OER Lab 7 - Detrmination of Ksp(Revised)-1

CHEM 1412 Lab – 7 (OER) Dr. Pahlavan 1 Determination of K sp of Calcium Hydroxide (Thermodynamics) Please Watch This Video: https://www.youtube.com/watch?v=0N174A4Hhcs&list=RDCMUCwYoNvQDSDDVqeIfD3qUWBw Objectives: ➢ Complete a reverse titration of an insoluble base with an acid titrant. ➢ Understand solubility equilibria as it is related to the relative solubility of a compound. ➢ Be able to calculate the pH of a salt solution at equilibrium. ➢ Determine the relationship between Gibb’s Free Energy, entropy, temperature, and enthalpy. ➢ Determine the relationship between the sign of Gibb’s Free Energy and spontaneity. ➢ Relate Ksp to spontaneity. Reagents: 1. 0.01M HCl 2. Ca(OH) 2 Solution of Unknown Concentration 3. Bromothymol blue Equipment and Materials: Burette stand magnetic stirrer (optional) Burette (butterfly) clamp magnetic stir bar + extractor Burette Funnel 50-100mL small beaker 25mL graduated cylinder 250mL Erlenmeyer flask (2) Safety: Acids, bases, and bromothymol blue are caustic skin and eye irritants. Use caution when handling. If any reagents contact the skin, rinse with plenty of water. Remove any clothing that has a reagent on it. Always use eye protection. Bromothymol blue can cause gastrointestinal irritation if ingested as well as being a respiratory irritant. Avoid inhalation. Wash your hands with soap and water after lab and always avoid touching your mouth or eating in the lab. Waste Disposal: Dispose of reagents as directed by your instructor. Bromothymol blue should not be poured down the drain.

CHEM 1412 Lab – 7 (OER) Dr. Pahlavan 2 Theoretical Background: While most hydroxide containing compounds are insoluble in water, except for salts of alkali metals and ammonium, there is still a minuscule amount of solute that can dissolve in each amount of solvent. For partially soluble salts, very little ionizes into solution. Most of the salt remains undissolved and thus in unionized form. Hence, why do we use the term solubility equilibrium to discuss the extent of solubility of such substances. This is like other weak electrolytes such as weak acids and bases, but with solubility being the factor for the lack of complete dissociation. So, to help determine the extent of solubility, we use the molar solubility equilibrium constant, Ksp , the number of moles of a given solute which can dissolve in a liter of an aqueous solution at a given temperature. Note that Ksp values 1 vary with temperature since an increase in temperature typically increases the solubility of a solid in a liquid. 1 John Rumble (18 June 2018). CRC Handbook of Chemistry and Physics 99 ed. CRC Press . Molar Solubility is the concentration of ions (M) produced in solution from a salt. The equilibrium constant expression of each insoluble salt can also be written using an ICE box to write the equilibrium expression (K). However, here, rather the Ka or Kb, for solubility equilibria, the equilibrium constant is called Ksp. The Ksp is used to determine how much of the salt ionizes in solution. These are reference values that can be looked up. The greater the Ksp, the more soluble the salt.

CHEM 1412 Lab – 7 (OER) Dr. Pahlavan 4 A quick calculation using the Ksp of Ca(OH) 2 allows us to determine just how much of this solute will dissolve in a liter of aqueous solution. Ca(OH) 2 (s) ⇄ Ca 2+ (aq) + 2 OH- (aq) I 0 0 C +x +2x E x 2x Ksp = [Ca 2+ ] [OH - ] 2 ➔ Ksp = (x) (2x) 2 ➔ Ksp = 4x 3 ➔ x = (Ksp) 1/3 (cube root) Given from table, at 25  C, the Ksp of Ca(OH) 2 is 6.50 x10 -6 : x = (Ksp) 1/3 = ( 6.50 x10 -6 ) 1/3 ➔ x = 0.0187 M molar solubility Therefore, at 25 o C ➔ [Ca 2+ ] = x = 0.0187 M and [OH-]= 2 x = 2(0.0187) = 0.0373 M at 25ᵒC Ksp can be related to the thermodynamics of solution. According to the First Law of Thermodynamics , energy cannot be created or destroyed and is therefore conserved. Energy can be transferred from one form to another. Enthalpy , symbol “H” is heat at constant pressure measured in units of kilojoules (kJ) . Entropy, symbol “S” is a measure of randomness or disorder . Entropy, like enthalpy, is a state function, which means that the entropy value of an element or compound is based on its physical state. Entropy is measured in units of Joules (J/K) . The Second Law of Thermodynamics states that entropy in the universe increases in spontaneous processes. The Third Law of Thermodynamics states that the entropy of a pure crystalline substance at absolute zero temperature is 0. Thus, at absolute zero, the entropy of a lattice structure is zero. Both enthalpy and entropy are determinants of spontaneity — they help determine whether a process is spontaneous or not. Since entropy and enthalpy have different units (J and kJ, respectively), one unit must be converted to the other when used in the same equation so that the units match. Otherwise, values will be off by 1000 or 10 3 . Spontaneous processes occur without any outside energy input or influence. Formation of a solution (i.e. solute dissolving in solvent) as well as physical states can influence the entropy of a substance. Solids states have the least entropy, followed by liquids, and gases. Thus, the dissolution of solid calcium hydroxide will certainly influence and increase the entropy of its system.

CHEM 1412 Lab – 7 (OER) Dr. Pahlavan 5 The following equation relates free energy to the equilibrium constant, K . ΔG 0 = - RT lnK The following equation relates free energy to the solubility product constant, Ksp . ΔG 0 = - RT lnKsp , where ( R=8.314 J/K. mol ) Thus, depending on whether a process will go forward without the input of additional energy or spontaneously, can be linked to the value of K. The following table summarizes the relationship between K and  G  . Rather than memorization, plugging in hypothetical values and observing the changes that result from multiple manipulations of the equation can prove helpful in predicting outcomes at equilibrium. Additionally, you may recall the value of K, above, equal, or below zero and what that predicts about the equilibrium of a reaction from prior topics. K ln K ΔG° Favor at Equilibrium =1 0 0 Products and Reactants Equally Favored ( ➔ ) >1 + - Products are Favored ( ➔ ) <1 - + Reactants are Favored (  ) The sign of ΔG  determines spontaneity: (-) = spontaneous ( ➔ ) and (+) = nonspontaneous (  ) Together with temperature, entropy, and enthalpy contribute to predicting if a process will be spontaneous using Gibbs Free Energy,  G, determined by an equation. Gibbs Free Energy is measured in units of kJ. Temperature units are in degrees Kelvin. ΔG o = Δ H o - TΔS o ( Note: Units of ΔG o and Δ H o are KJ while ΔS o is J/K. mol) Even without quantitative values, spontaneity can be determined using Gibb’s Free Energy equation. The following table summarizes how signs of H, S, and temperature level affect reaction spontaneity.

CHEM 1412 Lab – 7 (OER) Dr. Pahlavan 7 Procedure: Measure 15.0 mL of Ca(OH) 2 solution with a graduated cylinder and place it into 250 mL Erlenmeyer flask. Add 2-3 drops of bromothymol blue indicator to the solution. Note the color at this point, which should be blue, the color of this indicator at a basic pH. Prepare your titration apparatus set up rinsing the burette with water, ensuring the burette valve is operational, and securely placing it onto a butterfly clamp attached to the burette stand, Fig 1 . Ensure your burette valve is not open, that the burette has been lowered to a height that is suitable for the person filling it, and that you are utilizing a funnel at the top the burette to aid in the addition of the acid, if necessary. Simply fill your burette carefully with 0.01 M HCl solution using a small beaker and funnel, record the initial burette reading of acid after allowing a few milliliters of acid to cleanse out any residual water from the valve. It is recommended to fill the 0.0 mL mark line for ease of measuring and to lessen the need to refill the burette in the same titration. You may place a white piece of paper below your flask to aid in observing the appearance of the yellow color. Similarly, a dark piece of paper behind the burette can help see the white increments. You may then place your flask on a magnetic stirrer or gently swirl the flask manually during the titration. When ready, slowly begin adding acid to the base, swirling periodically or continuously stirring at slow speed, until the end point or yellow color has been reached, which is the color bromothymol blue turns when the pH has become acidic. Read and record the final burette reading of the acid titrant. Repeat these steps in trial 2 . Calculate the concentration of Ca(OH) 2 for each trial and the average molarity. Then calculate and complete the remainder of your report form. Fig 1.

CHEM 1412 Lab – 7 (OER) Dr. Pahlavan 8 Prelab Questions – Do these questions before the lab. 1. Why are some insoluble salts said to be in a state of equilibrium and thus given a K value? Explain 2. Calculate the Gibbs Free Energy for the following reaction at 25°C if the enthalpy value (ΔH o ) is 177.8 kJ and entropy value (ΔS o ) are 160.5 J. Is the reaction spontaneous at this temperature? Why or why not? CaCO 3 (s) ↔ CaO (s) + CO 2 (g) 3. a) Complete the following phase: If K is numerically _________, then lnK = _______, and the reaction is spontaneous going in the forward direction. b) Give two examples of processes that increase entropy. 1) _______________________________ 2) _____________________________________ 4. Write balanced equations for the dissolution reactions and solubility product expressions for the following compounds. Example: Ca(OH) 2 ( s ) ⇆ Ca 2+ ( aq ) + 2OH – ( aq ) , K sp = [Ca 2+ ][OH – ] 2 a) Al(OH) 3 b) Ba 3 (PO 4 ) 2 c) Pb(IO 3 ) 2 d) FeCO 3 f) Ag 2 S 5. Calculate Δ S in J at 25 ᵒ for the reaction if Δ H (heat of solution) is 132 kJ/mol K. Explain how the sign of Δ S supports the dissolution of Ca(OH) 2 using the laws of entropy.

CHEM 1412 Lab – 7 (OER) Dr. Pahlavan 10 Post lab Questions – Do these questions after the lab. 1. Define the Second and Third Laws of Thermodynamics. 2. What is molar solubility (molarity) of an Ag + ion if the Ksp of AgCl is 1.6 x 10 -10 ? (show your work) 3. What is the relationship between  G 0 and K as it appropriates to predicting the spontaneity of a reaction? 4. List the following salts in order of increasing solubility (lowest to highest) according to their Ksp values: Compound CdS BaF 2 Al(OH) 3 MgCO 3 MnS Ksp 8.0 x 10 -28 1.7 x 10 -6 1.8 x 10 -33 4.0 x 10 -5 2.3 x 10 -13 Lowest highest (compound) (compound) 5. Explain , how does temperature influence Gibbs Free Energy, entropy, and solubility of a solid solute in a liquid solvent? 6. Calculate Δ G o in kJ for the reaction at 25 ᵒ C given your experimental Ksp value. Explain why the sign of ΔG o supports the Ksp of calcium hydroxide using the magnitude of K and the sign of ΔG o to support your answer.