Calculation of pH for monoprotic acids and bases [PDF]

Calculation of pH for monoprotic acids and bases

Acid/base system Pure water and neutral salts Strong acids

Examples

Calculation of pH / pOH

Conditions

H2O, KCl, NaNO3, CsClO4...

[H+] = [OH–] =

under any conditions

HCl, HNO3, H2SO4 (only the first deprotonation step), HClO4, CF3SO3H NaOH, KOH, RbOH, CsOH...

[H+] = cstrong acid

CH3COOH, HNO2, HCOOH, NH4Cl (NH4+)... any monoprotic acid with a Ka NH3, (CH3)3N, CH3COONa (CH3COO–)... any monoprotic base with a Kb

c weak acid − [H + ] [H ] = K a ⋅ [H + ]

under any conditions

[H+] = K a ⋅ c weak acid

cweak acid >>> Ka

c weak base − [OH − ] [OH ] = K b ⋅ [OH − ]

under any conditions

[OH–] = K b ⋅ c weak base

cweak base >>> Kb

Strong and weak acid in the same solution

[H+] = cstrong acid

cstrong acid >> cweak

Strong and weak base in the same solution

[OH–] = cstrong base

Strong bases

Monoprotic weak acids and acidic salts Monoprotic weak bases and basic salts

Acidic buffers Basic buffers

KW

cstrong acid > 10–6 M

[H + ] = c strong acid +

KW [H + ]

[OH–] = cstrong base

[OH − ] = c strong base +

KW [OH − ]

+

−

under any conditions cstrong base > 10–6 M under any conditions

acid

[H + ] = c strong acid

c − [H + ] + K a ⋅ weak acid + [H ]

under any conditions cstrong base >> cweak base

c weak base − [OH − ] [OH − ] n = Ka ⋅ weak acid ... n weak base

[OH − ] = cstrong base + K b ⋅ CH3COOH + CH3COONa together NH3 + NH4Cl together

c weak acid c weak base c weak base/conjugate base pH = pKa + log c conjugate acid/weak acid [H+] = Ka ⋅

under any conditions

General equations for pH calculations: pH = –log[H+] [H+] = 10–pH

pOH = –log[OH–] [OH–] = 10–pOH

[H+][OH–] = KW in any aqueous solution pH + pOH = pKW = –logKW KaKb = KW for any conjugate acid-base pair pKa + pKb = pKW Some other concepts: The concept of degree of dissociation (α) is used when only a weak acid or base are present in the solution, no other chemicals affecting the pH. number of moles of the dissoc. form Degree of dissociation = total number of moles

Buffer capacity (unit: mol, mol/dm3, dm3 or cm3) is the amount of H+ and OH– ions (i.e. the amount of strong acid and strong base) which should be added to 1 dm3 of buffer solution to change its pH by 1 unit. Calculation of buffer capacity for strong acid (nstrong acid):

[H+]buffer – 1 = Ka ⋅

n weak acid + n strong acid

n weak base − n strong acid

Calculation of buffer capacity for strong base (nstrong base):

[H+]buffer + 1 = Ka ⋅

n weak acid − n strong base

n weak base + n strong base