Equilibrium

1. Equilibrium

2. Equilibrium • Products can not escape reaction vessel • Reaction becomes reversible • Rate of forward equals rate of reverse • Concentrations are constant

3. Equilibrium Constant • Equilibrium constants, Keq, are an important concept in chemistry. Equilibrium constants tell us the progress of a chemical reaction by relating the concentrations of both reactants and products at equilibrium to a numerical constant. If the equilibrium constant is greater than one, then there is more product formed at equilibrium than reactants remaining. If the equilibrium constant is less than one, there is less product than reactant. A good example of this concept is a special type of equilibrium constant, the ionization or acidity constant, Ki or Ka. It is used to compare the strengths of acids. The larger the ionization constant, the more ions and hence, the stronger the acid. Consider the ionization constant for acetic acid at 1.8 x 10-5. The magnitude of this Ki tells us that there are very few ions in a 1 M solution of acetic acid, about 0.4% at room temperature.

4. Another type of equilibrium constant is solubility product constant, Ksp. As the name implies, solubility product constants are used to compare the solubilities of similar substances. Again, the larger the constant, the greater to solubility at a given temperature. If we compare the Ksp of the Group II hydroxides in the adjacent table, we will note that the solubility of Mg(OH)2 is considerably less than the other Group II hydroxides. The solubility product constant can also be used to determine the actual ion concentration in a solution at a given temperature. Note that the Ksp of calcium hydroxide is 1.3 x 10-6 at 25 C. Using this value, we can predict the pH of a saturated calcium hydroxide solution to be 11.8 at 25 C.

5. How is the equilibrium constant determined? Given the expression for a general reaction where the brackets “[]” represent the concentration of aqueous solutions in moles/liter, M, we can write an equilibrium expression:

6. Rules for expression • There are some rules to following when writing an equilibrium expression and calculating its numerical value. • 1. The concentrations of the products are always in the numerator and the concentrations of the reactants are always in the denominator. • 2. The concentrations are raised to the power of the coefficients in the balanced equation of the reaction.

7. Rules • 3. Pure solids and liquids have a constant concentration and are not included in the equilibrium expression. • 4. Equilibrium constants are temperature dependent. Therefore, equilibrium constants are always stated at a given temperature, often 25 C.

8. In one experiment, a researcher mixed 25 ml of 0.20 M sodium fluoride solution with some solid magnesium hydroxide at 25EC. After two days, it was found that 0.40 ml of 0.10 M HCl was need to neutralize 0.85 ml of the solution in the flask. Assuming that the mixture is at equilibrium, we can determine the equilibrium constant from the reaction:

9. Since one mole of NaOH reacts with one mole of HCl by means of the relationship, NaOH(aq) + HCl(aq) = NaCl + H2O, then we can easily calculate the equilibrium concentration of sodium hydroxide. Where

11. Now that we know the concentration of the NaOH produced, we can calculate the concentration of the fluoride ions remaining at equilibrium. If “x” represents to concentration of NaOH at equilibrium, then 0.2 - x would represent the equilibrium concentration of sodium fluoride. The [F-] is 0.2 - x because we started with a 0.2 M sodium fluoride solution. We can make this statement as one mole of NaOH is formed when each mole of NaF reacts. The ratio is actually 2:2 but simplifies to 1:1.

12. Since the equilibrium concentration of NaOH is 0.047 M, then the equilibrium concentration of sodium fluoride would calculate to be 0.2 M - 0.047 M or 0.153 M.

13. Now that we know the concentrations of both the reactants and products, we are ready to calculate the value for the equilibrium constant, Keq, for this reaction. It is not necessary to know the concentrations for magnesium fluoride, MgF2, and magnesium hydroxide, Mg(OH)2, as they are solids and deleted from the equilibrium expression. Therefore, the equilibrium expression and constant become

14. What is the expected equilibrium constant for this reaction? The theoretical equilibrium constant for the reaction can be determined from the change in the free energy, ΔG reaction. It is calculated from the free energies of formation, ΔGfo, for the substances reacting and produced in the balanced chemical equation. Given the free energy values in Table #1, we can find the free energy change for the overall reaction.

15. The equilibrium constant for the reaction can now be determined from the change in free energy of +5.8 kJ (+5800 joules) according to the relationship:

16. The opposite relationship is also true. That is, once the equilibrium constant is determined, the change in free energy for the reaction can be found. In our example, the equilibrium constant was found to be 0.094. Therefore the change in free energy of the reaction is also +5800 joules or +5.8 kJ.

17. Another useful quantity is the enthalpy or heat of the reaction. The enthalpy or heat of the reaction is calculated in the same fashion as the change in the free energy, by finding the difference in the heats of formation between the reactants and products as given on Table #1.

18. What does the enthalpy or heat of the reaction tell us? The energy change in a reaction tells us whether or not the reaction is endothermic or exothermic. An endothermic reaction has a positive ΔH and requires energy for the reaction to proceed. Since endothermic reactions required energy, they are favored by an increase in the temperature of the reaction. If ΔH is negative, the reaction is exothermic. Exothermic reaction liberate heat as the reaction proceeds. Exothermic reactions are favored by a lower temperature than an exothermic reaction. In this case, ΔH is positive. Therefore, the reaction should be heated for it to proceed at a reasonable rate.

19. Indirect Method

20. Lab Procedure • Cut the very top of a jumbo polyethylene transfer pipet and pack it with about 2 cm (1") of cotton. This can be achieved by pushing small pieces of cotton into the bottom of pipet with a glass rod. Add dry calcium carbonate to the pipet in small portions, tapping the desk to pack the solid after each addition. When the level of solid has reached the bottom of the pipet bulb, insert the pipet into a small test tube. Wrap the open area between the test tube and pipet with plastic wrap to hold the pipet in place and inhibit the exchange of air with the filtrate. Fill the pipet bulb with 0.1 M NaF. Cover the top of the pipet with a small piece of plastic wrap and place the reaction system your lab drawer or another assigned area until the next laboratory period

21. Procedure • Remove the pipet filter from the test tube containing the equilibrium mixture from your lab drawer or designated area. While setting up the experiment, measure the temperature of the solution in the test tube. • If necessary, attach tip extenders to both hypodermic syringes. It is important to rinse and prepare the syringes as directed by your instructor. Be certain that you fill the syringe designated for acids with standardized 0.1 M hydrochloric acid solution and fill the “base” syringe with the filtrate. Note that both syringes are color coded. Record the initial volume of the solution in both syringes to the nearest 0.01 ml in the space provided on your data table. Partly fill a polyethylene transfer pipet with bromocresol green/methyl red solution, the acid-base indicator in this experiment.

22. Procedure • Add roughly 0.80 ml - 0.85 ml of the equilibrium mixture to a small beaker or plastic cup followed by one drop of the bromocresol green/methyl red indicator. Carefully add standardized 0.1 M HCl dropwise with constant with swirling until one drop of acid just turns the solution orange. Always wait between drops near the end point as the reaction slows. You may inadvertently add too much acid and miss the endpoint. The solution will turn from blue to red at the endpoint. When you are satisfied that the titration is complete, record the final volume of the solutions in both syringes to the nearest 0.01 ml in the space provided on your data table .

23. Procedure • Refill both the syringes with their respective solutions, rinse the beaker or plastic cup throughly with deionized or distilled water, and repeat the experiment as time permits. When you have completed the required number of trials, throughly rinse all glassware and the syringes. Return all common items to their storage area, pour the unused solutions into the sink, and flush with plenty of water.

24. Write the net ionic equation for the reaction studied in this experiment.

25. Calculate the concentration (molarity) of the sodium carbonate solution produced from the volumes of both solutions reacted and the concentration of the hydrochloric acid, 0.10 M HCl, titrated.

26. According the balanced equation for this reaction, what is the relationship between the change in the fluoride ion concentration and the change in the carbonate ion concentration?

30. Calculate the theoretical equilibrium constant from the free energy of the reaction determined in part (a) above

31. Using the theoretical equilibrium constant, calculate the expected concentrations of each reactant and product.

33. The solubility product of CaF2 is 1.6 x 10-10 and that of CaCO3 is 4.5 x 10-9 at 25 C. Given that information, calculate the equilibrium constant for the reaction studied in this experiment from the solubility product data. How does this value compare with the value obtained from the thermodynamic and your empirical data?

34. Given the standard enthalpies (heat) of formation, Hfo, for both the reactants and products in the Table #2 below, find the theoretical heat or enthalpy of the reaction