Consider the Ka expression marked [1]:
|
| [H+] [A¯]
|
| Ka =
| ––––––––
|
|
| [HA]
|
Divide by [H+]:
| [A¯]
|
| Ka
|
| –––––
| =
| ––––
|
| [HA]
|
| [H+]
|
Flip:
| [HA]
|
| [H+]
|
| –––––
| =
| ––––
|
| [A¯]
|
| Ka
|
|
| Consider the Kb expression marked [2]:
|
| [B+] [OH¯]
|
| Kb =
| –––––––––
|
|
| [BOH]
|
Divide by [OH¯]:
| [B+]
|
| Kb
|
| –––––
| =
| –––––
|
| [BOH]
|
| [OH¯]
|
Flip:
| [BOH]
|
| [OH¯]
|
| –––––
| =
| –––––
|
| [B+]
|
| Kb
|
|
| Consider [3] in a slightly modified way:
|
| [HA]
|
| [BOH]
|
| Kh =
| –––––
| x
| ––––––
|
|
| [A¯]
|
| [B+]
|
Substitute:
|
| [H+]
|
| [OH¯]
|
| Kh =
| –––––
| x
| ––––––
|
|
| Ka
|
| Kb
|
Since Kw = [H+] [OH¯], we have:
|