Equilibrium

Learning Objectives

  1. Measure the absorbance spectra of an equilibrium mixture
  2. Determine the equilbrium constant at varying concentrations
  3. Determine the equilibrium constant at varying temperatures
  4. Calculate the enthalpy of the reaction using the Van't Hoff equation

Suggested Reading

Silberberg, M.S. Amateis, P. Lavieri, S. and Venkateswaran, R. Chemistry: The Molecular Nature of Matter and Change, 2nd Canadian ed.; McGraw-Hill Ryerson Limited: 2016. Chapters 15.5 and 15.6.

Introduction

The purpose of this lab is to experimentally determine the equilibrium constant, $K_c$, for the following chemical reaction:

\begin{equation}\label{eq:overall} \underbrace{\ce{Fe^3+(aq)}}_\text{Iron III} \ce{+} \underbrace{\ce{SCN^{-}(aq)}}_\text{thiocyanate} \ce{ <=>} \color{red}{\underbrace{\ce{FeSCN^2+(aq)}}_\text{thiocyanoiron(III)} }\\ \end{equation}

The equilibrium constant is given by:

\begin{equation}\label{eq:equil} \ce{K_{c} = \frac{[FeSCN^{2+}]_{eq}}{[Fe^{3+}]_{eq} [SCN^{-}]_{eq}}} \end{equation}

When $\ce{Fe^3+}$ and $\ce{SCN^{-}}$ are combined, an equilibrium is established between these two ions and the $\ce{FeSCN^{2+}}$ ion. In order to calculate $K_c$ for the reaction, it is necessary to know the concentrations of all ions at equilibrium: $\ce{[FeSCN^2+]_{eq}}$, $\ce{[SCN^{-}]_{eq}}$, and $\ce{[Fe^3+]_{eq}}$. You will prepare four equilibrium systems containing different concentrations of these three ions. The equilibrium concentrations of the three ions will then be determined experimentally. These values will be substituted into the equilibrium constant expression to see if $\ce{K_{c}}$ is indeed constant.

In order to determine $\ce{[FeSCN^2+]_{eq}}$, you will use a colorimeter (Figure 1). Usually, molecules (or ions) only absorb at certain discrete wavelengths of light, which correspond to specific electronic transitions. The $\ce{FeSCN^2+}$ ion produces solutions with a red colour, indicating that the cyan light component of white light has been absorbed by the $\ce{FeSCN^2+}$ ion . Since the wavelengths ecomposing cyan light is close to the waveleghth of blue light, the blue LED setting on the colorimeter should be used; the computer-interfaced colorimeter then measures the amount of blue light absorbed by the coloured solutions. By comparing the absorbance of each equilibrium system, $A_{eq}$, to the absorbance of a standard solution, $A_{std}$, one can determine $\ce{[FeSCN^2+]_{eq}}$.

computer-interfaced colorimeter
Computer-interfaced colorimeter

Beer’s Law relates the absorbance of the solution to the concentration of the absorbing species:

\begin{equation}\label{eq:beer} \tag{Beer's Law} A = a b c \end{equation}
where:
$A$ Absorbance
$a$ Absorptivity constant (L mol-1 cm-1)
$b$ Path length of cell (cm)
$c$ Concentration of $\ce{FeSCN^{2+}}$ (mol L-1)

For a given species, $a$ and $b$ are constants at a given wavelength. The absorbance, is therefore proportional to the concentration.

Pre-Lab

Using a cell with a path length of 1.00 cm, you recorded an absorbance of 0.452 for solution #1. Knowing that the absorptivity constant of $\ce{FeSCN^2+}$ is 4700.0 L mol-1 cm-1 at the wavelength used, calculate the concentration of $\ce{FeSCN^{2+}}$ in solution #1. If you dilute this solution in the cell with a small amount of water, would you expect the absorbance to increase, decrease or remain the same?

Knowing $\ce{[FeSCN^2+]_{eq}}$ allows you to determine the concentrations of the other two ions at equilibrium. For each mole of $\ce{FeSCN^{2+}}$ ions produced, one mole of $\ce{Fe^{3+}}$ is consumed (see the 1:1 ratio of coefficients in equation \eqref{eq:overall}). Thus $\ce{[Fe^{3+}]}$ can be determined by:

\begin{equation} \ce{[Fe^{3+}]_{eq}} = \ce{[Fe^{3+}]_{o}} – \ce{[FeSCN^{2+}]_{eq}} \end{equation}

Because one mole of $\ce{SCN^{-}}$ is used up for each mole of $\ce{FeSCN^{2+}}$ ions produced, $\ce{[SCN^{–}]_{eq}}$ can be determined by:

\begin{equation} \ce{[SCN^{–}]_{eq}} = \ce{[SCN^{–}]_{o}} – \ce{[FeSCN^{2+}]_{eq}} \end{equation}

Knowing the values of $\ce{[Fe^{3+}]_{eq}}$, $\ce{[SCN^{–}]_{eq}}$, and $\ce{[FeSCN^{2+}]_{eq}}$, you can use equation \eqref{eq:equil} to calculate the value of $\ce{K_{c}}$, the equilibrium constant.

Apparatus and chemicals

Apparatus

Chemicals

Procedure

Caution

Fe(NO3)3 solutions in this experiment are prepared in 1.00 M HNO3 and should be handled with care. Wear gloves at all times during the lab.

  1. Label four 20 x 150 mm test tubes from 1-4. Pour about 30 mL of 0.002000 M $\ce{Fe(NO3)3}$ into a clean, dry 50 mL beaker. Pipet 5.00 mL of this solution into each of the four labeled test tubes. Pour about 25 mL of the 0.002000 M $\ce{KSCN}$ into another clean, dry 50-mL beaker. Pipet 2.00, 3.00, 4.00 and 5.00 mL of this solution into test tubes 1, 2, 3 and 4, respectively. Pour about 25 mL of distilled water into a 50 mL beaker. Then, pipet 3.00 mL, 2.00 mL and 1.00 mL of distilled water into test tubes 1, 2 and 3, respectively, to bring the total volume of each test tube to 10.00 mL. Cap each tube and mix thoroughly. Measure the room temperature and record its value in your data sheet, that is the temperature at which your calculated equilibrium constant $K_{c}$, is valid. Volumes of each solution added to each test tube are summarized in Table 1, below:
    Table 1 - Approximate composition of the solutions
    Test Tube Fe(NO3)3 KSCN H2O
    # mL mL mL
    1 5 2 3
    2 5 3 2
    3 5 4 1
    4 5 5 0
  2. To prepare the standard solution of $\ce{FeSCN^2+}$ (test tube #5), dispense about 9 mL of 0.20000 M $\ce{Fe(NO3)3}$ from the dispenser into a 10 mL graduated cylinder. Record the exact volume in the datasheet. Transfer the solution into a 20 mm X 150 mm test tube labeled #5. Pipet 1.00 mL of 0.002000 M $\ce{KSCN}$ into the same test tube. Cap and mix thoroughly.

    3. Pre-Lab

    What would you do if you spilled $\ce{Fe(NO3)3}$ solution on your hands when you weren't wearing any gloves?

  3. If the computer is not ready for data collection, open the file in the Experiment 20 folder of Chemistry with Computers. You should see a live Meter window to display absorbance, and a table window with columns for the trial number and the absorbance value.
  4. Prepare a blank by filling a cuvette 3/4 full with distilled water. To correctly use a colorimeter cuvette, remember:
    1. All cuvettes should be gently wiped clean and dried on the outside using a Kimwipe.
    2. Handle cuvettes only by their top edge.
    3. Position the cuvette in the cuvette holder of the colorimeter.
    4. All solutions should be free of bubbles.
  5. Calibrate the colorimeter.
    1. Holding the blank cuvette (3/4 filled with distilled water) by its upper edges, place it in the cuvette slot of the colorimeter.
    2. Press the < or > arrow buttons until your wavelenghth of interest, 470 nm (blue light), is selected. You can tell it is selected when the corresponding LED next to the 470 nm is lit up.
    3. Press the CAL button until the red LED begins to flash and then release the CAL button. When the LED stops flashing, the calibration is complete.
  6. You are now ready to measure the absorbances.
    1. Discard the cuvette contents into your 250 mL waste beaker. Rinse it twice with ~ 1mL portions of the test tube #1 solution discarding the waste into the waste beaker. Then fill the cuvette 3/4 full with the same solution.
    2. Wipe the outside of the cuvette with a tissue and then place the cuvette in the colorimeter. After closing the lid, wait for the absorbance value displayed in the meter window to stabilize. Record this absorbance value in the data sheet.
    3. Repeat Steps 6-a and Step 6-b to measure the absorbance of the solutions in test tubes #2, #3, #4.
    4. Once you determine the absorbance of the solution in test tube #4, do not discard the contents.
    5. For the standard, test tube #5 you will also repeat step 6-a and 6-b but use a second cuvette. Do not discard the contents of this cuvette as you will need it again.
  7. You should now have two filled cuvettes, one with the contents of test tube #4 and the other with test tube #5, make sure you know which is which by capping with the appropriately labelled cap. Put both cuvettes into water bath #1 for 5 minutes. Follow Step 6-b to find the absorbance of both cuvette #4 and cuvette #5. Record absorbance and temperature values in the datasheet.
  8. Put the same cuvettes in water bath #2 for 5 minutes. Follow Step 6-b to find the absorbances.
  9. Repeat Step 8 using water baths #3 and #4.
  10. Discard the contents of both cuvettes into your waste beaker.

Clean up

When you have completed the experiment, discard of the waste beaker into a yellow waste container. Wash all glassware and cuvette thoroughly with tap water and then rinse with distilled water followed by ethanol, and finally return everything in the exact same arrangement a you found them.

Pre-Lab

Write out the procedure in your own words in point form. You do not need to include precedural elements related to the use of the Vernier interface. You may write it out by hand or type it and print it.

Calculations

Note

This example will help guide you through the calculations, but the values themselves are arbitrary. Do not be concerned if your values are not the same as the example.

  1. Calculate $\ce{[Fe^{3+}]_{o}}$, (the initial concentrations of $\ce{Fe^{3+}}$) and $\ce{[SCN^{-}]_{o}}$, (the initial concentration of $\ce{SCN^{-}}$ for each tube. Initial means after mixing but before any reaction has taken place. Record in Table 5 of the lab results (the excel file). NOTE: The total volume is the sum of the volumes added.
  2. Calculate $\ce{[FeSCN^2+]eq}$ (the equilibrium concentration of $\ce{FeSCN^2+}$) for each tube, and record in Table 5 (results file). The standard solution has a very large initial concentration of $\ce{Fe^3+}$, but a small initial concentration of $\ce{SCN^{-}}$. $\ce{[Fe^{3+}]_{o}}$ in the standard solution is also 100 times larger than $\ce{[Fe^3+]}$ in the other four equilibrium mixtures. According to LeChatelier's principle, this high concentration forces the reaction far to the right, using up nearly 100% of the $\ce{SCN^{-}}$ ions. According to the balanced equation, for every one mole of $\ce{SCN^{-}}$ reacted, one mole of $\ce{FeSCN^2+}$ is produced. Thus $\ce{[FeSCN^2+]_{std}}$ is assumed to be equal to $\ce{[SCN^{-}]_{o}}$. Given that absorbance of $\ce{FeSCN^2+_{eq}}$ is directly related to its concentration via \eqref{eq:beer}, the concentration of $\ce{FeSCN^2+}$ for any of the equilibrium systems (tubes 1-4) can be found by the following equation:
    \begin{equation} \ce{[FeSCN^2+]_{eq}} = \frac{A_{eq}}{A_{std}}\ce{[FeSCN^2+]_{std}} \end{equation}
  3. Calculate $\ce{[Fe^3+]_{eq}}$ and $\ce{[SCN^{-}]_{eq}}$ (the equilibrium concentrations of $\ce{Fe^3+}$ and $\ce{SCN^{-}}$) for each tube. Record your values in Table 5 (results file).
  4. For each solution that was studied, calculate $\ce{K_{c}}$. Record the results in Table 5 (results file).

Example

Assume a solution is prepared in tube #1 by mixing 5.00 mL of .002000 M $\ce{Fe^3+}$, 3.2 mL of 0.002080 M $\ce{SCN^{-}}$ and 1.9 mL of $\ce{H2O}$.

  1. Dilution:
    $\frac{(5.00 \, mL) \times (0.002000 \, M) \ce{Fe^3+}}{10.1 \,mL}$ = 0.000990 M = $[\ce{Fe^3+}]_o$
    $\frac{(3.2 \, mL) \times (0.002080 \, M) \ce{SCN^{-}}}{10.1 \, mL}$ = 0.00066 M = $[\ce{SCN^{-}}]_o$
    The $o$ subscript denotes material that has been diluted but still unreacted
  2. If the absorbance recorded for tube #1 is 0.153 ($A_{eq}=0.153$), the absorbance recorded for the standard solution is 0.750 ($A_{std}=0.750$), and the concentration of the standard solution is 0.0001800 M $\ce{FeSCN^2+}$, we have:
    $\frac{0.153}{0.750} \times 0.0001800 \, M$ = 0.0000370 M = $\ce{[FeSCN^2+]_{eq}}$
    The $eq$ subscript denotes concentration once equilibrium has been reached.

  3. In tabular form using the ICE method this would be represented as:

    $\ce{Fe^3+}$ $+$ $\ce{SCN^{-}}$ $\ce{ <=>}$ $\ce{FeSCN^2+}$
    Initial(after mixing) $0.000990$ $0.00066$ $0$
    Change $-x$ $-x$ $+x$
    Equilibrium $\underbrace{0.000990 - x}_{\ce{[Fe^3+]_{eq}}}$ $\underbrace{0.00066 - x}_{\ce{[SCN^{-}]_{eq}}}$ $0.0000370$

    Value of $x$ is obtained from the last column, where $0 + x = 0.0000370$

  4. Solve for $\ce{K_{c}}$ using Equation \ref{eq:overall}:

    $\ce{K_{c}}$ = $\frac{0.0000370 \, M}{(0.000953 \, M)(0.00062 \, M)}$ = $62 \, M^{-1}$

Enthalpy

We can use the Van't Hoff equation to see how the equilibrium constant is affected by changes in temperature.

\begin{equation} \tag{Van't Hoff Equation} \ln K_{c} = - \frac{{\Delta H^\circ}}{RT}+ \frac{{\Delta S^\circ }}{R} \end{equation}

where:

$K_{c}$ equilibrium constant
$\Delta H^\circ$ reaction enthalpy
$R$ ideal gas constant 8.314 J K -1 mol-1
$T$ absolute temperature of the system
$\Delta S^\circ$ entropy of the system

Considering the general equation for a linear graph ($y = mx + b$) we see that if we were to graph $\ln K_{c}$ vs. $1/T$, the slope of the curve will be $ - \Delta H^\circ /R$ and the intercept will be $\Delta S^\circ /R$. See chapter 15.6 of your textbook for some background information on these topics. myCourses has guidelines posted if you need help preparing your graph.

Equilibrium Datasheet

Hand one copy in before leaving lab and keep one copy for yourself

First and Last Name:
Student ID Number:
Demonstrator:
Lab Section:
Date:
Device ID:
Table 2 - Stock solution concentrations
$\ce{SCN^{-}}$ all tubes $\ce{Fe^3+}$ for tubes 1-4 $\ce{Fe^3+}$ for tube 5
(mol/L) (mol/L) (mol/L)
Table 3 - Absorbances and volume used to compose solutions
Tube Absorbance * $\ce{H2O}$ $\ce{SCN^{-}}$ $\ce{Fe^{3+}}$ Total Volume
# (mL) (mL) (mL) (mL)
1 3.00 2.00 5.00 10.00
2 2.00 3.00 5.00 10.00
3 1.00 4.00 5.00 10.00
4 5.00 5.00 10.00
5 1.00
*Temperature:
Table 4 - Absorbances at various temperatures
Tube #4 Temperature Absorbances
(°C) cuvette #4 cuvette #5
after bath #1
after bath #2
room temperature
after bath #3
after bath #4

Pre-Lab Questions (Compiled from the Lab Manual)

  1. Using a cell with a path length of 1.00 cm, you recorded an absorbance of 0.452 for solution #1. Knowing that the absorptivity constant of $\ce{FeSCN^2+}$ is 4700.0 L mol-1 cm-1 at the wavelength used, calculate the concentration of $\ce{FeSCN^{2+}}$ in solution #1. If you dilute this solution in the cell with a small amount of water, would you expect the absorbance to increase, decrease or remain the same?
  2. What should you do if you spilled $\ce{Fe(NO3)3}$ solution on your hands when you weren't wearing any gloves?
  3. Write out the procedure in your own words in point form. You do not need to include precedural elements related to the use of the Vernier interface. You may write it out by hand or type it and print it.