1. Previously in Chem104: the concept of K w the concept of the K w circle p-functions (pH, pK a, pK w ) pH scale P-functions in calcs Today in Chem104: How K a relates to K b and pK a to pK b More ways to use the K w circle Group worksheet on The Most Important Equilibrium on the Planet (Part 1) What I had to use to find logarithms

2. Lauren said: “Cl- is a very weak base because HCl is a strong acid” How did she know that? AH + H 2 OA - + H 3 O+ acid conjugate base conjugate acid Now write the K a expression for AH and the K b expression for A-.

3. K w = 10 -14 Alright, now we’re can understand what Lauren said: We proved K w = K a x K b Use the K w circle! KaKa KbKb

4. KwKw If AH has a larger K a, like 10 -4 then A- must have a smaller K b like 10 -10 KaKa KbKb The stronger the acid (K a large), the weaker the conjugate base, (K b small) Because K w = K a x K b must = 10 -14

5. KwKw KaKa KbKb If A- has a larger K b, like 10 -3 then AH must have a smaller K a like 10 -11 The stronger the base (K b large), the weaker the conjugate acid, (K a small) Because K w = K a x K b must = 10 -14

6. Now do the same with K w = K a x K b = 10 -14 p of K w = p of [K a x K b ] = p of 10 -14 Let’s apply P-Functions We already did this one: K w = [H 3 O+][OH-] = 10 -14  pK w = pH + pOH = 14 -log K w = -log (K a x K b )= -log 10 -14 pK w = pK a + pK b = 14 -log K w = -log K a + ( -log K b ) = -log 10 -14

7. pK w Now apply this equation: pK w = pK a + pK b = 14 to this picture pK a pK b

8. Let’s do some problems !!