1. 15.5-15.6 Autoionization of Water and pH, and Finding the [H 3 O + ] and pH of Strong and Weak Acid Solutions

2. Autoionization of Water Autoionization – the process by which water acts as an acid and a base with itself. H 2 0(l) H + (aq) + OH - (aq) The equilibrium constant for this reaction is: K w = [H 3 O + ][OH - ] = [H + ][OH - ] K w is known as the ion product (or dissociation) constant for water. At 25 o C (298 K), Kw = 1.0X10 -14. In pure water, the number of H 3 O + and OH - ions are equal, and the solution is neutral. In a neutral solution [H 3 O + ] = [OH - ] = K w of 1.0X10 -7 In an acidic solution [H 3 O + ] > [OH - ] In a basic solution [H 3 O + ] < [OH - ] In all aqueous solutions [H 3 O + ][OH - ] = 1.0X10 -14 (at 25 o C) Remember, equilibrium constants are temperature dependent.

3. The pH Scale The pH identifies the hydrogen potential of a solution. A low pH signifies an acidic solution while a high pH represents a basic solution. In general, the pH scale ranges from 0-14, with 7 representing a neutral solution. 1 pH unit corresponds to a 10-fold change in H 3 O + concentration. pH = -log[H 3 O + ] = -log[H + ] When calculating the correct number of significant figures when performing a logarithm, the log must have the same number of decimal places as the original numbers significant figures. For example, if you were to take the log of 1.0X10 -4, which has two sig figs., your answer should be reported to two decimal places: 4.00

4. Let’s Try a Practice Problem! Calculate [H 3 O + ] at 25 o C for the following solution and determine if the solution is acidic, basic, or neutral. [OH - ] = 1.5x10 -2 K w = [H 3 O + ][OH - ] K w 1.0x10 -14 [H 3 O + ] = --------- = ------------------ = 6.7x10 -13 [OH - ] 1.5x10 -2 [OH - ] > [H 3 O + ], so the solution is basic

5. Let’s Try a Few Practice Problems! Calculate the pH of the solution and indicate whether the solution is acidic or basic: [H 3 O + ] = 9.5X10 -9 M pH = -log[H 3 O + ] = - log(9.5x10 -9 ) = 8.02, this solution is basic! Calculate the [H 3 O + ] for a solution with a pH of 8.37. pH = -log[H 3 O + ] 8.37 = -log[H 3 O + ] [H 3 O + ] = 10 -8.37 = 4.27x10 -9

6. pOH and other p Scales Similar to the pH scale, but with respect to [OH - ] A low pOH represents a basic solution, while a high pOH represents a solution that is acidic. pOH = -log[OH - ] The following two relationships are also on the reference table! K w = [H + ][OH - ] = 1.0x10 -14 at 25 o C pH + pOH = 14 The pKa of a weak acid can also be used to quantify its strength. pKa = -log Ka

7. Strong vs. Weak Acids For strong acids: the concentration of H 3 O + in a strong acid solution is equal to the concentration of the strong acid. For example: A 0.10 M HCl solution has a H 3 O + concentration of 0.10 M and a pH of 1.00. For weak acids: This is not the case. Remember, weak acids only partially ionize, and different weak acids at the same concentration, can have different pH values. – For these types of problems, we have to solve an equilibrium problem, using an ICE table as we did in the previous chapter. – The initial H 3 O + concentrations are approximately zero because of the negligible small contribution of H 3 O + due to the autoionization of water. – In many cases, we can apply the x is small approximation (in these cases, where the ration of x to the number it is subtracted from < 5.0 %, it is valid).

8. Finding the [H 3 0 + ] and pH of Strong and Weak Acid Solutions When a solution contains either a strong or weak acid, there are two sources of hydronium ions: HA(aq) + H 2 O(l) H 3 O + (aq) + A - (aq) Strong or Weak Acid H 2 O(l) + H 2 O(l) H 3 O + (aq) + OH - (aq) K w = 1.0X10 -14 *side note: HA is a strong or weak acid. In most strong or weak acid solutions, the autoionization of water produces such a small amount of H 3 O + than in pure water, and can be ignored.

9. Let’s Try a Practice Problem! Find the H 3 0 + concentration of a 0.250 M hydrofluoric acid solution. (Here the K a value is 3.5x10 -4 according to table 15.5 within the chapter) HF(aq) + H 2 O(l) H 3 O + (aq) + F - (aq) [H 3 O + ][F - ] (x)(x) K a = ---------------- = ------------- Continued on the next slide  [HF] 0.250 - x [HF] M[H 3 O + ] M[F - ] M Initial0.250~00 Change-x+x Equilibrium0.250 - xxx

10. [H 3 O + ][F - ] (x)(x) K a = ---------------- = -------------- [HF] 0.250 – x  x is a small value Now I will plug in my K a and solve for x: x 2 3.5x10 -4 = --------- 0.250 X 2 = 8.75x10 -5 so, x = 9.35x10 -3 Now we can check if x is valid: 9.35x10 -3 ------------- X 100 = 3.74 % so x is valid. 0.250 So, the H 3 O + concentration is: 9.4X10 -3 M

11. Let’s Try Another! A 0.175 M weak acid solution has a pH of 3.25. Find K a for the acid. For this problem, first we need to solve for the hydronium ion concentration: pH = -log[H 3 O + ] -3.25 = log[H 3 O + ] [H 3 O + ] = 10 -3.25 = 5.6x10 -4 M Now set up an ICE table! [H 3 O + ][A - ] K a = --------------- [HA] Continued on the next slide  [HA] M[H 3 O + ] M[A - ] M Initial0.175~00 Change- 5.6x10-4+ 5.6x10 -4 Equilibrium 0.175 -5.6x10 -4 = 0.174 5.6x10 -4

12. [H 3 O + ][A - ] K a = --------------- [HA] (5.6x10 -4 ) 2 K a = -------------- 0.174 K a = 1.8x10 -6

13. Let’s Try Another!! The initial concentration and K a ’s of several weak acid (HA) solutions are listed here. For which of these is the x is small approximation least likely to work in finding the pH of a solution? a.) initial [HA] = 0.100 M; K a = 1.0x10 -5 b.) initial [HA] = 0.10 M; K a = 1.0x10 -6 c.) initial [HA] = 0.0100 M; K a = 1.0x10 -3 d.) initial [HA] = 1.0 M; K a = 1.5x10 -3 c.) initial [HA] = 0.0100 M; K a = 1.0x10 -3 (the validity of the x is small approximation depends on both the value of the equilibrium constant and the initial concentration – the closer these are to one another, the less likely the approximation will be valid.

14. Let’s Try Another!!! Which solution is most acidic? (That is, which one has the lowest pH) (a)0.10 M HCl (b)0.10 M HF (c)0.20 M HF (a) 0.10 M HCl (a weak acid solution will usually be less than 5% dissociated. Since HCl is a strong acid, the 0.10 M solution is much more acidic than either a weak acid with the same concentration or even a weak acid that is twice as concentrated.)

15. Percent Ionization of a Weak Acid Another way to quantify the ionization of a weak acid, is to calculate the percent ionization (the percentage of acid molecules that actually ionize). conc. of ionized acid [H 3 O + ] equil Percent ionization = --------------------------------------------------- X 100 initial concentration of acid [HA] initial The equilibrium H 3 O + concentration of a weak acid increases with the increasing concentration of the acid The percent ionization of a weak acid decreases with increasing the concentration of the acid.

16. Let’s try a practice problem! Find the percent ionization of a 0.250 M HC 2 H 3 O 2 solution at 25 o C. (K a of acetic acid is 1.8x10 -5 ) [H 3 O + ] equil Percent ionization = --------------- X 100 [HA] initial [H 3 0 + ][C 2 H 3 O 2 - ] x 2 K a = ---------------------- = 1.8x10 -5 = ----------- [HC 2 H 3 O 2 ] 0.250 –x X 2 = 4.5x10 -6 so, x = 2.12x10 -3 [H 3 O + ] equil 2.13x10 -3 Percent ionization = --------------- X 100 = -------------- x 100 = 0.85% [HA] initial 0.250 [HC 2 H 3 O 2 ] M[H 3 0 + ]M[C 2 H 3 O 2 - ] Initial0.250~00 Change-x+x Equilibrium0.250-xxx

17. Let’s Try Another!!! Which of these weak acid solutions has the greatest percent ionization? Which solution has the lowest (most acidic pH)? a.) 0.100 M HC 2 H 3 O 2 b.) 0.500 M HC 2 H 3 O 2 c.) 0.0100 M HC 2 H 3 O 2 c.) 0.0100 M HC 2 H 3 O 2 would have the greatest percent ionization because percent ionization increases with decreasing weak acid concentration. But b.) 0.500 M HC 2 H 3 O 2 would have the lowest pH, because the equilibrium H 3 O + concentration increases with increasing weak acid concentration.

18. Mixture of Acids If we were tasked with finding the pH of a mixture of acids we would: – 1.) See if one of the acids were strong, and if so, we could neglect the weaker acid. – 2.) See if we are dealing only with weak acids. If we are, and the concentrations are similar, but the Ka’s are sufficiently different (differ by more than a factor of several hundred), then again, we can focus on the stronger acid as the weaker makes an insignificant contribution. – If we were asked to find the concentration of a part of the weak acid, we have to set up an ICE table, except here, we can’t place a zero in for the initial hydronium ion concentration. Instead, the initial hydronium ion concentration is equal to the hydronium ion concentration formed by the strong(er) acid.

19. Let’s Try a Practice Problem that Deals with a Mixture of Two Weak Acids! Find the pH of a mixture that is 0.150 M in HF and 0.100 M HClO. The following are given: HF(aq) + H 2 O(l) H 3 O + (aq) + F - (aq) K a = 3.5x10 -4 HClO(aq) + H 2 O(l) H 3 O + (aq) + ClO - (aq) K a = 2.9x10 -8 H 2 O(l) + H 2 O(l) H 3 O + (aq) + OH - (aq) K w = 1.0x10 -14 [H 3 O + ][F - ] x 2 K a = ---------------- = 3.5X10 -4 = ------------- x = 7.2x10 -3 [HF] 0.150 – x Let’s check if x is valid: (7.2x10 -3 / 0.150) X 100 = 4.8%  Valid, but barely pH mix = -log(7.2x10 -3 ) = 2.14 [HF] M[H 3 O + ] M[F - ] M Initial0.150~00 Change-x+x Equilibrium0.150-xxX

20. Let’s Try Another!! Use the information from the previous problem, to find the ClO - concentration of the mixture of HF and HClO. [H 3 O + ][ClO - ] (7.2x10 -3 +x)(x) K a = ------------------- 2.9x10 -8 = ------------------- [HClO] 0.100-x x = 4.0x10 -7 [ClO-] = 4.0x10 -7 M [HClO] M[H 3 O + ] M[ClO - ] M Initial0.1007.2x10 -3 0 Change-x+x Equilibrium0.100-x7.2x10 -3 +xx

21. Let’s Try Another Practice Problem!!! Which solution is most acidic (that is, which has the lowest pH)? a.) 1.0 M HCl b.) 2.0 M HF c.) A solution is 1.0 M in HF and 1.0 in HClO a.) 1.0 M HCl, this is the only strong acid of the acids listed above.

22. 15.5-15.6 pgs. 746-747 #’s 48, 50, 56, 58, 66, 70, 74, 80 (a’s only) Read 15.7-15.8 pgs. 720-731