Purpose

To determine [latex]\Delta G_\textrm{rxn}^\circ[/latex], [latex]\Delta H_\textrm{rxn}^\circ[/latex] and [latex]\Delta S_\textrm{rxn}^\circ[/latex] for the solvation of Ca(OH)₂.

Expected Learning Outcomes

• Observe the relationship between solubility and equilibrium constant in a reaction.
• Obtain further practice in the use of titration-based techniques to determine concentrations of acids and bases.
• Experimentally determine thermodynamic parameters associated with equilibria.

Textbook Reference

Tro, Chemistry: Structures and Properties, 2nd Ed., Ch. 18.9.

Theoretical Background

As you may know, the Gibbs free energy change for a reacting mixture, [latex]\Delta G_\textrm{rxn}[/latex], is given by

\begin{equation}
\Delta G_\textrm{rxn} = \Delta G_\textrm{rxn}^\circ + RT \ln Q \label{404:deltaG_Q}
\end{equation}

where [latex]\Delta G_\textrm{rxn}^\circ[/latex] is the standard free energy change for a given reaction and Q is the reaction quotient as defined in thermodynamics.^[1]

At equilibrium, [latex]\Delta G=0[/latex] as the system will experience no net change. In this case, [latex]Q = K_\textrm{eq}[/latex], the equilibrium constant as defined in thermodynamics, and hence the equation above can be rewritten as

\begin{equation}
\Delta G^\circ = -RT \ln K_\textrm{eq} \label{404:deltaG_K}
\end{equation}

Under constant temperature and pressure

\begin{equation}
\Delta G_\textrm{rxn}^\circ = \Delta H_\textrm{rxn}^\circ – T\Delta S_\textrm{rxn}^\circ
\end{equation}

where [latex]\Delta H_\textrm{rxn}^\circ[/latex] is the standard reaction enthalpy and [latex]\Delta S_\textrm{rxn}^\circ[/latex] is the entropy change associated with this reaction.

For a given reaction where

• K₁ is the equilibrium constant at temperature T₁.
• K₂ is the equilibrium constant at temperature T₂.

We can show that

\begin{equation} \label{404:2pt_KG}
\ln \left(\frac{K_2}{K_1}\right) = -\frac{\Delta H_\textrm{rxn}^\circ}{R} \left(\frac{1}{T_2} – \frac{1}{T_1}\right)
\end{equation}

Using this equation, the reaction enthalpy can be determined. Also, using the values of K₁ and K₂, [latex]\Delta G_\textrm{rxn}^\circ[/latex] can be solved for each temperature.  This will then allow us to find [latex]\Delta S_\textrm{rxn}^\circ[/latex] can be determined for the reaction.

In this experiment, you will study the solvation of calcium hydroxide, for which the net ionic equation is

\begin{equation} \label{404:CaOH2_dissoc}
\textrm{Ca}(\textrm{OH})_2 (s) \rightleftharpoons \textrm{Ca}^{2+}(aq) + 2\textrm{OH}^- (aq)
\end{equation}

Procedure

Preparation of Filtered, Saturated Calcium Hydroxide at Room Temperature (In Pairs)

Since undissolved calcium hydroxide will, upon neutralization of OH^–, be driven into solution (Think about this based on Le Chatelier’s Principle!), it is important that the solution is filtered prior to use. To do this, you will filter out any solid calcium hydroxide present using gravity filtration before performing the titration.

1. Obtain about 100 mL of the saturated calcium hydroxide.
2. Check that the Buchner filter is clean and dry.
3. Vacuum filter as quickly as possible the saturated calcium hydroxide.  Record the temperature of this calcium hydroxide solution.
4. After all of the calcium hydroxide is filtered, seal the product using a piece of Parafilm.

Titration of Filtered Saturated Calcium Hydroxide (Individual)

You will titrate the hydroxide in the calcium hydroxide solution using hydrochloric acid

\begin{equation}
\textrm{Ca}(\textrm{OH}_2 (aq) + 2\textrm{HCl}(aq) \to \textrm{CaCl}_2(aq) + 2\textrm{H}_2\textrm{O}(l)
\end{equation}

Unlike the previous titrations we’ve done, we will use calcium hydroxide as the analyte (in the Erlenmeyer flask) and hydrochloric acid as the titrant.

5. Obtain approximately 50 mL standardized hydrochloric acid. Be sure to record the concentration of this hydrochloric acid solution.
6. Rinse the buret using deionized water and standardized hydrochloric acid. Fill the buret with standardized HCl up to approximately the 10.00 mL mark.
7. Rinse the pipet using deionized water and filtered calcium hydroxide solution.
8. Pipet 5.00 mL of the filtered calcium hydroxide solution using a volumetric pipet into a 125 mL Erlenmeyer flask and add five drops of bromothymol blue indicator.
9. Titrate the calcium hydroxide solution using HCl until you reach the yellow end-point.
10. Repeat steps 8 and 9 twice, so you would have done the titration three times..

Tips

• You should be able to use the first titration as a rough titration.  For subsequent titrations, quickly put in about 2 mL less HCl as you used the first time, and then add in HCl dropwise.

Preparation of Saturated Calcium Hydroxide Solution Near 100°C (in pairs)

11. Obtain approximately 65 mL of deionized water and boil it on a hot-plate in a 250 mL beaker. Place a clean stir-bar in the solution and start stirring the water using the stir-bar.
12. Put approximately 1.3 g of solid calcium hydroxide to the water, and allow the mixture to boil and be stirred for about five minutes.
13. Vacuum filter this solution as quickly as possible.  Measure the temperature of this solution immediately after filtration.

Titration of Filtered Saturated Calcium Hydroxide (individual)

14. Allow the mixture to cool to room temperature.
15. Determine the concentration of OH^– in the solution following steps 8-10.

Clean-up and Waste Disposal

Wash all glassware carefully to ensure there is no solid residue. Rinse the waste down the drain with plenty of tap water.

Data Analysis

Determination of [latex]K_\textrm{sp}[/latex] at Each Temperature

In the titration, the dissolved OH^– will react with H⁺ from hydrochloric acid in a neutralization reaction. Based on the stoichiometry of the reaction

\begin{equation}
\textrm{H}^+(aq) + \textrm{OH}^-(aq) \to \textrm{H}_2\textrm{O}(l) \label{404:neutralize}
\end{equation}

determine the moles of OH^– in a 5.00 mL aliquot of the filtrate using the stoichiometric ratio, the molarity of the standardized hydrochloric acid, and the average volume of HCl required to reach the titration end-point.

Since there were initially no calcium ions in the solution, from the dissociation process you should be able to find the number of moles of Ca²⁺ in the solution from the number of moles of OH^–.  Hence, you can determine the molarity of Ca²⁺ in the saturated solution. Report K_sp to the appropriate number of significant figures.

Determine [latex]\Delta H_\textrm{rxn}^\circ[/latex] for the Solvation of Calcium Hydroxide

Being sure to use the correct units for each relevant quantity, substitute the K_sp for each temperature T into the equation

\begin{equation}
\ln \left(\frac{K_2}{K_1}\right) = -\frac{\Delta H_\textrm{rxn}^\circ}{R} \left(\frac{1}{T_2} – \frac{1}{T_1}\right)
\end{equation}

Be sure that the temperature is expressed in Kelvins. Report the enthalpy of solvation to three significant figures.

Determine [latex]\Delta G_\textrm{rxn}[/latex] for the Solvation of Calcium Hydroxide at Two Different Temperatures

Using the equation

\begin{equation}
\Delta G^\circ = -RT \ln K_\textrm{eq}
\end{equation}

and by making appropriate unit conversions, determine – at each temperature – the change in Gibbs free energy [latex]\Delta G_\textrm{rxn}[/latex] associated with solvation.

Determine [latex]\Delta S_\textrm{rxn}^\circ[/latex] for the Solvation of Calcium Hydroxide

Given that you now know [latex]\Delta G[/latex] at two different temperatures T₁ and T₂, based on equation \ref{404:G_and_HS}, we can write the simultaneous equations

\begin{equation}
\Delta G_1 = \Delta H_1^\circ – T_1\Delta S^\circ \label{404:Ge1}
\end{equation}
\begin{equation}
\Delta G_2 = \Delta H_2^\circ – T_2\Delta S^\circ \label{404:Ge2}
\end{equation}

Assuming that [latex]\Delta H_\textrm{rxn}[/latex] and [latex]\Delta S_\textrm{rxn}[/latex] are temperature-independent, we can find from the equatiions above that

[latex]\Delta G_1 - \Delta G_2= \Delta S_\textrm{rxn}^\circ (T_2 - T_1)[/latex]

by which [latex]\Delta S_\textrm{rxn}^\circ[/latex] can be determined by substituting appropriate values from previous calculations.