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Wize University Chemistry Textbook > Acids and Bases

Acid Base Equations Summary

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Important Relationships:

pH=−log⁡⁡[H3O+] and [H3O+]=10−pHpH=-\log⁡[H_3O^+]\ and\ [H_3O^+]=10^{-pH}

pOH=−log⁡⁡OH−and OH−=10−pOHpOH=-\log⁡OH^-and\ OH^-=10^{-pOH}


2H2O⇌H3O++OH−2H_2 O⇌H_3 O^++OH^-

In pure water, at 25 °C:
[H3O+]=[OH−]=1.0×10−7M[H_3O^+]=[OH^-]=1.0\times10^{-7}M
Kw=[H3O+][OH−]=1.0×10−14 at 25°CK_w=[H_3O^+][OH^-]=1.0\times10^{-14}\ at\ 25°C
pH+pOH=pKw=14.00 at 25°CpH+pOH=pK_w=14.00\ at\ 25°C

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Ka is the acid dissociation constant and is defined as the equilibrium constant for the reaction below:

HA(aq)+H2O(l)⇌A−(aq)+H3O+(aq)HA(aq)+H_2O(l)⇌A^-(aq)+H_3O^+(aq)
Ka=[H3O+][A−][HA]K_a=\cfrac{[H_3 O^+ ][A^- ]}{[HA]}
pKa=−log⁡⁡Ka and Ka=10−pKapK_a=-\log⁡K_a\ and\ K_a=10^{-pK_a}

Strong acids dissociate completely.
HNO3(aq)→H+(aq)+NO3−(aq)HNO_3 (aq)→H^+ (aq)+NO_3^- (aq) (not an equilibrium, Ka is very large)

Weak acids partially dissociate to give H+ or H3O+
CH3COOH(aq)⇌CH3COO−(aq)+H+(aq)CH_3 COOH(aq)⇌CH_3 COO^- (aq)+H^+ (aq) (equilibrium, Ka)
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Kb is the base dissociation constant and is defined as the equilibrium constant for the reaction below:

B(aq)+H2O(l)⇌BH+(aq)+OH−(aq)B(aq)+H_2 O(l)⇌BH^+ (aq)+ OH^- (aq)
Kb=[BH+][OH−][B]K_b=\cfrac{[BH^+ ][OH^- ]}{[B]}
pKb=−log⁡⁡Kb and Kb=10−pKbpK_b=-\log⁡K_b\ and\ K_b=10^{-pK_b}
Strong bases dissociate completely.
LiOH(s)→Li+(aq)+OH−(aq)LiOH(s)→Li^+(aq)+OH^-(aq) (not an equilibrium, Kb is very large)

Weak bases partially dissociate (they accept protons to give OH-, but the reaction is not complete)

CH3NH2(aq)+H2O(l)⇌CH3NH3+(aq)+OH−(aq)CH_3NH_2(aq)+H_2O(l)⇌CH_3NH_3^+(aq)+OH^-(aq)

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For a given conjugate acid-base pair:

HA+H2O⇌A−+H3O+                   KaHA+H_2O⇌A^-+H_3O^+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \color{red}{K_a}
A−+H2O⇌HA+OH−                   Kb‾\underline{A^-+H_2O⇌HA+OH^-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \color{red}{K_b}}
2H2O⇌H3O++OH−                      Kw2H_2 O⇌H_3 O^++OH^- \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \color{red} K_w
Ka×Kb=Kw=1×10−14 and pKa+pKb=pKw=14.00 (at 25°C)K_a×K_b=K_w=1×10^{-14} \ and \ pK_a+pK_b=pK_w=14.00\ (at\ 25 °C)

Acid/Base Important Relationships Cheatsheet