Acids and Bases – Formula Sheet:
Arrhenius Definition:
• Acids produce H+ ions in solutions.
• Bases produce OH- ions in solutions.
𝑝𝐻 = − log[𝐻 + ]
𝑝𝑂𝐻 = − log[𝑂𝐻 − ]
𝑝𝐻 + 𝑝𝑂𝐻 = 14
Bronsted-Lowry Definition:
• Acids are proton donors.
• Bases are proton acceptors.
[𝐻 + ] = 10−𝑝𝐻
Lewis Definition:
• Acids are electron pair acceptors.
• Bases are electron pair donors.
Strong Acids:
HCl / HBr / HI / HNO3 / HClO4 / H2SO4
[𝑂𝐻 − ] = 10−𝑝𝑂𝐻
[𝐻 + ][𝑂𝐻− ] = 1 𝑥 10−14
[𝐻 + ] = [𝐻3 𝑂+ ]
Autoionization of Water:
𝐻2 𝑂(𝑙) + 𝐻2 𝑂(𝑙) → 𝐻3 𝑂+ (𝑎𝑞) + 𝑂𝐻 − (𝑎𝑞)
Weak Acids:
HF / HNO2 / HClO / HCN / HC2H3O2
Strong Bases: NaOH / KOH
Acid-Base Equations: (0.1 M HCl or 0.15M KOH)
𝑲𝒘 = [𝐻 + ][𝑂𝐻 − ]
Weak Bases: NH3
pH of a Weak Base: (0.25 M NH3)
𝑲𝒘 = 1 𝑥 10−14 𝑎𝑡 25 ℃
pH of a Weak Acid: (0.5M HC2H3O2)
𝐵(𝑎𝑞) + 𝐻2 𝑂(𝑙) → 𝐻𝐵 + (𝑎𝑞) + 𝑂𝐻 − (𝑎𝑞)
𝐻𝐴(𝑎𝑞) + 𝐻2 𝑂(𝑙) → 𝐻3 𝑂+ (𝑎𝑞) + 𝐴− (𝑎𝑞)
[𝐻𝐵 + ] [𝑂𝐻− ]
𝑲𝒃 =
[𝐵]
[𝐻3 𝑂+ ] [𝐴− ]
𝑲𝒂 =
[𝐻𝐴]
If 𝑲𝒃 < 1 x 10-4, then → [𝑂𝐻 − ] ≈ √[𝐵] ∙ 𝐾𝑏
𝑝𝑂𝐻 = − log[𝑂𝐻 − ]
𝑝𝐻 =
𝑝𝐻 = 14 − 𝑝𝑂𝐻
1
(14 + 𝑝𝐾𝑎 + log[𝐵])
2
If Ka < 1 x 10-4, then → [𝐻 + ] ≈ √[𝐻𝐴] ∙ 𝐾𝑎
𝑝𝐻 = − log[𝐻 + ]
𝑝𝐻 =
1
(𝑝𝐾𝑎 − log[𝐻𝐴])
2
Percent Ionization for Acids:
Acidic Ions:
𝑁𝐻4 +
𝐴𝑙 3+
𝐹𝑒 3+
𝐶𝑢2+
Neutral Ions:
𝐶𝑙 −
𝐵𝑟 −
𝐼−
𝑁𝑂3 −
𝐶𝑙𝑂4 −
𝐻𝑆𝑂4 −
Strong Base Ions:
𝑂𝐻 −
www.Video-Tutor.net
Weak Basic Ions:
𝐹−
𝐶𝑁 −
𝐶2 𝐻3 𝑂2 −
𝑁𝑂2 −
𝐶𝑙𝑂−
𝐶𝑂3 2−
𝑂2−
𝐻−
𝑁𝐻2 −
% 𝐼𝑜𝑛𝑖𝑧𝑎𝑡𝑖𝑜𝑛 =
[𝐻 + ]
× 100%
[𝐻𝐴]
Percent Ionization for Bases:
% 𝐼𝑜𝑛𝑖𝑧𝑎𝑡𝑖𝑜𝑛 =
[𝑂𝐻 − ]
× 100%
[𝐵]
Acid-Base Dissociation Constant Equations:
Acid:
𝐻𝑁𝑂2
𝐻𝐹
𝐻𝐶2 𝐻3 𝑂2
𝐻𝐶𝑙𝑂
𝐻2 𝑃𝑂4 −
𝑁𝐻4 +
𝐻𝐶𝑁
Ka Value:
4.0 × 10−4
7.2 × 10−4
1.8 × 10−5
3.5 × 10−8
6.2 × 10−8
5.6 × 10−10
6.2 × 10−10
𝑝𝐾𝑎 = − log 𝐾𝑎
𝑝𝐾𝑎 + 𝑝𝐾𝑏 = 14
𝐾𝑎 = 10−𝑝𝐾𝑎
pH - Buffer Solution: (0.5M NH4Cl / 0.4M NH3)
Henderson-Hasselbalch Equation:
𝑝𝐻 = 𝑝𝐾𝑎 + log (
Examples of Buffer Solutions:
1. HF / NaF
2. NH4Cl / NH3
3. HC2H3O2 / NaC2H3O2
Note: 𝑝𝐻 = 𝑝𝐾𝑎 𝑤ℎ𝑒𝑛 [𝐴− ] = [𝐻𝐴]
Dissociation Constants for H3PO4
𝐻3 𝑃𝑂4
𝐾𝑎1 = 7.5 × 10−3
𝐻2 𝑃𝑂4 −
𝐾𝑎2 = 6.2 × 10−8
𝐻𝑃𝑂4 2−
𝐾𝑎3 = 4.8 × 10−13
Note: The 1st step is most important for
calculating the pH of the solution:
pH of a Polyprotic Acid: (0.25M H3PO4)
𝐻3 𝐴(𝑎𝑞) + 𝐻2 𝑂(𝑙) → 𝐻3 𝑂+ (𝑎𝑞) + 𝐻2 𝐴− (𝑎𝑞)
[𝐻3 𝑂+ ] [𝐻2 𝐴− ]
𝑲𝒂𝟏 =
[𝐻3 𝐴]
𝑝𝐻 = − log[𝐻3 𝑂+ ]
------------------------------------------------------------𝐻2 𝐴− (𝑎𝑞) + 𝐻2 𝑂(𝑙) → 𝐻3 𝑂 + (𝑎𝑞) + 𝐻𝐴2− (𝑎𝑞)
[𝐻3 𝑂+ ] = [𝐻2 𝐴− ]
𝐾𝑎2 = [𝐻𝐴2− ]
[𝐻3 𝑂+ ] [𝐻𝐴2− ]
𝑲𝒂𝟐 =
[𝐻2 𝐴− ]
Amphoteric Ion Reactions in Water:
pH of an Amphoteric Salt: (0.4M NaH2PO4)
𝐻2 𝐴− (𝑎𝑞) + 𝐻2 𝑂(𝑙) → 𝐻3 𝑂+ (𝑎𝑞) + 𝐻𝐴2− (𝑎𝑞) 𝑲𝒂𝟐
𝐻2 𝐴− (𝑎𝑞) + 𝐻2 𝑂(𝑙) → 𝑂𝐻 − (𝑎𝑞) + 𝐻3 𝐴(𝑎𝑞)
𝑲𝒃𝟑 =
𝑝𝐻 ≈
1
(𝑝𝐾𝑎1 + 𝑝𝐾𝑎2 ) "𝐼𝑠𝑜𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐 𝑃𝑜𝑖𝑛𝑡"
2
𝑲𝒃𝟑
[𝐻3 𝐴] [𝑂𝐻 − ]
[𝐻2 𝐴− ]
[𝐻 + ] ≈ √𝐾𝑎1 ∙ 𝐾𝑎2
[𝐻 + ] = √𝐾𝑎1 ∙ 𝐾𝑎2 ∙
www.Video-Tutor.net
[𝐴− ]
)
[𝐻𝐴]
[𝐴− ]
= 10𝑝𝐻−𝑝𝐾𝑎
[𝐻𝐴]
𝑝𝐻 > 𝑝𝐾𝑎 𝑤ℎ𝑒𝑛 [𝐴− ] > [𝐻𝐴]
𝑝𝐻 < 𝑝𝐾𝑎 𝑤ℎ𝑒𝑛 [𝐴− ] < [𝐻𝐴]
[𝐻3 𝑂+ ] [𝐻𝐴2− ]
[𝐻2 𝐴− ]
𝐾𝑏 = 10−𝑝𝐾𝑏
𝐾𝑎 × 𝐾𝑏 = 1 × 10−14
Note: A buffer solution is made up of a weak acid
and its conjugate weak base. Buffer solutions
resist changes to its pH.
𝑲𝒂𝟐 =
𝑝𝐾𝑏 = − log 𝐾𝑏
𝐾𝑏3 =
𝐾𝑤
𝐾𝑎1
[𝐻3 𝐴]
[𝐻2 𝐴− ]
Standard Form of a Quadratic Equation:
𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0
The Quadratic Formula:
𝐻𝐴(𝑎𝑞) + 𝐻2 𝑂(𝑙) → 𝐻3 𝑂+ (𝑎𝑞) + 𝐴− (𝑎𝑞)
𝑲𝒂
𝐵(𝑎𝑞) + 𝐻2 𝑂(𝑙) → 𝐻𝐵 + (𝑎𝑞) + 𝑂𝐻 − (𝑎𝑞)
𝑲𝒃
𝐻2 𝑂(𝑙) + 𝐻2 𝑂(𝑙) → 𝐻3 𝑂+ (𝑎𝑞) + 𝑂𝐻 − (𝑎𝑞) 𝑲𝒘
−𝑏 ± √𝑏 2 − 4𝑎𝑐
2𝑎
𝑥=
pH of a Weak Acid / Weak Base Salt: (0.2M NH4F)
Dilution Formula:
[𝐻 + ] ≈ √
𝐾𝑎 𝐾𝑤
𝐾𝑏
𝐼𝑓 [𝐵] ≈ [𝐻𝐴]
𝑀1 𝑉1 = 𝑀2 𝑉2
Moles:
[𝐻 + ] = √
𝑛 = 𝑀𝑉
Titration:
Strong Acid – Strong Base
Weak Acid – Strong Base
Weak Base – Strong Acid
pH at Equiv. point
pH = 7
pH > 7
pH < 7
𝐾𝑎 𝐾𝑤 [𝐵] [𝐻𝐵 + ]
∙
∙
𝐾𝑏 [𝐻𝐴] [𝐴− ]
Acid-Base Titrations:
• ICE Tables – Use Molarity
• BCA Tables – Use Moles
At ½ Veq (Equivalence Volume):
𝑝𝐻 = 𝑝𝐾𝑎
𝑎𝑛𝑑
[𝐴− ] = [𝐻𝐴]
Acid-Base Indicators:
Indicator:
Methyl Orange
Methyl Red
Bromthymol Blue
Phenolphthalein
www.Video-Tutor.net
𝑲𝒂
3.4 × 10−4
7.9 × 10−6
1.0 × 10−7
5.0 × 10−10
𝒑𝑲𝒂
3.5
5.1
7.0
9.3
𝑯𝑰𝒏 𝒕𝒐 𝑰𝒏−
𝑹𝒆𝒅 𝑡𝑜 𝒀𝒆𝒍𝒍𝒐𝒘
𝑹𝒆𝒅 𝑡𝑜 𝒀𝒆𝒍𝒍𝒐𝒘
𝒀𝒆𝒍𝒍𝒐𝒘 𝑡𝑜 𝑩𝒍𝒖𝒆
𝐶𝑙𝑒𝑎𝑟 𝑡𝑜 𝑷𝒊𝒏𝒌