Ka and Kb Calculations

For Weak Acid Reactions: HA + H 2 O  H 3 O + + A - K a = [H 3 O + ][A - ] K a < 1 [HA]

For Weak Base Reactions: B + H 2 O  HB + + OH - K b = [HB + ][OH - ] K b < 1 [B]

Notice that K a and K b expressions look very similar. The difference is that a base produces the hydroxide ion in solution, while the acid produces the hydronium ion in solution.

Another note on this point: H + and H 3 O + are both equivalent terms here. Often water is left completely out of the equation since it does not appear in the equilibrium. This has become an accepted practice. (*However, water is very important in causing the acid to dissociate.)

H 2 O(l) + H 2 O(l) H 3 O + (aq) + OH - (aq) K eq [H 2 O] 2 = K w = [H 3 O + ][OH - ] K w = 1.0 x K w = K a x K b (Another useful equation) Knowing this value allows us to calculate the OH - and H + concentration for various situation s.

[OH - ] = [H + ] : solution is neutral (in pure water, each of these is 1.0 x ) [OH - ] > [H + ] : solution is basic [OH - ] < [H + ] : solution is acidic

K w = [H + ] [OH - ] = 1.0 X M Calculate [H + ] or [OH - ] as required for each of the following solutions at 25°C, and state whether the solution is neutral, acidic, or basic. a. 1.0 X M OH - b. 1.0 X M OH - c M H +