Lab 11 - Spectroscopic Determination of an Equilibrium Constant

Goal and Overview

The reaction of iron (III) with thiocyanate to yield the colored product, iron (III) thiocyanate, can be described by the following equilibrium expression.

( 1 )

Fe³⁺ + SCN⁻ equilibrium arrow

FeSCN²⁺

You will study this equilibrium using the Spec 20 UV-visible spectrometer. The wavelength of light absorbed most strongly by the product will be determined from the spectral profile of FeSCN²⁺. A Beer's Law plot will be made for a series of FeSCN²⁺ solutions of known concentration. Then, the concentrations of FeSCN²⁺ will be measured spectroscopically for a set of solutions made with different initial concentrations of reactants. This data will be used to determine

K_eq,

the equilibrium constant for the reaction.

Objectives and Science Skills

•
Perform volumetric dilutions and calculate resulting molarities.
•
Understand and explain absorption spectroscopy and the mathematical relationships between percent transmittance, absorbance, concentration, path length, and extinction coefficient.
•
Apply linear fitting methods to find relationships between dependent and independent variables, such as percent transmittance (absorbance) and concentration.
•
Explain and apply Beer's Law; describe the assumptions and limitations imposed by the nature of the equilibrium on the calculation of FeSCN²⁺ associated with the absorption data.
•
Use absorption data to qualitatively and quantitatively analyze the concentration of FeSCN²⁺ in solution.
•
Identify and discuss factors or effects that may contribute to the uncertainties in values or assessments made from experimental data.
•
Analyze, quantify, and discuss the uncertainty in results when assumptions are used.

Background

This experiment investigates the equilibrium established by the reaction of the iron (III), Fe³⁺, and the thiocyanate, SCN^–, ions. See Eq. 1. The reactants are colorless, but the FeSCN²⁺ ion is orange-red colored. At equilibrium, the concentrations of these three ions must be related to each other according to the equilibrium constant expression.

( 2 )

K =

[FeSCN²⁺]

[Fe³⁺][SCN⁻]

One goal in this experiment is to measure the value of K, using the spectrometer to quantitatively analyze the concentration of FeSCN²⁺ ion. Absorption spectroscopy and Beer's Law were discussed in detail and were used in the Allura Red Lab. This same method will be utilized to determine [FeSCN²⁺], the colored product.

( 3 )

A = −log(T) = εbc

( 4 )

T =

100%

= 10^−εbc = 10^−A

Then, you will use your understanding of equilibrium processes to deduce the equilibrium concentrations of the reactants. Knowing all three concentrations listed above in Eq. 2 allows the equilibrium constant for this reaction to be calculated.

Procedure

Part 1: Qualitative Observations: Is the reaction exothermic or endothermic?

Using a 10 mL graduated cylinder, measure out approximately 2 mL of 2 × 10^–3 M NaNO₃ and put it in a test tube.

Add approximately 8 mL of 2 × 10^–3 M NaSCN.

Add approximately 10 mL of 2 × 10^–3 M Fe(NO₃)₃. Note the color of the solution.

Fill a Spec 20 cuvette no more than 2/3 full, and split the remaining solution among three test tubes.

Place one tube in an ice bath and one in the hot water bath on the hot plate.

After about 10 minutes, compare them with the solution at room temperature.

Discuss the implications of your observations, basing your discussion on your knowledge of Le Châtelier's principle.

Do your observations imply an exothermic or endothermic reaction?

Part 2: Spectral Profile and
λ_max
(most sensitive wavelength) of FeSCN²⁺

Measure transmittance (%T) to 0.1% of the mixtures in your cuvette in the range from 370 to 560 nm.

a
Use a cuvette containing 2 × 10^–3 M NaNO₃ as a blank to set 100% transmission.
b
Check the %T readings at 20 nm intervals.
c
When you reach the region of minimum transmittance, reduce the intervals to 10 or even to 5 nm.

For the wavelength of minimum %T, calculate the absorbance, A, of the solution (A = –log T) to the appropriate number of significant figures.

Identify the wavelength of maximum absorbance, the experimental value of

λ_max.

How does your

λ_max

compare with your answer to Question 1 of the pre-lab assignment?

Set your spectrometer to

λ_max

for parts 3 and 4.

Part 3: Beer's Law Curve for FeSCN²⁺: determining ε of the product at
λ_max

To make solutions of known concentrations of FeSCN²⁺, you cannot simply dissolve a salt containing FeSCN²⁺ in water because the ion will dissociate in order to satisfy the equilibrium constant expression. If

K_eq

were known, solutions with known initial concentrations of FeSCN²⁺ could be made, and algebra could be used to find equilibrium concentrations of Fe³⁺, SCN^–, and FeSCN²⁺. However, K is what you are trying to find in Part 4. In order to overcome this difficulty, you will take spectral data for a set of solutions made by mixing a very high Fe³⁺ concentration with extremely small SCN^– concentrations. Assume that SCN^– is the limiting reactant (i.e., that essentially all of it is used up to make FeSCN²⁺). By doing this, you can equate the equilibrium concentration of iron (III) thiocyanate,

[FeSCN²⁺]_eq

to the initial concentration of thiocyanate,

[SCN⁻]_initial.

Once you have actually determined

K_eq,

you must return to this assumption and verify its validity. Note for Parts 3 & 4: You may wish to split the dilution work with your partner to save time. One person could do Part 3 while the other is doing Part 4.

Take about 100 mL of 0.1 M Fe³⁺ solution (solution B) in a small labeled beaker.

Make the strongest colored solution of NaSCN and Fe(NO₃)₃ (solution A).

a
Using a volumetric pipet, put 5 mL of 2 × 10^–3 M NaSCN (concentration known to 1%) into a 50 mL volumetric flask.
b
Fill to the mark with solution B (above; 0.1 M Fe³⁺ solution).

Use only volumetric glassware, not graduated pipets or cylinders.

•
You have the following volumetric pipets available: 1, 2, 5, 10 mL.
•
You have the following volumetric flasks available: 10, 50, 100 mL.

Accurately create 10 mL volumes of the following dilutions of solution A with solution B. As each of these solutions is created, measure its %T to 0.1%.

a
Pure B for use as a blank (faint straw-colored, no colored complex); this is 0.1 M Fe(NO₃)₃.
b
1 mL A into 10 mL flask, filled to mark with B
c
3 mL A into 10 mL flask, filled to mark with B
d
5 mL A into 10 mL flask, filled to mark with B
e
7 mL A into 10 mL flask, filled to mark with B
f
9 mL A into 10 mL flask, filled to mark with B
g
Pure A, the pure, most red-orange solution

Calculate absorbance for each solution: A = –log(%T/100%).

Make a Beer's Law plot of absorption versus concentration of FeSCN²⁺ (A vs [FeSCN²⁺]) for these 7 points. Use two significant figures in your concentration values and three for your absorbance values.

Draw the best-fit straight line to the points.

This best-fit line mathematically has the form of Beer's Law: A = εbc, with slope = εb and y-intercept = 0; ε = molar extinction coefficient in L/mol · cm, b = pathlength in cm, and c = concentration in mol/L. Determine the slope to the ones place.

Using the measured pathlength b of your cuvette (to 0.01 cm) and your slope, calculate the value of the extinction coefficient for FeSCN²⁺ at its

λ_max

to the ones place.

Record which Spec 20 you used so you can use the same one for Part 4.

Summary of Desired Quantities Parts 1 – 3.

•
Temperature Dependence: Is the reaction exothermic or endothermic? Explain.

•
Spectral Profile: What is
λ_max?

•
Beer's Law Plot: Graph of Absorbance versus [FeSCN²⁺] noting ε at
λ_max.

Part 4: Equilibrium Constant for the Formation of FeSCN²⁺

In this part of the experiment, you will prepare five solutions with the same initial concentration of Fe³⁺ ion but different initial concentrations of SCN^– ion. As you make each solution, measure its percent transmittance at

λ_max

(Part 2) and use your Beer's Law plot (Part 3) to establish the equilibrium FeSCN²⁺ concentration. From the initial concentrations of the reactants and the equilibrium concentration of the product, you can calculate the experimental value of

K_eq

for each of the five solutions using Eq. 2.

Use the solutions provided, each of which is 2 × 10^–3 M: NaSCN, Fe(NO₃)₃, and NaNO₃.

Use volumetric pipets and a 10 mL volumetric flask to prepare each of the following five solutions.

•
NaSCN and Fe(NO₃)₃ deliver SCN^– and Fe³⁺ to the solution.
•
NaNO₃ is used to fill the flask to 10 mL.
•
The "Total used" row is designed to help you estimate how much of the stock solutions you should take in labeled beakers to your lab station.
•
Please minimize waste – do not take extra and please share leftovers.

Waste disposal:		The solutions must be put into the labeled waste bottles in the back hood.
		Nothing can go down the sink.
		If you are ever in doubt, ask your TA.

Find equilibrium concentrations of Fe³⁺, SCN^–, and FeSCN²⁺ to two significant figures. (See Equations 1 and 2.)

ICE tables will help you determine these values. Initial amounts, changes in amounts, and final equilibrium amounts are shown. These values must be in moles/L.

•
initial amounts of reactants (amounts before the reaction begins): determined using the dilution equation
- •
  To find the initial concentration of SCN^–, use the dilution equation: (M₁V₁)/V₂ = M₂, where
  V₂ = 10 mL.
- •
  To find the initial concentration of Fe³⁺, use the dilution equation: (M₁V₁)/V₂ = M₂, where V₂ = 10 mL.
•
initial amount of product (the amount before the reaction begins): zero
•
equilibrium concentration of product
([FeSCN²⁺]_eq):
determined spectroscopically

[FeSCN²⁺] at equilibrium is determined using Beer's Law; x is the amount of FeSCN²⁺ created (determined experimentally).

( 5 )

x = [FeSCN²⁺]_eq =

εb

= A / slope

To complete your ICE tables, one for each trial in Part 4 (concentrations should have two significant figures):

a
Begin by filling out the product column from the bottom up. Because the stoichiometry is 1:1:1, the amount of reactant consumed is equal to the amount of product formed.
b
Fill in the rest of the ICE table box-by-box until the equilibrium reactant concentrations are determined.

Use Eq. 2 and the equilibrium concentrations from the bottom row of each ICE table to calculate K_eq to two significant figures for the five trials in Part 4.

Find the average value of K_eq, the standard deviation, and the relative error (standard deviation divided by the average). Are the values of K for all trials similar? Should they be?

Assumption Check Used in Making Beer's Law Plot

Given your value of K, go back and check the validity of the assumption you made in Part 3.

Rewrite Eq. 2 so that the ratio of

[FeSCN²⁺]_eq

[SCN⁻]_eq, [FeSCN²⁺]_eq/[SCN⁻]_eq,

is on one side.

Calculate the approximate ratio of

[FeSCN²⁺]_eq/[SCN⁻]_eq

using

K_eq

and [Fe³⁺]. Use your average value for

K_eq.

The Fe³⁺ concentration was approximately 0.1 M in Part 3; the change in its concentration should have been negligible.

The assumption that essentially all of the SCN^– reacted to form FeSCN²⁺ would mean that this ratio would need to be large. Is it? If the ratio is small, the assumption was clearly a bad one and the experiment is useless in determining the equilibrium FeSCN²⁺ concentration and

K_eq.

At least 95% of the initial SCN^– should react to form FeSCN²⁺ at equilibrium.

Discuss how good the assumption was and how the assumption affected the calculated values of

K_eq.

•
For example, if
K_eq
is 350, then
[FeSCN²⁺]_eq/[SCN⁻]_eq ≈ 35.

•
This means that 35 out of 36 SCN^– initially present have been converted to FeSCN²⁺ at equilibrium; 1 out of 36 is present as SCN^–.
•
That is about a 3% error in the FeSCN²⁺ concentration due to just the assumption.
•
And,
[FeSCN²⁺]_eq
is used to determine the other values at equilibrium; 3% error in concentrations translates into roughly 9% error in
K_eq
(again, this is just from the assumption and does not consider other experimental variables).

Checking the assumption is only part of a thorough experimental analysis; it should not be considered the main point of the lab.

Results

Complete your lab summary or write a report (as instructed).

Abstract

Results

Observations for Part 1
λ_max and absorbance at λ_max for Part 2
Beer's Law plot for Part 3 including slope(εb)
Ice tables, individual and average
K_eq
values

Sample Calculations

Absorbance from transmittance
Concentration calculations
K_eq
calculation
Assumption testing

Discussion/Conclusions

What you found out and how
Relating results to predictions/theory
How was Part 3 dependent on Part 2?
Validity of the assumption
What can you conclude from this experiment

Lab 11 - Spectroscopic Determination of an Equilibrium Constant

Goal and Overview

Objectives and Science Skills

Suggested review and external reading

Background

Procedure

Part 1: Qualitative Observations: Is the reaction exothermic or endothermic?

Part 2: Spectral Profile and
λ_max
(most sensitive wavelength) of FeSCN²⁺

Part 3: Beer's Law Curve for FeSCN²⁺: determining ε of the product at
λ_max

Part 4: Equilibrium Constant for the Formation of FeSCN²⁺

Assumption Check Used in Making Beer's Law Plot

Results

Abstract

Results

Sample Calculations

Discussion/Conclusions

Review Questions

Lab 11 - Spectroscopic Determination of an Equilibrium Constant

Goal and Overview

Objectives and Science Skills

Suggested review and external reading

Background

Procedure

Part 1: Qualitative Observations: Is the reaction exothermic or endothermic?

Part 2: Spectral Profile and λmax (most sensitive wavelength) of FeSCN2+

Part 3: Beer's Law Curve for FeSCN2+: determining ε of the product at λmax

Part 4: Equilibrium Constant for the Formation of FeSCN2+

Assumption Check Used in Making Beer's Law Plot

Results

Abstract

Results

Sample Calculations

Discussion/Conclusions

Review Questions

Part 2: Spectral Profile and
λ_max
(most sensitive wavelength) of FeSCN²⁺

Part 3: Beer's Law Curve for FeSCN²⁺: determining ε of the product at
λ_max

Part 4: Equilibrium Constant for the Formation of FeSCN²⁺