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Wize University Chemistry Textbook > Acids and Bases

Acid Base Equations Summary

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Important Relationships:

pH=βˆ’log⁑⁑[H3O+] and [H3O+]=10βˆ’pHpH=-\log⁑[H_3O^+]\ and\ [H_3O^+]=10^{-pH}

pOH=βˆ’log⁑⁑OHβˆ’and OHβˆ’=10βˆ’pOHpOH=-\log⁑OH^-and\ OH^-=10^{-pOH}


2H2Oβ‡ŒH3O++OHβˆ’2H_2 Oβ‡ŒH_3 O^++OH^-

In pure water, at 25 Β°C:
[H3O+]=[OHβˆ’]=1.0Γ—10βˆ’7M[H_3O^+]=[OH^-]=1.0\times10^{-7}M
Kw=[H3O+][OHβˆ’]=1.0Γ—10βˆ’14 at 25Β°CK_w=[H_3O^+][OH^-]=1.0\times10^{-14}\ at\ 25Β°C
pH+pOH=pKw=14.00 at 25Β°CpH+pOH=pK_w=14.00\ at\ 25Β°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)β‡ŒAβˆ’(aq)+H3O+(aq)HA(aq)+H_2O(l)β‡ŒA^-(aq)+H_3O^+(aq)
Ka=[H3O+][Aβˆ’][HA]K_a=\cfrac{[H_3 O^+ ][A^- ]}{[HA]}
pKa=βˆ’log⁑⁑Ka and Ka=10βˆ’pKapK_a=-\log⁑K_a\ and\ K_a=10^{-pK_a}

Strong acids dissociate completely.
HNO3(aq)β†’H+(aq)+NO3βˆ’(aq)HNO_3 (aq)β†’H^+ (aq)+NO_3^- (aq) (not an equilibrium, Ka is very large)

Weak acids partially dissociate to give H+ or H3O+
CH3COOH(aq)β‡ŒCH3COOβˆ’(aq)+H+(aq)CH_3 COOH(aq)β‡ŒCH_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)β‡ŒBH+(aq)+OHβˆ’(aq)B(aq)+H_2 O(l)β‡ŒBH^+ (aq)+ OH^- (aq)
Kb=[BH+][OHβˆ’][B]K_b=\cfrac{[BH^+ ][OH^- ]}{[B]}
pKb=βˆ’log⁑⁑Kb and Kb=10βˆ’pKbpK_b=-\log⁑K_b\ and\ K_b=10^{-pK_b}
Strong bases dissociate completely.
LiOH(s)β†’Li+(aq)+OHβˆ’(aq)LiOH(s)β†’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)β‡ŒCH3NH3+(aq)+OHβˆ’(aq)CH_3NH_2(aq)+H_2O(l)β‡ŒCH_3NH_3^+(aq)+OH^-(aq)

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For a given conjugate acid-base pair:

HA+H2Oβ‡ŒAβˆ’+H3O+                   KaHA+H_2Oβ‡ŒA^-+H_3O^+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \color{red}{K_a}
Aβˆ’+H2Oβ‡ŒHA+OHβˆ’                   Kbβ€Ύ\underline{A^-+H_2Oβ‡ŒHA+OH^-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \color{red}{K_b}}
2H2Oβ‡ŒH3O++OHβˆ’                      Kw2H_2 Oβ‡ŒH_3 O^++OH^- \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \color{red} K_w
KaΓ—Kb=Kw=1Γ—10βˆ’14 and pKa+pKb=pKw=14.00 (at 25Β°C)K_aΓ—K_b=K_w=1Γ—10^{-14} \ and \ pK_a+pK_b=pK_w=14.00\ (at\ 25 Β°C)

Acid/Base Important Relationships Cheatsheet