Acids Lesson 9 Weak Acids pH Calculations

1. Calculate the pH of 0.45 M HCN. You need an ICE chart for weak acids or bases! HCN ⇄ H+ + CN- I 0.45 M 0 0 C x x x E 0.45 - x x x Ka = [H+][CN-] = 4.9 x 10-10 [HCN] Ka = x2 = 4.9 x 10-10 0.45 - x

The Ka is small, so x is small We will find that x = 0.000015 0.45 - 0.000015 = 0.45 This means we can make the approximation that 0.45 - x = 0.45 We can do this anytime the Ka has an exponent of 10-4 or less Ka = x2 = 4.9 x 10-10 0.45 - x 0 small ka

x2 = 4.9 x 10-10 0.45 x = [H+] = 0.000014849 M pH = -Log[0.000014849] pH = 4.83 2 sig figs due to molarity and Ka

2. Calculate the pH of 0.60 M H3BO3 H3BO3 ⇄ H+ + H2BO3- I 0.60 M 0 0 C x x x E 0.60 - x x x 0 small ka x2 = 7.3 x 10-10 0.60

x2 = 7.3 x 10-10 0.60 x = [H+] = 2.09 x 10-5 M pH = -Log[2.09 x 10-5] pH = 4.68 2 sig figs due to molarity and Ka

3. Calculate the pH of a 0.20 M diprotic acid with a Ka = 4.7 x 10-7 H2X ⇄ H+ + HX- I 0.20 M 0 0 C x x x E 0.20 - x x x 0 small ka x2 = 4.7 x 10-7 0.20

x = [H+] = 3.066 x 10-4 M pH = -Log[3.066 x 10-4] pH = 3.51 2 sig figs due to molarity and Ka

4. Calculate the pH of a saturated solution of Mg(OH)2. This is a solubility equilibrium- no ICE Mg(OH)2(s) ⇄ Mg2+ + 2OH- s s 2s Ksp = [Mg2+]][OH-]2 = 5.6 x 10-12 [s][2s]2 = 5.6 x 10-12 4s3 = 5.6 x 10-12 s = 1.119 x 10-4 M

2s = [OH-] = 2.237 x 10-4 M pOH = 3.65 pH = 10.35