Kw & Strong Bases

01Kw & Strong Bases

Ionic product of water

This section covers the equilibrium in water and the ionic product expression Kw.

Dissociation of water

Water dissociates only slightly, establishing an equilibrium that produces hydrogen and hydroxide ions.

HX2O(l)HX+(aq)+OHX(aq)\ce{H2O(l) <=> H+(aq) + OH-(aq)}

An equilibrium constant can be written for this process:

Kc=[HX+][OHX][HX2O]K_c=\frac{[\ce{H+}][\ce{OH-}]}{[\ce{H2O}]}

The concentration of liquid water is effectively constant, so it is incorporated into a new constant called the ionic product of water, KwK_w.

Kw=[HX+][OHX]K_w=[\ce{H+}][\ce{OH-}]

At 298 K298\ \mathrm{K}:

Kw=1.00×1014 mol2dm6K_w=1.00\times10^{-14}\ \mathrm{mol^2\,dm^{-6}}

The KwK_w expression can be rearranged to calculate either ion concentration when the other is known:

Finding [HX+][\ce{H+}]

[HX+]=Kw[OHX][\ce{H+}]=\frac{K_w}{[\ce{OH-}]}

Finding [OHX][\ce{OH-}]

[OHX]=Kw[HX+][\ce{OH-}]=\frac{K_w}{[\ce{H+}]}

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