Experiment 1:
Determination of an Equilibrium Constant
Purpose
The purpose of this experiment is to use spectrometry to determine the equilibrium constant of the reaction of
Fe3+ (aq) with SCN – (aq).
Learning Objectives
Prepare a set of standard solutions of known concentration of FeNCS2+ and measure their absorbance
values using a spectrometer.
Construct a calibration curve using the absorbance values and known concentrations.
Determine equilibrium concentrations of the reaction of Fe3+ (aq) with SCN – (aq) by measuring the
absorbance and comparing to the calibration curve.
Apply the information from the balanced chemical equation of the reaction, and data obtained in the
laboratory, to determine the concentrations of reactants and Products at equilibrium.
Calculate the value of the equilibrium constant using data obtained in the laboratory.
Laboratory Skills
Use of volumetric pipet.
Use of volumetric flask.
Use of a spectrometer.
Preparation of a calibration curve.
Equipment
Chemicals
Volumetric pipets
Test tube
2.00 × 10−3 M KSCN
Fe(NO3 )3 in 1 M
and bulb
Pasteur pipets
0.200 M Fe(NO3 )3
HNO3
100-mL beakers
Spectrometer
2.00 × 10−3 M
Distilled water
Volumetric flasks and
Cuvette
stoppers
Laboratory Manual Prepared by Catalyst Education, LLC for the University of California at Riverside
Department of Chemistry.
1.1
Determination of an Equilibrium Constant
Introduction
You might expect that a mixture of two or more substances would react until one of the substances is completely
consumed. This is true if a product of the reaction is effectively removed from the reaction mixture as (1) a slightly
ionized substance, or (2) a slightly soluble precipitate or gas, or if (3) a large amount of energy is released by the
reaction. If, on the other hand, all of the products remain in contact, they may interact to re-form the reactants.
Reactions that behave in this manner are called reversible reactions.
In Experiment 7 of CHEM 1LB/2LB, we measured rates of chemical reactions at their very start, just as products
were being formed. We will now discuss the situation where products re-form reactants. The forward and reverse reactions will at first proceed at different rates, but a time will come when the reverse rate is equal to the
forward rate. This is equilibrium, the state where the concentrations of the reactants and the concentrations of
the products each remain constant in time.
Equilibrium does not mean that the chemical reaction has stopped! It simply means that on a macroscopic scale
there is no change in the concentrations of the reactants and products. On the microscopic (molecular) scale,
however, there is much activity as reactants are converted into products and products are converted into reactants.
Consider two reactive substances, A and B, that may interact to form two other substances, C and D, according
to:
A (g) + B (g) −−−→ C (g) + D (g)
(Equation 1.1)
If the previous reaction is reversible, as soon as C and D have been formed we will also have the concurrent
reaction:
C (g) + D (g) −−−→ A (g) + B (g)
(Equation 1.2)
The effect of these two reactions is that the initial concentrations of A and B will decrease and the concentrations
of C and D will increase until the concentrations of all of the substances have been adjusted to a steady state (such
that the forward and reverse reactions occur at equal rates). This is referred to as chemical equilibrium, and may
be expressed using double arrows in an equation:
−−−−−
⇀
C (g) + D (g) ↽
− A (g) + B (g)
(Equation 1.3)
It is important to note that the equilibrium concentrations of reactants and products do not have to be equal; they
will be constantly adjusted so that the opposing reaction rates are equal.
Let us now consider an actual example—the reaction of hydrogen and iodine (at elevated temperature):
−−−−
⇀
H2 (g) + I2 (g) −
↽
− 2 HI (g)
Laboratory Manual Prepared by Catalyst Education, LLC for the University of California at Riverside
Department of Chemistry.
(Equation 1.4)
1.2
Determination of an Equilibrium Constant
Imagine we have two glass containers. Container A holds 1 mole of hydrogen and 1 mole of iodine. Container B
holds 2 moles (the equivalent amount) of hydrogen iodide (HI). Both containers are heated and maintained at an
elevated temperature so that all substances are gases. At the start of the reaction of these two containers, container
A will be violet colored due to the iodine vapor present, and container B will be colorless (HI is colorless). After
some time both containers will have identical intermediate violet coloration, indicating that the forward and
reverse reactions have occurred until the same relative concentrations of hydrogen, iodine, and hydrogen iodide
are present in each container. One way to study a chemical reaction in equilibrium is to look at its equilibrium
constant, K. For the following generic reaction:
−−−−
⇀
𝑎A + 𝑏B −
↽
− 𝑐C + 𝑑D
(Equation 1.5)
the equilibrium constant has the following form:
𝐾=
[C]𝑐 [D]𝑑
[A]𝑎 [B]𝑏
(Equation 1.6)
It is important to remember that the concentrations used in the calculation of the equilibrium constant, K, are
the species’ concentrations at equilibrium. Here is an example using a balanced chemical equation:
−−−−−
⇀
NO2 (g) + CO (g) ↽
− NO (g) + CO2 (g)
(Equation 1.7)
The equilibrium constant is:
𝐾=
[NO][CO2 ]
[NO2 ][CO]
(Equation 1.8)
If the equilibrium concentrations of the species in the reaction are found to be (mol/L): NO2 = 0.02, CO = 0.3,
NO = 1.5, and CO2 = 1.0, then:
𝐾=
1.5 × 1.0
= 250
0.02 × 0.3
The value of the equilibrium constant can be interpreted as follows. First notice that since concentrations can
never be negative, the equilibrium constant K will always be positive. A large value of K (>1) means that the
equilibrium favors the formation of the products.
In this experiment we will examine the equilibrium properties of the following reaction:
2+
−−−−−
⇀
Fe3+ (aq) + SCN− (aq) ↽
− FeNCS (aq)
(Equation 1.9)
When a solution of iron(III) ions and thiocyanate ions are mixed, the deep red-colored FeNCS2+ complex ion is
Laboratory Manual Prepared by Catalyst Education, LLC for the University of California at Riverside
Department of Chemistry.
1.3
Determination of an Equilibrium Constant
produced. The equilibrium constant for this reaction is:
𝐾=
[FeNCS2+ ]
[Fe3+ ][SCN− ]
(Equation 1.10)
Since we will be monitoring a chemical reaction in equilibrium, the value of K should remain constant regardless
of the initial amounts of reactants used. We will find the value of K for reactions with various concentrations of
reactants to prove this concept. By combining our knowledge of the initial concentrations of the reactants with
the equilibrium concentration of FeNCS2+ (determined by spectrophotometric analysis of the red FeNCS2+ ion
solutions), we will be able to calculate the equilibrium constants (K) for these reactions.
As mentioned, we will be determining the [FeNCS2+ ] by using a spectrophotometer. This instrument will be used
to measure the amount of light absorbed by the red FeNCS2+ complex, which has a maximum absorbance at 447
nm. Recall from Beer’s law (Experiment 6 in CHEM 1LB) that the absorbance of the FeNCS2+ complex (A) is
directly proportional to the concentration (C):
𝐴 = 𝜖𝑏𝐶
(Equation 1.11)
...where:
A = absorbance of the solution
𝜖 = molar absorptivity of the species at the measured wavelength, with units of liter/mol⋅cm
b = path length of the solution in cm
C = concentration of species in mol/L
A graph of the absorbance of FeNCS2+ versus the concentration will yield a linear “calibration curve.” An explanation of how to construct a calibration curve (from which you can find the [FeNCS2+ ]) is provided in the
experimental section. See the section entitled “Operating the Ocean Optics Spectrometer” in Appendix H of this
manual for information on how to use the spectrophotometer.
The calculation of the equilibrium constant may be a bit confusing. In order to illustrate the calculation procedure, let us look at a specific example. Let’s say we prepared a solution by mixing 10.0 mL of 2.00 × 10−3 M
Fe(NO3 )3 with 10.0 mL of 2.00 × 10−3 M KSCN. The equilibrium concentration of FeNCS2+ ion formed in this
reaction was found to be 1.50 × 10−4 M (using a spectrophotometer). To calculate K we need to complete the
following five steps:
Step 1. Calculating the Initial Moles of Reactant Used
Because we know the molarity and the volumes of the solutions used, we can quickly determine the number of
moles of reactants by:
Moles of reactant = (Molarity × Volume)
(Equation 1.12)
The volume for each solution will be 10.0 mL (0.0100 L) and the molarity of the reactants will be 2.00 × 10−3 M.
Laboratory Manual Prepared by Catalyst Education, LLC for the University of California at Riverside
Department of Chemistry.
1.4
Determination of an Equilibrium Constant
Thus the initial moles of reactants are:
Initial mol Fe3+ = 𝑀Fe3+ × 𝑉 = (2.00 × 10−3 M) × (0.0100 L) = 20.0 × 10−6 mol
Initial mol SCN− = 𝑀SCN− × 𝑉 = (2.00 × 10−3 M) × (0.0100 L) = 20.0 × 10−6 mol
Step 2. Calculating the Moles of Product Formed
Again we can use Equation 1.12 to calculate the number of moles. If the concentration of FeNCS2+ ion formed
in this reaction was experimentally determined to be 1.50 × 10−4 M and the volume of the mixture is the sum of
the two volumes that were mixed (20.0 mL or 0.0200 L), the number of moles of FeNCS2+ is calculated by:
Mol of FeNCS2+ = 𝑀FeNCS2+ × 𝑉 = (1.50 × 10−4 M) × (0.0200 L) = 3.00 × 10−6 mol
The number of moles of Fe3+ and SCN – that were consumed in the reaction must also
both be equal to 3.00 × 10−6 moles since, according to Equation 1.10, it takes one mole
of Fe3+ and one mole of SCN – to Produce one mole of FeNCS2+ .
Step 3. Calculating the Moles of Reactant Present at Equilibrium
We know the initial moles of reactants (Step 1) and we found how many moles of reactants were consumed (Step
2). The number of moles left at equilibrium is:
Equilibrium moles = initial moles − moles consumed
(Equation 1.13)
Equil. moles Fe3+ = 20.0 × 10−6 mol − 3.00 × 10−6 mol = 17.0 × 10−6 mol
Equil. moles SCN− = 20.0 × 10−6 mol − 3.00 × 10−6 mol = 17.0 × 10−6 mol
Step 4. Calculating the Concentrations of Species at Equilibrium
We determined the number of moles of Fe3+ and SCN – present at equilibrium in Step 3. We also know the volume
at equilibrium is equal to the sum of the two volumes mixed. We can obtain the concentrations of these species
from:
Molarity =
moles
volume
(Equation 1.14)
We experimentally found the equilibrium concentration of FeNCS2+ to be 1.50 × 10−4 M. We can calculate the
concentrations of Fe3+ and SCN – present at equilibrium using Equation 1.13:
𝑀Fe3+ =
mol Fe3+
17.0 × 10−6 mol
=
= 8.50 × 10−4 M
volume of solution
0.0200 L
Laboratory Manual Prepared by Catalyst Education, LLC for the University of California at Riverside
Department of Chemistry.
1.5
Determination of an Equilibrium Constant
𝑀SCN− =
mol SCN –
17.0 × 10−6 mol
=
= 8.50 × 10−4 M
volume of solution
0.0200 L
Step 5. Calculating the Equilibrium Constant for the Reaction
Once the equilibrium concentrations of the reactants and products have been determined, substitution of the
values into Equation 1.10 yields K:
𝐾=
[FeNCS2+ ]
1.5 × 10−4
=
= 208
3+
−
(8.50 × 10−4 ) × (8.50 × 10−4 )
[Fe ][SCN ]
In this experiment the data you obtain will be similar to that shown in the preceding example, and the calculations
involved will be completely analogous.
Note that for the calibration curve solutions, the concentration of Fe3+ is very large compared to the concentration
of SCN – . The large excess drives the equilibrium essentially completely to the right, so that you can assume that
one mole of FeNCS2+ complex is produced for each mole of SCN – ion. Thus the concentration of FeNCS2+ is
known and can be plotted vs. the absorbance (the “calibration curve”).
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Department of Chemistry.
1.6
Determination of an Equilibrium Constant
Procedure
Safety Precautions
Experimental Procedure Notes
1.
You will work with a partner on this experiment.
2.
Refer to Appendix H for instructions in using the spectrometer and conducting a Beer’s law experiment.
3.
Since the quality of your results will be dependent upon your ability to properly use volumetric glassware, you should review the relevant sections in Appendix D.
Part A. Preparing the Calibration Curve
You will prepare a calibration curve by measuring the absorbance of a series of solutions containing known
concentrations of the FeNCS2+ complex.
1.
Prepare the first solution, C1, by delivering 1.00 mL of 2.00 × 10−3 M KSCN using a volumetric pipet and
diluting with 19.0 mL of 0.200 M Fe(NO3 )3 . Use the appropriate combination of volumetric pipets to deliver
this volume of Fe(NO3 )3 .
2.
Prepare solutions C2 and C3 by mixing solution C1 with 0.200 M Fe(NO3 )3 , as specified in Table 1.1.
Table 1.1: Solution Preparation
Solution
[FeNCS2+ ]
mL of C1
mL of 0.200 M
Fe(NO3 )3
C1
10.0 × 10−5
—
—
C2
3.0 × 10−5
3.0
7.0
C3
6.0 × 10−5
6.0
4.0
Laboratory Manual Prepared by Catalyst Education, LLC for the University of California at Riverside
Department of Chemistry.
1.7
Determination of an Equilibrium Constant
Note that [Fe3+ ] in these solutions is more than 103 higher than [SCN – ]. This drives the
equilibrium reaction (Equation 1.9) completely to the right. Because the reaction now
goes to completion with SCN – as the limiting reactant, we can calculate the concentration of FeNCS2+ formed from the moles of SCN – initially present in the solution.
3.
Before measuring the absorbance of the calibration curve solutions, you will need to prepare a “blank” to
calibrate the spectrometer. Pipet 5.00 mL of 2.00 × 10−3 M Fe(NO3 )3 into a test tube, add 5.00 mL of distilled
water, and mix thoroughly.
4.
Next, open the file “Expt 1 Equilibrium Constant” on the computer desktop. This will bring up the Logger
Pro software for running the spectrometer. Make sure the display indicates that the spectrometer is set to
measure at 447.1 nm.
5.
Fill a cuvette about 3/4 full with the blank solution and insert it in the sample compartment of the spectrometer. Handle the cuvette only by the frosted edges. Make sure that the clear sides of the cuvette are aligned
in the path of the light beam.
6.
Choose “Calibrate > Spectrometer” from the “Experiment” menu at the top of the Logger Pro screen.
7.
Rinse the cuvette with about 1 mL of solution C1, then fill it 3/4 full and place it in the sample compartment.
8.
Press the green “Start” button, then the “Keep Current Value” icon in the Logger Pro toolbar. In the dialog
box that appears, type the concentration of FeNCS2+ for this solution.
9.
Repeat this step for the remaining two solutions, making sure to rinse the cuvette each time with the new
solution. Be sure to record each absorbance value in Report Table 1.1 in the Report Sheet.
10. After all three solutions have been measured, click the “Stop Collection” button. Click the “Linear Fit” icon
in the toolbar to determine the best straight line through the three data points. An information box will
display the slope and y-intercept of the Beer’s law calibration curve.
11. Select “Page Setup” from the File menu. Click on the “landscape” (sideways) orientation. This will maximize the size of the graph on the page. Choose “Print Graph” from the “File” menu. Type the name of both
Laboratory Manual Prepared by Catalyst Education, LLC for the University of California at Riverside
Department of Chemistry.
1.8
Determination of an Equilibrium Constant
partners, your TA’s name, and the day/time of your lab in the printing options box, and click “OK.” In the
print dialog box, enter “2” for the number of copies and click the “Print” button.
Part B. Measuring the Absorbance of the Equilibrium Mixtures
Prepare four equilibrium mixtures according to Table 1.2 and the directions following.
Table 1.2: Equilibrium Mixture Preparation
Equilibrium Mixture
1
2
3
4
Volume Fe(NO3 )3 soln. (mL)
5.00
5.00
5.00
5.00
Volume KSCN soln. (mL)
1.00
2.00
3.00
4.00
Volume H2 O (mL)
4.00
3.00
2.00
1.00
1.
Pour about 30 mL of 2.00 × 10−3 M Fe(NO3 )3 (in 1 M HNO3 ) into a clean, dry 100-mL beaker.
2.
For each mixture, pipet 5.00 mL of this solution into a 10-mL volumetric flask.
3.
Next add about 20 mL of 2.00 × 10−3 M KSCN to another 100-mL beaker.
4.
Pipet the appropriate volume (as shown in Table 1.2) of the KSCN solution into the volumetric flask.
5.
Finally, use a plastic Pasteur pipet to dilute the mixture to the 10-mL mark with distilled water (the volume
of H2 O added will be approximately that shown in Table 1.2).
6.
Mix the solution thoroughly.
7.
Repeat the procedure for the remaining mixtures.
8.
Measure the absorbance of each mixture within 7–10 minutes after it is prepared. For each measurement,
Laboratory Manual Prepared by Catalyst Education, LLC for the University of California at Riverside
Department of Chemistry.
1.9
Determination of an Equilibrium Constant
rinse the cuvette with 2–3 mL of the solution to be measured. It is usually best to begin with the least
concentrated solution and then work your way up in concentration. (Question for your understanding: why
is this?) After inserting the cuvette in the spectrometer, allow a moment for the displayed absorbance to
stabilize, then record the value in the Report Sheet.
9.
From the equation of the line obtained for your Beer’s law calibration graph, use the absorbance values for
each mixture to calculate [FeNCS2+ ] at equilibrium.
10. Obtain the equilibrium constant, K, by substituting [Fe3+ ], [SCN – ], and [FeNCS2+ ] into Equation 1.10. Report the average K using the three values that are in closest agreement.
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Department of Chemistry.
1.10
Name:
Section:
Report Sheet:
Determination of an Equilibrium Constant
Date:
The following Report Sheet is provided to help you organize your data, calculations, and results before submitting
them via the Report interface.
Part A. Preparing the Calibration Curve
Report Table 1.1: Calibration Curve Absorbance Data
Solution
Absorbance
C1
C2
C3
Part B. Measuring the Absorbance of the Equilibrium Mixtures
Complete Report Table 1.2. The values for [FeNCS2+ ] are obtained from the graph of absorbance vs. [FeNCS2+ ]
(calibration curve) prepared in Part A.
Report Table 1.2: Equilibrium Mixture Absorbance Data
Equilibrium
Mixture
Volume of
2.00 × 10−3 M
Fe(NO3 )3 (mL)
Volume of
2.00 × 10−3 M
KSCN (mL)
Volume of
water (mL)
Absorbance
[FeNCS2+ ]
(M)
1
2
3
4
Laboratory Manual Prepared by Catalyst Education, LLC for the University of California at Riverside
Department of Chemistry.
1.1
Determination of an Equilibrium Constant Report Sheet
Calculation of the Equilibrium Constant, K
The equilibrium constant will be calculated as described in steps 1–5 in the discussion. Enter your results in
Report Table 1.3. Show all your calculations for each step.
Step 1: Find the initial number of moles of Fe3+ and SCN – . Use Equation 1.12 and enter your results into the
first two rows of Report Table 1.3.
Step 2: Enter the equilibrium value of [FeNCS2+ ] from Report Table 1.2. Use Equation 1.12 to find the number
of moles of FeNCS2+ in each of the mixtures. Enter your results in the fifth row of Report Table 1.3. (Note that
this is also the number of moles of Fe3+ and SCN – consumed in the reaction.)
Step 3: Calculate the number of moles of Fe3+ and SCN – that remain at equilibrium for each of the mixtures.
Use Equation 1.13 and enter the results in rows 3 and 4 in Report Table 1.3.
Laboratory Manual Prepared by Catalyst Education, LLC for the University of California at Riverside
Department of Chemistry.
1.2
Determination of an Equilibrium Constant Report Sheet
Step 4: Calculate the concentrations of all of the species at equilibrium using Equation 1.14 and the results of
Step 3. The volume of the mixture is 10.00 mL (0.0100 L) for all mixtures. Enter your results into the appropriate
rows in Report Table 1.3.
Step 5: Calculate the equilibrium constant, K, for the reaction by substituting the values obtained for [Fe3+ ],
[SCN – ], and [FeNCS2+ ] into Equation 1.10. Calculate the 𝐾avg from the three values that are in closest agreement.
Report Table 1.3: Equilibrium Constant Calculations
Equilibrium Mixture
1
2
3
4
Initial number of moles
Fe3+
SCN –
Equilibrium number of moles
Fe3+
SCN –
FeNCS2+
Equilibrium concentrations
Fe3+
SCN –
FeNCS2+
K
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Department of Chemistry.
1.3