another, the forward and reverse reactions are occurring at the same rate. In this particular
experiment, a complex of [Fe(H2O)5]3+ reacted with SCN- to produce the complex
[Fe(H2O)5SCN]2+. Of course, not all the reactants formed products, and some of the reactant
concentration remained. In order to predict the concentration of the products and reactants at
equilibrium, the Keq (or equilibrium constant) expression is used, which generically looks like:
[𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠]
𝑏𝑠 = [𝑅𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠] . This is the value that is “observed,” hence Kobs(These concentrations are
recorded at equilibrium, not before the reaction.) A higher “K-value” means that the product
concentrations are more favored at equilibrium, and, conversely, a lower K implies that reactants
are favored.
But this way of just “churning” out the numbers does not account for the entire story –
since there are “spectator ions” floating about in the solution, this will be a non-ideal solution,
and the activities and ionic strength of all the ions must be accounted for. In short, the actual
“K” value will be KobsKγ=K. More of this detailed information will be given in the results and
conclusion sections.
Procedure:
This experiment consisted of two parts: In part one, we prepared and diluted solutions of
Fe3+ and SCN-, and in part two, we added more Fe3+ solution to the already-made SCN- solution
and took absorbance readings from the spectrophotometer.
Part One Procedure:
We diluted a 0.002M KSCN solution to a final volume of 100mL by using 10mL of this
solution with 25mL of 2.0M HNO3. These two chemicals were diluted and mixed with distilled
water in a 100mL volumetric flask. Then the contents were poured into a 250mL beaker. A
“blank” was made utilizing 1mL of Fe(NO3)3 in 0.5M HNO3 with 25mL of 2.0M HNO3 and then
diluting in a 100 mL volumetric flask with the rest of the solution being distilled water.
Part Two Procedure:
The “blank” solution was measured in the Spectrophotometer at λ=450nm and then the
instrument was zeroed to this reading. Periodic “checks” of this zero were done to make sure the
instrument did not “drift.” The 250mL beaker was stirred with a magnetic stirrer continuously
throughout this part of the experiment. 1mL increments of the undiluted iron solution were
pipetted into the SCN solution. After equilibration and rinsing of the cuvette with this solution,
an absorbance reading was made. This solution was then placed back into the beaker and
another 1mL of the undiluted iron solution was pipetted into here. Again, an absorbance reading
was made after rinsing the cuvette. This solution was poured back into the main SCN solution in
the 250mL beaker, and this process was repeated for 15 total trials (for a total solution volume of
115mL). Waste was put into the designated container in the fume hood.
Results:
First, the Kobs value was calculated using ideas from Beer’s law and mass balance ideas.
𝐴 = 𝜀𝑏𝐶, and here C is the molar concentration of the [Fe(H2O)5SCN]2+. At any time
CSCN=[SCN-] + [[Fe(H2O)5SCN]2+ and CFe= [[Fe(H2O)63+]] + [Fe(H2O)5SCN]2+. This implies
that:
𝐴
)
𝜀𝑏)
(
[Fe(H2O)5SCN]2+]

𝐾𝑜𝑏𝑠 = [[Fe(H2O)63+]][SCN−] =

⇒ [𝐶𝐹𝑒 𝐶𝑆𝐶𝑁 − 𝐶𝑆𝐶𝑁 (𝜀𝑏) − 𝐶𝐹𝑒 (𝜀𝑏) + (𝜀𝑏) ] 𝐾𝑜𝑏𝑠 = (𝜀𝑏)

⇒ [𝐶𝐹𝑒 𝐶𝑆𝐶𝑁 − 𝐶𝑆𝐶𝑁 (𝜀𝑏) − 𝐶𝐹𝑒 (𝜀𝑏) + (𝜀𝑏) ] 𝐾𝑜𝑏𝑠 − (𝜀𝑏) = 0

⇒ [𝐶𝐹𝑒 𝐶𝑆𝐶𝑁 − 𝐶𝑆𝐶𝑁 (𝜀𝑏) − 𝐶𝐹𝑒 (𝜀𝑏) + (𝜀𝑏) ] 𝐾𝑜𝑏𝑠 − (𝜀𝑏) = 0

⇒ [−𝐶𝑆𝐶𝑁 (𝜀𝑏) − 𝐶𝐹𝑒 (𝜀𝑏) + (𝜀𝑏) ] − (𝜀𝑏) (𝐾𝑜𝑏𝑠) + 𝐶𝐹𝑒 𝐶𝑆𝐶𝑁 = 0

⇒ (𝜀𝑏) − [𝐶𝐹𝑒 + 𝐶𝑆𝐶𝑁 + 𝐾𝑜𝑏𝑠] (𝜀𝑏) + 𝐶𝐹𝑒 𝐶𝑆𝐶𝑁 = 0

[𝐶𝐹𝑒 −(
𝐴
𝐴
)][𝐶𝑆𝐶𝑁 −( )]
𝜀𝑏)
𝜀𝑏)
𝐴
𝐴
𝐴 2
𝐴
𝐴
𝐴
𝐴 2
𝐴
𝐴
𝐴
𝐴 2
𝐴
𝐴
𝐴 2
𝐴
𝐴 2
1
𝐴
1
𝐴
𝑇ℎ𝑒𝑛 𝑎 𝑟𝑒𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑜𝑓 𝑠𝑒𝑟𝑖𝑒𝑠 𝑚𝑒𝑡ℎ𝑜𝑑 𝑦𝑖𝑒𝑙𝑑𝑠:
𝐴
𝐶𝐹𝑒 𝐶𝑆𝐶𝑁
(𝐶𝐹𝑒 𝐶𝑆𝐶𝑁 )2

(𝜀𝑏) =

Simplifying to a more readily linear function, and assuming the second term in the
previous line equals zero implies:

(𝜀𝑏) (𝐶𝐹𝑒 +𝐶𝑆𝐶𝑁 + (𝐾𝑜𝑏𝑠)) = 𝐶𝐹𝑒 𝐶𝑆𝐶𝑁

⇒ (𝜀𝑏) (𝐶𝐹𝑒 +𝐶𝑆𝐶𝑁 + (𝐾𝑜𝑏𝑠)) =
1
𝐶𝐹𝑒 +𝐶𝑆𝐶𝑁 +(
)
𝐾𝑜𝑏𝑠
𝐴
+
1
)]3
𝐾𝑜𝑏𝑠
[𝐶𝐹𝑒 +𝐶𝑆𝐶𝑁 +(
1
1
𝐶𝐹𝑒 𝐶𝑆𝐶𝑁
1
1
1
𝐶𝐹𝑒 𝐶𝑆𝐶𝑁
𝐴
1

= (𝜀𝑏) (𝐶𝐹𝑒 +𝐶𝑆𝐶𝑁 ) + (𝜀𝑏)(𝐾𝑜𝑏𝑠) {Equation 1}
𝐴
Using this equation developed leads to a graph of CFeCSCN/A versus CFe+CSCN having a straight
line relationship. The slope:intercept ratio is equal to Kobs. See below for the data used, the
graph developed, and the analysis of the straight-line relationship. Representative formulas
appear below each column, and the error propagation appears in the appendix.
Table 1
Table 2
These values from table 2 are the ones plotted below:
CFeCSCN/A vs CFe + CSCN
CFeCSCN/A
0.0000045
y = 0.0002x + 2E-06
R² = 0.9999
0.0000035
0.0000025
0.0000015
0.001
0.003
0.005
0.007
CFe + CSCN
Chart 1
0.009
0.011
0.013
Value of Slope
Std Dev of Slope
R^2
0.000234051
7.42837E-07
0.999869066
Value of Intercept
Std Dev Intercept
Std Error of Y
1.80652E-06
6.12333E-09
1.05643E-08
Slope:Intercept Ratio 129.6 +/- 0.3
Next, the values of the Iron Complex were calculated according to the formula:
𝐾𝑜𝑏𝑠𝐶𝐹𝑒𝐶𝑆𝐶𝑁
[[𝐹𝑒(𝐻2𝑂)5𝑆𝐶𝑁]2 +] = 1+(𝐶𝐹𝑒+𝐶𝑆𝐶𝑁)𝐾𝑜𝑏𝑠 {Equation 2} These values for each were

calculated using excel. Please note that cell “E20” is the Kobs value in the representative
formula.
Table 3
These values need to be in molalities and not molarities, so a conversion factor of 1.02 kg L-1
was used to divide all the molarities. Note that the conversion to molality’s formula states:
𝑐𝑖
 𝑏𝑖 = 𝜌−∑ 𝑐𝑖∗𝑀𝑖{Equation 3} where bi is the molal concentration, ci is the molar
concentration, Mi is the molar mass (in kg mol-1) and ρ is the density (in kg mol-1).
The summation term is for all other parts of the solution, except the solute. An assumption of the
summation term being 0 is valid here (see appendix), so these molarity terms given above were
simply divided by 1.02. This yields:
Table 4
(“Above” signifies to the particular ion in the corresponding row of the above table.)
In order to calculate the Ionic strength, the following formula was employed:
 𝐼 = 0.5 ∑𝑖(𝑚𝑖+ (𝑧𝑖+ )2 + 𝑚𝑖− (𝑧𝑖− )2 ) {Equation 4} with m being the molality and z being
the charge of the species, respectively.
This was, like all other calculations, done in excel with a representative formula below the
column:
Table 5
We then calculated the activity coefficients for the [Fe(H2O)5SCN]2+ complex, the [Fe(H2O)5]3+ ,
and the [SCN-] according to the formula:
𝐼

𝑙𝑛𝛾+/− =
2
−1.173𝑧+/−
[
√ 𝑜
𝑚
𝐼
1+√ 𝑜
𝑚
𝐼
− 0.30 (𝑚𝑜 )] {Equation 5} z is the charge, I is the ionic
strength of the solution, and mo is a standard molal concentration of 1.0 mol kg-1.
Note that the +/- is for either the cation or the anion, each is calculated separately. See below for
the corresponding values for lnγ and γ:
Table 6
The Kγ values were then calculated according to the formula:
𝛾[Fe(H2O)5SCN]2+
 𝐾𝛾 = 𝛾[Fe(H2O)5]3+∗γ[SCN−] {Equation 6}
The results for each solution are shown below:
Table 7
Finally the Ka values can be calculated using 𝐾𝑎 = 𝐾𝛾 𝐾𝑜𝑏𝑠 :{Equation 7}
Table 8
Discussion:
Even though the data analysis contained many more assumptions for error propagation, this
value turned out to be much more “precise” than what was observed in the “FeSCN equilibrium”
experiment earlier this semester. The average Ka value obtained here was 819 +/- 3, whereas the
values obtained in the earlier experiment were as bad as 246+/-95779. The precision of this
experiment is thus much better, as is the accuracy. Even though the Ka value falls outside the
95% CL of the literature value (9.2 (+/-0.4) x 10^2) by 61 for this rendition of the experiment,
the accuracy is much better because the relative error is 11% versus 73% in the previous
experiment.
This experiment factored in the activities of the ions, and that made the Ka a much more realistic
approximation of the equilibrium constant as shown by the calculations. In order to make this
experiment even closer to the “true,” accepted value for Ka, it would be prudent to allow the
solution to equilibrate for a longer time period before taking an absorbance reading. This
observation comes from the progressively lower K values as more iron solution was added,
meaning that it is possible that we may have taken readings before equilibrium was established.