Chemistry 12
Santa Monica College
Determination of Kc for a Complex Ion Formation
Objectives
•
•
Find the value of the equilibrium constant for formation of FeSCN2+ by using the visible light
absorption of the complex ion.
Confirm the stoichiometry of the reaction.
Background
In the study of chemical reactions, chemistry students first study reactions that go to completion.
Inherent in these familiar problems—such as calculation of theoretical yield, limiting reactant,
and percent yield—is the assumption that the reaction can consume all of one or more reactants
to produce products. In fact, most reactions do not behave this way. Instead, reactions reach a
state where, after mixing the reactants, a stable mixture of reactants and products is produced.
This mixture is called the equilibrium state; at this point, chemical reaction occurs in both
directions at equal rates. Therefore, once the equilibrium state has been reached, no further
change occurs in the concentrations of reactants and products.
The equilibrium constant, K, is used to quantify the equilibrium state. The expression for the
equilibrium constant for a reaction is determined by examining the balanced chemical equation.
For a reaction involving aqueous reactants and products, the equilibrium constant is expressed
as a ratio between reactant and product concentrations, where each term is raised to the power
of its reaction coefficient:
c
aA (aq) + bB (aq) ! cC (aq) + dD (aq)
Kc =
d
[C] [D]
[A] a [B] b
(1)
When an equilibrium constant is expressed in terms of molar concentrations, the equilibrium
constant is referred to as Kc. The value of this constant at equilibrium is always the same at a
! concentrations. Whether the reactants are
given temperature, regardless of the initial reaction
mixed in their exact stoichiometric ratios or one reactant is initially present in large excess, the
ratio described by the equilibrium constant expression will be achieved once the reaction
composition stops changing.
We will be studying the reaction that forms the reddish-orange iron(III) thiocyanate complex ion,
Fe(H2O)5 SCN2+(aq). The chemical equation describing the formation of this complex ion is
Fe(H2O)63+(aq) + SCN–(aq)
! Fe(H2O)5SCN2+(aq) + H2O(l)
(2)
Notice that the reaction involves the displacement of a water ligand by a thiocyanate ligand,
SCN–. However, for simplicity, and because water ligands do not change the net charge of the
species, water can be omitted from the formulas of Fe(H2O)63+(aq) and Fe(H2O)5SCN2+(aq) in
our chemical equation. Thus, the chemical formula Fe(H2O)63+(aq) may be simplified as Fe3+(aq)
and Fe(H2O)5SCN2+(aq) as FeSCN2+(aq). Making these changes, we can rewrite the simplified
chemical equation for the reaction and its corresponding equilibrium constants expression as:
Determination of Kc
Page 1 of 6
Chemistry 12
Santa Monica College
[FeSCN ]
=
[Fe ][SCN ]
2+
3+
–
Fe (aq) + SCN (aq)
! FeSCN (aq)
2+
Kc
3+
(3)
"
In this experiment you will create several different aqueous mixtures of Fe3+ and SCN–. Because
this reaction reaches equilibrium nearly instantly, these mixtures turn reddish-orange very
quickly due to the formation of the product !FeSCN2+(aq). The intensity of the color of the
mixtures is proportional to the concentration of product formed at equilibrium. As long as all
mixtures are measured at the same temperature, the ratio described in Equation (3) will be the
same because the value of Kc is a constant.
Measurement of [FeSCN2+]:
Because the complex ion product is the only strongly colored species in the system, its
concentration can be determined by measuring the intensity of the orange color in equilibrium
systems of these ions. This method relies on Beer's Law, which is given by the equation:
A = "!c
(4)
where A is the absorbance of light by the solution; c is the molar concentration of the solution; !
is the path length, or the distance that the light travels through the solution; and ! is the molar
! expresses the absorbing ability of a chemical species at a
absorptivity, which is a constant that
particular wavelength. The absorbance, A, is roughly correlated with the color intensity observed
!
visually; the more intense the color, the greater the absorbance.
By using a spectrophotometer, the absorbance, A, of a solution can be measured directly.
Solutions containing FeSCN2+ are placed into the spectrophotometer and their absorbances at
447 nm are measured. The path length, ! , is the same for all measurements and has a value of
1.00 cm. Rearrangement of Equation (4) allows for calculation of the molar concentration, c,
from the known value of the constant " # ! . The value of this constant is determined by plotting
the absorbances, A, vs. molar concentrations, c, for several solutions with known concentration
!
of FeSCN2+(aq) as shown in Figure 1. The slope of this calibration curve is then used to find
unknown concentrations of FeSCN2+(aq) in the experiment from their measured absorbances.
!
Absorbance
x
x
light
x
x
Slope = ! x l
Molar Concentration
l
2+
Figure 1: Plots of A vs. c for solutions with known concentrations of FeSCN (aq) can be
2+
used as a calibration curve. This plot is used to determine the FeSCN (aq) concentration in
solutions where that value is not known. The path length, l, is demonstrated in the diagram of
a cuvet and is taken to be 1.00 cm in this experiment.
Determination of Kc
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Chemistry 12
Santa Monica College
Calculations
In order to determine the value of Kc given by Equation (3), the equilibrium values of [Fe3+],
[SCN–], and [FeSCN2+] must be found. These values can be determined from a reaction table
('ICE' table), as shown in Table 1:
Table 1: Reaction ICE Table
Fe3+(aq)
+
SCN–(aq)
!
FeSCN2+(aq)
[Fe3+]i
[SCN–]i
0
Change in Concentration
–x
–x
+x
Equilibrium Concentration
3+
–
x = [FeSCN2+]
Initial Concentration
[Fe ]i – x
[SCN ]i – x
The reaction "ICE" table demonstrates the method used in order to find the equilibrium
concentrations of each species. The values that come directly from the experimental
procedure are found in the shaded regions. From these values, the remainder of the table
can be completed.
The initial concentrations of the reactants in Table 1—that is, [Fe3+] and [SCN–] prior to any
reaction—can be found by a dilution calculation based on the values from Table 2 found in the
procedure. Once the reaction reaches equilibrium, we assume that the reaction has shifted
forward by an amount, x. Notice from Table 1 that the value of x is simply equal to the
equilibrium concentration of FeSCN2+(aq), or that x = [FeSCN2+] at equilibrium. The equilibrium
value of [FeSCN2+] is determined spectroscopically using Beer’s Law. Its initial value in the table
is zero because no FeSCN2+(aq) is added to the initial solution. Finally, the equilibrium
concentrations of the reactants, Fe3+(aq) and SCN–(aq), are found by subtracting the equilibrium
concentration of FeSCN2+(aq) from the initial concentrations of Fe3+(aq) and SCN–(aq), as
shown in the table above. Once all the equilibrium values are known, they can be applied to the
equilibrium constant expression in Equation (3) to determine the value of Kc.
Standard Solutions of FeSCN2+(aq)
In order to find the equilibrium concentration of FeSCN2+ in our solutions we require the
preparation of standard solutions with known [FeSCN2+]. These are prepared by mixing a small
amount of dilute KSCN solution with a more concentrated solution of Fe(NO3)3. The solution has
overwhelming amount of the excess reagent (Fe3+), driving the equilibrium position far towards
products. So at equilibrium the concentration of Fe3+(aq) is very high due to its large excess,
and therefore the equilibrium concentration of SCN–(aq) must be very small. In other words, we
assume that essentially all of the SCN–(aq) present becomes FeSCN2+(aq) product. Examine
the Kc equilibrium-constant expression to prove this to yourself.
Determination of Kc
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Chemistry 12
Santa Monica College
Procedure
Safety
GENERAL SAFETY: Students must wear safety goggles at all times.
CHEMICAL HANDLING: The iron(III) nitrate solutions contain nitric acid. Avoid contact with skin
and eyes; wash hands frequently during the lab and wash hands and all glassware thoroughly
after the experiment.
WASTE DISPOSAL: All chemicals used must go in the proper waste container for disposal.
Materials and Equipment
You will need the following additional items for this experiment:
5-mL volumetric pipet
10-mL graduated pipet
rubber pipet bulb
Spectrometer
5 cuvets
Part A. Solution Preparation
Your instructor will demonstrate the proper use of the volumetric glassware used in this
experiment.
Label two clean, dry 50-mL beakers, and pour 30-40 mL of 2.00 x 10–3 M Fe(NO3)3 (already
dissolved by the stockroom in 1 M HNO3) into one beaker. Then pour 25-30 mL of 2.00 x 10–3 M
KSCN into the other beaker. There are two Fe(NO3)3 solutions used for this experiment, be
certain to use the 2.00 x 10–3 M Fe(NO3)3 solution for this step.
At your work area, label five clean and dry medium test tubes to be used for the five test
mixtures you will make. Using your volumetric pipet, add 5.00 mL of your 2.00 x 10–3 M
Fe(NO3)3 solution into each of the five test tubes.
Using your graduated pipet, add the correct amount of KSCN solution to each of the labeled test
tubes, according to Table 2 below.
Rinse out your graduated pipet with deionized water, and then use it to add the appropriate
amount of deionized water into each of the labeled test tubes, according to Table 2 below.
Stir each solution thoroughly with your stirring rod until a uniform orange color is obtained. To
avoid contaminating the solutions, rinse and dry your stirring rod after stirring each solution.
Determination of Kc
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Chemistry 12
Santa Monica College
Table 2: Test mixtures
Mixture
Fe(NO3)3 solution
KSCN solution
water
1
5.00 mL
5.00 mL
0 mL
2
5.00 mL
4.00 mL
1.00 mL
3
5.00 mL
3.00 mL
2.00 mL
4
5.00 mL
2.00 mL
3.00 mL
5
5.00 mL
1.00 mL
4.00 mL
Five solutions will be prepared from 2.00 x 10–3 M KSCN and 2.00 x 10–3 M Fe(NO3)3
according to this table. Note that the total volume for each mixture is 10.00 mL, assuming
volumes are additive. If the mixtures are prepared properly, the solutions will gradually
become lighter in color from the first to the fifth mixture. Use this table to perform dilution
calculations to find the initial reactant concentrations to use in Table 1.
Part B. Preparation of a Stock Solution of FeSCN2+
Before examining the five test mixtures, prepare a stock solution with known concentration of
FeSCN2+(aq). Obtain 15 mL of 0.200 M Fe(NO3)3(aq). Rinse your volumetric pipet with a few
milliliters of this solution, and add 10.00 mL of this solution into cleaned and dried large test tube
labeled “stock solution”. There are two Fe(NO3)3 solutions used for this experiment, be
certain to use the 0.200 M Fe(NO3)3 solution for this step.
Using your graduated pipet, add 8.00 mL deionized water to the large test tube.
Rinse your graduated pipet with a few milliliters of 2.00 x 10–3 M KSCN. Then add 2.00 mL of
the KSCN solution to the large test tube.
Mix the solution with a clean and dry stirring rod until a uniform dark-orange solution is obtained.
This stock solution should be darker than any of the other five solutions prepared previously.
Part C. Creating a Calibration Curve
To determine the concentrations of your equilibrium mixtures of FeSCN2+(aq) prepared in Part A
you will measure the absorbance of each mixture using a spectrophotometer. To do so you will
need to create a calibration curve. A calibration curve is a plot of the absorbance at 447 nm vs.
molar concentration for a series of standard solutions of known FeSCN2+(aq) concentration.
From this curve, you can determine the value of [FeSCN2+] in each equilibrium mixture from its
absorbance at 447 nm.
A few dilutions of the stock solution prepared in Part B will be used to prepare four standard
solutions for your calibration curve. In addition, one “blank” solution containing only Fe(NO3)3
will be used to zero the spectrophotometer. Table 3 shows the preparation method for each of
the standards. You should prepare each of these solutions accordingly using your volumetric
glassware as in the previous parts of the experiment. Use clean dry large test tubes for this
step. Swirl each of these standard solutions well to mix the contents before continuing.
Determination of Kc
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Chemistry 12
Santa Monica College
Table 3: Standard Solutions
Tube
Composition
Blank
0.200 M Fe(NO3)3 in 1 M HNO3
1
Stock Solution (Part B)
2
4.00 mL Stock + 1.00 mL H2O
3
4.00 mL Stock + 2.00 mL H2O
4
4.00 mL Stock + 3.00 mL H2O
Four standard solutions and one blank solution will be prepared for the calibration curve.
Once each of these standard solutions has been prepared have your instructor come over and
show you how to operate the spectrometer.
Fill a cuvet to just below the label with the blank solution. If your instructor has assigned your
group a temperature then heat or cool the cuvet until its contents are at the desired temperature
and record this value on your data sheet. Carefully wipe off the outside with a tissue. Insert the
cuvet into the spectrometer and make sure it is oriented correctly by aligning the mark on cuvet
towards the front. Close the lid. Use this solution to zero your spectrometer.
For each standard solution in Table 3, rinse your cuvet twice with a small amount (~0.5 mL) of
the standard solution to be measured, disposing of the rinse solution each time. Then fill the
cuvet with the standard, heat or cool (if required) and record the temperature, insert the cuvet
into the spectrometer as before, and record the absorbance reading on your data sheet.
You will use these absorbance values to plot your calibration curve. Calculate the concentration
of FeSCN2+(aq) in each of these standard solutions using the dilution equation, M1V1 = M2V2.
Now plot your measured absorbance for each of these solutions versus their respective
concentration value using Excel. A computer is available in the balance room or you may do so
down in the Science Computer Lab. Add a best-fit line to this plot using the Excel trendline
function. Select “Display Equation on Chart” from the trendline function options menu. In
addition, because you used your blank solution to zero your spectrometer you should also
select the option, “set intercept = 0,” from this menu. This will cause your plot to pass through
the origin. Your plot should be a perfectly straight line and your best-fit line should pass directly
through each of your data points. If any of your data points fall off of your best-fit line, you
should remake that particular solution, measure its absorbance again, and replot your data
using this new value until a perfectly straight line through all of your data points is obtained.
Part D. Spectrophotometric Determination of [FeSCN2+]
Use your spectrometer to measure the absorbance of each of the five equilibrium mixtures of
unknown FeSCN2+(aq) concentration you prepared in Part A according to Table 1. Be sure to
heat or cool each cuvet if your group was assigned a temperature. Record the temperature and
absorbance of each solution on your data sheet. The value of [FeSCN2+] for each of these
solutions is determined using your calibration curve.
Determination of Kc
Page 6 of 6
Name: ____________________________
Date: ________________________
Lab Partner: ________________________
Lab Section: __________________
Lab Report: Determination of the Equilibrium Constant For a Reaction
Experimental Data
Part A. Initial Concentrations of Fe3+ and SCN– in Unknown Mixtures
Tube
Reagent Volumes / mL
2.00 x 10-3 M
2.00 x 10-3 M
Fe(NO3)3
KSCN
Initial Concentrations / M
Water
1
5.00
5.00
0
2
5.00
4.00
1.00
3
5.00
3.00
2.00
4
5.00
2.00
3.00
5
5.00
1.00
4.00
[Fe3+]i
[SCN–]i
Show a sample dilution calculation below for determining the value of [Fe3+]i for Tube 1:
Part C. Creating a Calibration Curve
Tube
Absorbance
Blank
1
[FeSCN2+] / M
Temp / ºC
3+
2
3
4
Show sample dilution calculations below for determining the values of [FeSCN2+] for Tubes 1 and 2:
Determination of Kc
–
Note that since [Fe ] >> [SCN ]
in the Standard Solutions, the
reaction is forced to completion,
thus causing essentially all the
–
added SCN (aq) to be
2+
converted to FeSCN (aq).
Page 1 of 4
Use Excel to create a plot of “absorbance versus concentration” for the data from your standard
solution. Your graph should have an appropriate title and labeled axes with an appropriate scale.
Add a trendline to the data points. Select “Display Equation on Chart” and “set intercept = 0” in the
trendline function options menu. As described in the procedure, your plot should be a perfectly
straight line and your best-fit line should pass directly through each of your data points.
Submit this graph with your report.
Record the equation of the best-fit line obtained from this graph here: _____________________
Using the equation of your best-fit line and taking the value of the path length, ! , to be 1.00 cm,
determine the value of the molar absorptivity, !, of these solutions at 447 nm as described by Beer’s
Law given by Equation (4). What are the units of ! ? Hint: The value of the absorbance, A, is unitless.
!
Value and units of ! : ____________________
Part D. Spectrophotometric Determination of [FeSCN2+]
Use your measured absorbances and the value of ! you determined above for Equation (3) to
determine the concentration of FeSCN2+(aq) in each of the equilibrium mixtures you prepared in Part A.
Enter these values in the table below.
Equilibrium
Mixture
Measured
Absorbance
[FeSCN2+] / M
Temp / ºC
1
2
3
4
5
Show a sample calculation below for [FeSCN2+] in equilibrium mixture 1:
Determination of Kc
Page 2 of 4
Analysis
The chemical equation describing the reaction that is assumed to occur in this experiment is:
Fe3+(aq) + SCN–(aq) ! FeSCN2+(aq)
Write the equilibrium constant expression for this equation below:
Using your data from the previous pages of this report, write out a complete Reaction Table (or ICE table)
below for the reaction occurring in Equilibrium Mixture 1 (see Table 2):
Determine the value of Kc for Equilibrium Mixture 1 from these data. Show your calculations below:
Using the same method, complete the table below for all the equilibrium concentrations and values of Kc for
each of the five equilibrium mixtures prepared in Part A. Determine the average value of Kc.
Mixture
Equilibrium Concentrations / M
[Fe3+]
[SCN–]
[FeSCN2+]
Kc
1
2
3
4
5
Average value of Kc : ___________________
Determination of Kc
Page 3 of 4
Additional Analysis: Is an Alternative Reaction Stoichiometry Supported?
Suppose that instead of forming the FeSCN2+ complex ion, the reaction between Fe3+(aq) and SCN–(aq)
resulted in the formation of a complex ion with a chemical formula of Fe(SCN)2+ according to,
Fe+3 (aq) + 2 SCN– (aq) ! Fe(SCN)2+ (aq)
Write the corresponding equilibrium-constant expression for Kc for this chemical equation:
Create a new Reaction Table (or ICE Table) for Equilibrium Mixture 1 below using the stoichiometry of the
alternative chemical equation above as the basis for your calculations:
Determine the value of Kc for Equilibrium Mixture 1 from these data. Show your calculations below:
Using the same method, complete the table below for all the equilibrium concentrations and values of Kc for
each of the five equilibrium mixtures based on the alternative chemical equation above.
Mixture
Equilibrium Concentrations / M
3+
[Fe ]
[SCN–]
[FeSCN2+]
Kc
1
2
3
4
5
Based on the calculated values of Kc in this table and those in the table at the bottom of the previous page,
can you tell which, if either, reaction equation best describes the equilibrium reaction occurring in your
mixtures? Justify your response (continue your answer on the back of this sheet if needed):
Determination of Kc
Page 4 of 4