Determination of An Equilibrium Constant Lab Report

CHEMISTY 135/150/175Chemistry Lab
Determination of an Equilibrium Constant
Show above is a laboratory sample—from chemistry, not phlebotomy. [1]
Is the deep red-looking product the main component of this solution,
or is it just a minor but highly visible component?
How would you know?
DEPARTMENT OF CHEMISTRY
UNIVERSITY OF KANSAS
1
Introduction
A system is at equilibrium when the macroscopic variables describing it are constant with time. These variables
include pressure and temperature. In addition, for a solution that can contain multiple species, the concentrations
are also independent of time at equilibrium. While equilibrium indicates an unchanging state, note that this is
reflected in the macroscopic variables. At the molecular level there is tremendous movement of molecules,
exchange of energy, and interconversion of the various molecular species. However, at equilibrium all of these
processes are “balanced” such that the rate of depletion of a molecular species is balanced by the rate of formation
of the same species.
The equilibrium between different molecular species is characterized by an equilibrium constant. Consider as an
example the ionization of the weak acid HF:
HF(aq) + H2O(l) ⇌ H3O+ (aq) + F- (aq)
(Reaction 1)
The equilibrium is established between the forward and backward reactions and is characterized by the
concentrations of the reactants and products of the reactions at equilibrium, i.e., after the concentrations stop
changing. Specifically, the equilibrium constant is given by the ratio
Kc = [H3O+][F-]/[HF]
(Eqn 1)
where [HF] is the concentration of the acid. Note that the equilibrium constant is given by the product of the
product concentrations (raised to their stoichiometric coefficients) divided by the product of the reactant
concentrations (also raised to their stoichiometric coefficients). The solvent, here water, is not included
because its “concentration,” which is present in great excess, does not change due to the reactions.
In this experiment the equilibrium constant for a reaction involving the complexation of two species will be
measured. To do so, a measurable quantity that is proportional to the concentration of a species must be
available. The approach here will be to use spectroscopy, where the absorbance at a particular wavelength
is proportional to the concentration of the species which absorbs light at that wavelength.
The species involved in this laboratory experiment are Fe(NO 3)3 and KSCN in aqueous solution (which also
contains nitric acid, HNO3 for reasons not important to the equilibrium). These species are simply the
precursors to those involved in the equilibrium. Namely, Fe(NO 3)3 decomposes as
Fe(NO3)3 (aq) ⇌ Fe3+ (aq) + 3 NO3- (aq)
(Reaction 2)
providing Fe3+ in solution. Similarly, KSCN decomposes as
KSCN (aq) ⇌ K+ (aq) + SCN- (aq)
(Reaction 3)
to provide SCN- (thiocyanate) in solution. These processes themselves involve equilibria, but the
equilibrium of interest in this experiment is the resulting one between iron and thiocyanate:
Fe3+ (aq) + SCN- (aq) ⇌ FeSCN2+ (aq)
(Reaction 4)
for which the equilibrium constant is
Kc = [FeSCN2+]/([Fe3+][SCN-])
(Eqn 2)
To determine Kc, the three concentrations involved must be determined. For the reactants this will be based
on the amount of the precursor compounds added to solution. For the products, spectroscopy will be used.
2
Safety
Goggles must be worn at all times. Most chemicals can be toxic and hazardous if splashed on clothing,
exposed skin or in the eyes. At the very least, some of the compounds used in this laboratory can
permanently stain your clothes. If chemicals splash on skin or clothes, remove the affected clothing and
flush the affected areas thoroughly with cold water.
Iron/thiocyanate solutions should be collected in a separate container as waste.
Procedure
Part 1 – Spectroscopic Measurement of the Equilibrium Concentration
In this part of the experiment, successive portions of 0.100 M Fe(NO3)3 in 0.5 M HNO3 are added to a known
volume of 1.200×10-4 M KSCN in 0.5 M HNO3. Both solutions contain 0.5 M HNO3 to maintain a constant ionic
strength and acidity. The procedure should be repeated three times to compare results and determine an average
value.
1. Set up the Vernier spectrophotometer. Remember to calibrate the instrument.
2. Transfer 50.0 mL of the KSCN solution to a 250-mL beaker using the 25 mL volumetric pipet.
3. Transfer about 10 mL of the Fe(NO3)3 solution into a clean 25-mL beaker.
4. Pipet successive 1-mL portions of the Fe(NO3)3 solution into the KSCN solution using the 1 mL volumetric
pipet. After each addition, stir the solution thoroughly. Then use a Pasteur pipette from the back of the lab
to transfer a portion of the solution to a clean cuvette (cuvettes should be about two-thirds to three-quarters
full). Measure the absorbance at 445 nm. After you have measured the absorbance, carefully return the
contents of the cuvette to the parent solution. Be careful not to spill any of your solution!
5. Perform at least 10 subsequent 1-mL additions of Fe(NO3)3 and record the absorbance for each. Do not use
distilled water or tap water to rinse your cuvette or pipette until you’re completely finished with this
trial. Use the same cuvette and the same pipette for all of your measurements.
An example data table is below with the first two lines of volumes and concentrations filled out for you. This table
will be important in your calculations!
6. Repeat this procedure for a total of three times.
3
Part 2 – Data Analysis to Obtain an Equilibrium Constant
In this part of the experiment, the data obtained from the three runs in Part 1 will be used to calculate an average
value of the equilibrium constant Keq. Your TA will work through the equations you will need to determine Keq
from the results of the measurements in Part 1. You will need to determine the equilibrium constants obtained
from each of the three runs in Part 1.
2+
An important piece of the analysis is determining the concentration of FeSCN from the absorbance
measurements in Part 1. Previous experiments performed by you and your group members illustrated that the
absorbance measured is directly related to the concentration of the absorbing species. It is also related to the
distance the light must travel through the solution, which is called the pathlength. Specifically, the transmittance
of light through a solution is an exponential function of the pathlength and the concentration of the absorbing
species. Since absorbance is proportional to the logarithm of the transmittance, it depends linearly on the
pathlength. In 1852, a scientist named Beer put together these findings into an equation of the form:
Absorbance = A = εlc
This equation is known as Beer’s law. Here, ε is called the molar absorptivity, l is the pathlength of the cell in which
the absorbance is measured, and c is the concentration of the absorbing species. The molar absorptivity, ε, is a
constant that depends upon the molecular properties of the absorbing species and the wavelength of light. In this
equation l, the pathlength, is expressed in centimeters; in many spectrophotometers it is 1 cm; indeed, the
pathlength of the Ocean Optics cuvettes is 1.00 cm.
In this lab, the absorbance, A, was measured in Part 1; with some guidance from your TA, you will see how this data
can be used—based on its relationship to the concentration—to obtain the equilibrium constant. As discussed in the
Introduction section, this experiment is concerned with the equilibrium of the complexation reaction:
Fe3+ (aq) + SCN- (aq) ⇌ FeSCN2+ (aq)
The concentrations of the starting species are important in this reaction. In particular, the SCN – concentration,
3+
[SCN-] must be kept low enough so that species with one Fe and multiple SCN ligands, such as Fe(SCN)2+ or
Fe(SCN)3 are not present (as is the case for higher SCN- concentrations). When [SCN-] is held around 1 mM
+
2+
(millimolar), the amount of these Fe(SCN)2 or Fe(SCN)3 species will never be more than 0.1% of the FeSCN
concentration. In Part 1 of this experiment [SCN-] was held constant while [Fe3+] was increased. As the [Fe3+]
2+
is increased, more FeSCN complex will be formed since
Kc = [FeSCN2+]/([Fe3+][SCN-])
so,
[FeSCN2+] = Kc [Fe3+][SCN-]
and since Kc is a constant and [SCN-] is held constant, as [Fe3+] increases, so does [FeSCN2+]. The rate at
which [FeSCN2+] grows as [Fe3+] is increased is related to Kc and that is how we can determine the
equilibrium constant.
Reference(s)
[1] http://chemistryexperimentphotogallery.blogspot.com/2010_11_01_archive.html accessed June 30, 2016.
4
Glossary
Absorbance
Equilibrium Constant; K
the ability, tendency, or capacity of a substance to
absorb light of a specified wavelength; absorbance is
the negative of the logarithm of the transmittance.
the ratio, at equilibrium, of the concentrations of the
products of a reaction raised to their stoichiometric
coefficients to the concentrations of the reactants
raised to their stoichiometric coefficients; a measure
of the extent to which a reaction proceeds in the
forward direction, i.e., favoring products, based on
comparing the equilibrium constant’s value to the
number 1 (products are favored with K >> 1)
Blank
a solution containing all of the components of a
sample except the analyte
Spectrophotometer
Calibration
a device that passes a beam of light of known
intensity through a sample and measures the
intensity of light that reaches a detector on the other
side of the sample; spectrophotometers measure
absorbance or transmittance of a sample at one or
more wavelengths of light
the alignment of measured amounts or increments
on a device with standard values for amounts or
increments
Cuvette
a vessel or container that holds a fluid sample in a
spectrophotometer or other instrument; cuvettes
generally do not absorb any of the wavelengths of
light being used for the experiment.
Transmittance
the ratio of amount of light energy exiting a sample
or leaving a substance to the amount of light energy
entering a sample or falling upon a substance. 100%
Transmittance means all the light entering a sample
passes through it, with the sample absorbing or
scattering none of it.
Equilibrium
a state of “equal balance”; in chemistry, the condition
of unchanging concentrations due to the equal
balance of forward and reverse reaction rates; at
equilibrium, forward and reverse reaction rates are
equal, while concentrations of reactants and products
need not be equal
5
Report Guidelines – Determination of an Equilibrium Constant
1. Introduction. The introduction should be a detailed description of the purpose of the
experiment. It should include the following and be no less than a half page in length:
a. Fundamental background information for all concepts related to the experiment.
i. Brief description of chemical equilibrium and the equilibrium constant
b. The theoretical basis for all instrumentation techniques (if used) should also
discussed.
i. Spectrometer and how it was used in the experiment
c. Any useful equations with defined variables should be stated and related to the
experiment.
i. Chemical reactions being carried out
ii. Beer’s Law
d. A brief description of the objective/purpose of the experiment.
2. Procedure/Experimental. A procedure/experimental section should be a detailed description
of what actions were taken during the performance of the lab. The section should include the
following:
a. Complete sentences in paragraph form written in past tense.
b. All equipment and actions are described accurately (i.e., a beaker, pipet, or burette
was used to dispense a liquid) so that the procedure is repeatable (i.e., the reader
should be able to repeat your actions in full).
c. Quantities should be written as they were measured. (e.g., 20.0 mL of water was
dispensed into a beaker and stirred).
3. Results. A results section is where figures and data are presented in an organized fashion.
The results section typically include:
a. A results section should include well-organized tables and figures of important data.
b. All important content (i.e., data, figures, tables, and calculations) should be included.
i. Table from procedure
ii. Create 3 additional new tables with headers that include A/[Fe3+] and the
corresponding absorbances for the trials
iii. Create 3 linear plots of Absorbance (y-axis) versus Absorbance/[Fe3+] (x-axis).
Include linear equation and R2 value on plot.
c. Tables and figures be outfitted with appropriately located captions/titles and 1-3
descriptive sentences below them. See writing reports module for examples of welllabelled figures and tables.
d. All calculations done should be expressed at least once (i.e., a sample calculation
should be shown). Calculations can be made in Word using the Insert -> Equation
function.
i. Sample calculation for each calculated value in tables (i.e., all dilution
calculations)
ii. Calculate the equilibrium constant from each plot and determine an average and
standard deviation in the equilibrium constant
iii. The expected equilibrium constant for the reaction is 138 (i.e., Kc should equal
138) at room temperature. Calculate a %error in your average measured K c.
4. Discussion of the work done in this experiment.
a. A discussion is a detailed analysis of the results. As such, making direct references to
figures (e.g., see figure 1) to support your thoughts is necessary.
i. Mention chemical reaction being studied, and its equilibrium expression,
Kc=[FeSCN2+]/[Fe3+][SCN-]
ii. General description of expt. strategy, e.g., portion wise addition of Fe3+ to
SCN- soln. and use of absorbance (A445) measurements
iii. Note the relationship between color change and concentration of iron
thiocyanate complex (i.e., making assumption that [FeSCN2+] is
proportional to absorbance per Beer’s Law)
iv. Mention linear (y=mx+b) nature of A versus A/[Fe3+] plot
v. Mention specific use of plot for determination of Kc
vi. Discuss the expected vs. obtained results
b. An assessment of the possible sources of error AND the impact of such sources of
error on the results.
5. Conclusion. Recap of the experiment and should include:
a. Restatement of all major quantitative and qualitative results.
b. Summarize experimental approach.
c. Restatement of the experimental objective(s).
6. References
a. References should use the ACS citation format.
b. References list must show at least one citation (i.e., the lab procedure) though
additional resources are encouraged.
7. Grammar, Spelling, and Formatting
a. Do not use personal pronouns (e.g., I, you, we, me, her, him, us, our, ours).
b. Data has appropriate units
c. Do not use unusual fonts; employ 10-12 pt. font, regular margins, and 1.5-2.0 spacing