Acids and Bases Notes

Acids & Bases

General Properties of Acids & Bases

Many common substances in our daily lives are acids and bases.
Examples of acids: Oranges, lemons, vinegar, and stomach acids.
Examples of bases: Antacid tablets and ammonia cleaning solutions.

General Properties of Acids:

Sour taste
Change color of litmus from blue to red
React with metals to produce $H_2$ gas
React with bases to produce salt & water

General Properties of Bases:

Bitter taste
Change color of litmus from red to blue
Slippery, soapy feeling
React with acids to produce salt & water

Arrhenius Acids & Bases

Formulated by Swedish chemist Svante Arrhenius in 1884.

Arrhenius Acids:

Substances that produce hydronium ions ( $H_3O^+$ ) in aqueous solution.
Example: $HCl (g) + H2O (l) \rightleftharpoons H3O^+ (aq) + Cl^- (aq)$
Commonly written as: $HCl (g) \rightleftharpoons H^+ (aq) + Cl^- (aq)$

Arrhenius Bases:

Substances that produce hydroxide ions ( $OH^-$ ) in aqueous solution.
Example: $NaOH (s) \rightleftharpoons Na^+ (aq) + OH^- (aq)$
Another example: $NH3 (aq) + H2O (l) \rightleftharpoons NH_4^+ (aq) + OH^- (aq)$

Brønsted-Lowry Acids & Bases

A broader definition developed by Brønsted and Lowry in the early 20th century, not limited to aqueous solutions.

Brønsted-Lowry Acids:

Proton donors.

Brønsted-Lowry Bases:

Proton acceptors.
Example: $HCl (g) + H2O (l) \rightarrow H3O^+ (aq) + Cl^- (aq)$
- Acid: $HCl$
- Base: $H_2O$
Example: $NH3 (aq) + H2O (l) \rightarrow NH_4^+ (aq) + OH^- (aq)$
- Base: $NH_3$
- Acid: $H_2O$
A substance that can act as both a Brønsted-Lowry acid and base is called amphiprotic (e.g., water).

Conjugate Acid-Base Pairs

Any pair of molecules or ions that can be inter-converted by the transfer of a proton.
Example: $HCl (g) + H2O (l) \rightarrow H3O^+ (aq) + Cl^- (aq)$
- Acid: $HCl$
- Base: $H_2O$
- Conjugate acid: $H_3O^+$
- Conjugate base: $Cl^-$
Example: $NH3 (aq) + H2O (l) \rightarrow NH_4^+ (aq) + OH^- (aq)$
- Base: $NH_3$
- Acid: $H_2O$
- Conjugate acid: $NH_4^+$
- Conjugate base: $OH^-$

Examples of Conjugate Acid-Base Pairs

$H_2O + Cl^- \rightleftharpoons HCl + OH^-$
- Acid: $H_2O$
- Base: $Cl^-$
- Conjugate acid: $HCl$
- Conjugate base: $OH^-$
$C6H5OH + C2H5O^- \rightleftharpoons C6H5O^- + C2H5OH$
- Acid: $C6H5OH$
- Base: $C2H5O^-$
- Conjugate acid: $C2H5OH$
- Conjugate base: $C6H5O^-$

Conjugate Acid Formulas

$HS^- + H^+ \rightarrow H_2S$
$NH3 + H^+ \rightarrow NH4^+$
$CO3^{2-} + H^+ \rightarrow HCO3^-$

Conjugate Base Formulas

$HI - H^+ \rightarrow I^-$
$CH3OH - H^+ \rightarrow CH3O^-$
$HNO3 - H^+ \rightarrow NO3^-$

Acid & Base Strength

Strong acids and bases ionize completely in water and are strong electrolytes.
Weak acids and bases ionize partially in water and are weak electrolytes.
The strength of acids and bases, according to the Arrhenius definition, is based on the amount of their ionization in water.
Illustrative example:
- Strong acid: 1M $HA \rightarrow$ 1M $H_3O^+$ + 1M $A^-$ (100% ionization)
- Weak acid: 1M $HA \rightarrow$ ~0.01M $H_3O^+$ + ~0.01M $A^-$ (~1% ionization)

Common Acids

Strong Acids:
- $HCl$ (Hydrochloric acid)
- $HBr$ (Hydrobromic acid)
- $HI$ (Hydroiodic acid)
- $HNO_3$ (Nitric acid)
- $H2SO4$ (Sulfuric acid)
Weak Acids:
- $HC2H3O_2$ (Acetic acid)
- $H2CO3$ (Carbonic acid)
- $H3PO4$ (Phosphoric acid)
- $HF$ (Hydrofluoric acid)
- $HCN$ (Hydrocyanic acid)
- $H_2S$ (Hydrosulfuric acid)

Common Bases

Strong Bases:
- $LiOH$ (Lithium hydroxide)
- $NaOH$ (Sodium hydroxide)
- $Ca(OH)_2$ (Calcium hydroxide)
- $KOH$ (Potassium hydroxide)
- $Ba(OH)_2$ (Barium hydroxide)
Weak Bases:
- $NH_3$ (Ammonia)
- $CO(NH2)2$ (Urea)

Comparison of Acids & Bases

Characteristic	Acids	Bases
Reaction: Arrhenius	Produce $H^+$	Produce $OH^-$
Reaction: Brønsted-Lowry	Donate $H^+$	Accept $H^+$
Electrolytes	Yes	Yes
Taste	Sour	Bitter, chalky
Feel	May sting	Slippery
Litmus	Red	Blue
Phenolphthalein	Colorless	Pink
Neutralization	Neutralize bases	Neutralize acids

Ionization of Water

Water can act both as an acid and a base (amphiprotic).
In pure water, one water molecule donates a proton to another.
$H2O + H2O \rightleftharpoons H_3O^+ + OH^-$
- Acid: $H_2O$
- Base: $H_2O$
- Conjugate acid: $H_3O^+$
- Conjugate base: $OH^-$
In pure water, the transfer of protons produces equal numbers of hydronium and hydroxide ions.
$[H_3O^+] = [OH^-] = 1.0 x 10^{-7} M$
The ion-product constant ( $K_w$ ) is formed by multiplying the concentrations of hydronium and hydroxide ions.
$Kw = [H3O^+][OH^-] = [1.0 x 10^{-7}][1.0 x 10^{-7}] = 1.0 x 10^{-14}$
All aqueous solutions have $H_3O^+$ and $OH^-$ ions.
An increase in the concentration of one ion will cause a decrease in the other due to equilibrium shift.

Acidic & Basic Solutions

Neutral solution: $[H_3O^+] = [OH^-]$
Acidic solution: [H_3O^+] > [OH^-]
- Example: If $[H_3O^+] = 1.0 x 10^{-4} M$ , then $[OH^-] = 1.0 x 10^{-10} M$
Basic solution: [OH^-] > [H_3O^+]
- Example: If $[OH^-] = 1.0 x 10^{-6} M$ , then $[H_3O^+] = 1.0 x 10^{-8} M$

Calculations

Example 1: Calculate $[OH^-]$ in a solution with $[H_3O^+] = 2.3 x 10^{-4} M$ . Classify as acid or basic.
- $[OH^-] = \frac{Kw}{[H3O^+]} = \frac{1.0 x 10^{-14}}{2.3 x 10^{-4}} = 4.3 x 10^{-11} M$
- Acidic, since [H_3O^+] > 1.0 x 10^{-7} M and [OH^-] < 1.0 x 10^{-7} M
Example 2: Calculate $[H_3O^+]$ in a solution with $[OH^-] = 3.8 x 10^{-6} M$ . Classify as acid or basic.
- $[H3O^+] = \frac{Kw}{[OH^-]} = \frac{1.0 x 10^{-14}}{3.8 x 10^{-6}} = 2.6 x 10^{-9} M$
- Basic, since [OH^-] > 1.0 x 10^{-7} M and [H_3O^+] < 1.0 x 10^{-7} M
Example 3: Calculate $[OH^-]$ in a solution with $[H_3O^+] = 5.8 x 10^{-8} M$ . Classify as acid or basic.
- $[OH^-] = \frac{Kw}{[H3O^+]} = \frac{1.0 x 10^{-14}}{5.8 x 10^{-8}} = 1.7 x 10^{-7} M$
- Basic, since [H_3O^+] < 1.0 x 10^{-7} M and [OH^-] > 1.0 x 10^{-7} M
Example 4: Calculate $[H_3O^+]$ in a solution with $[OH^-] = 1.3 x 10^{-2} M$ . Classify as acid or basic.
- $[H3O^+] = \frac{Kw}{[OH^-]} = \frac{1.0 x 10^{-14}}{1.3 x 10^{-2}} = 7.7 x 10^{-13} M$
- Basic, since [OH^-] > 1.0 x 10^{-7} M and [H_3O^+] < 1.0 x 10^{-7} M

pH Scale

The acidity of a solution is commonly measured on a pH scale.
The pH scale ranges from 0-14.
- Acidic solutions: pH < 7
- Basic solutions: pH > 7
$pH = -log[H_3O^+]$

pH Scale Classifications

Acidic solutions: pH < 7, H_3O^+ > 1 x 10^{-7} M
Neutral solutions: pH = 7, $H_3O^+ = 1 x 10^{-7} M$
Basic solutions: pH > 7, H_3O^+ < 1 x 10^{-7} M

pH Calculations

The number of decimal places in a logarithm is equal to the number of significant figures in the measurement.
Example 1: The $[H_3O^+]$ of a liquid detergent is $1.4 x 10^{-9} M$ . Calculate its pH.
- $pH = -log[H_3O^+] = -log[1.4 x 10^{-9}] = -(-8.85) = 8.85$
- Solution is basic.
Example 2: The pH of black coffee is 5.3. Calculate its $[H_3O^+]$ .
- $[H_3O^+] = antilog(-pH) = 10^{-pH} = 10^{-5.3} = 5 x 10^{-6} M$
- Solution is acidic.
Example 3: The $[H_3O^+]$ of a solution is $3.5 x 10^{-3} M$ . Calculate its pH.
- $pH = -log[H_3O^+] = -log[3.5 x 10^{-3}] = -(-2.46) = 2.46$
- Solution is acidic.
Example 4: The pH of tomato juice is 4.1. Calculate its $[H_3O^+]$ .
- $[H_3O^+] = antilog(-pH) = 10^{-pH} = 10^{-4.1} = 8 x 10^{-5} M$
- Solution is acidic.
Example 5: The $[OH^-]$ of a cleaning solution is $1.0 x 10^{-5} M$ . What is the pH of this solution?
- $[H3O^+] = \frac{Kw}{[OH^-]} = \frac{1.0 x 10^{-14}}{1.0 x 10^{-5}} = 1.0 x 10^{-9} M$
- $pH = -log[H_3O^+] = -log(1.0 x 10^{-9}) = 9.00$
- Solution is basic.
Example 6: The pH of a solution is 11.50. Calculate the $[H_3O^+]$ for this solution.
- $[H_3O^+] = antilog(-pH) = 10^{-pH} = 10^{-11.50} = 3.2 x 10^{-12} M$
- Solution is basic.

General Properties of Acids & Bases

Acids: Sour taste, turn litmus red, react with metals to produce $H_2$ , and neutralize bases.
Bases: Bitter taste, turn litmus blue, slippery feel, and neutralize acids.

Arrhenius Acids & Bases

Arrhenius Acids: Produce hydronium ions ( $H_3O^+$ ) in water.
Arrhenius Bases: Produce hydroxide ions ( $OH^-$ ) in water.

Brønsted-Lowry Acids & Bases

Brønsted-Lowry Acids: Proton donors.
Brønsted-Lowry Bases: Proton acceptors.
Amphiprotic: Substances that can act as both acids and bases (e.g., water).

Conjugate Acid-Base Pairs

Molecules or ions inter-converted by proton transfer.

Acid & Base Strength

Strong acids/bases ionize completely; weak acids/bases ionize partially.

Common Acids

Strong Acids: $HCl$ , $HBr$ , $HI$ , $HNO3$ , $H2SO_4$
Weak Acids: $HC2H3O2$ , $H2CO3$ , $H3PO4$ , $HF$ , $HCN$ , $H2S$

Common Bases

Strong Bases: $LiOH$ , $NaOH$ , $Ca(OH)2$ , $KOH$ , $Ba(OH)2$
Weak Bases: $NH3$ , $CO(NH2)_2$

Comparison of Acids & Bases

Characteristic	Acids	Bases
Reaction: Arrhenius	Produce $H^+$	Produce $OH^-$
Reaction: Brønsted-Lowry	Donate $H^+$	Accept $H^+$
Taste	Sour	Bitter, chalky
Feel	May sting	Slippery
Litmus	Red	Blue
Phenolphthalein	Colorless	Pink
Neutralization	Neutralize bases	Neutralize acids

Ionization of Water

Water is amphiprotic: $H2O + H2O \rightleftharpoons H_3O^+ + OH^-$
$[H_3O^+] = [OH^-] = 1.0 x 10^{-7} M$
$Kw = [H3O^+][OH^-] = 1.0 x 10^{-14}$

Acidic & Basic Solutions

Neutral: $[H_3O^+] = [OH^-]$
Acidic: [H_3O^+] > [OH^-]
Basic: [OH^-] > [H_3O^+]

pH Scale

Measures acidity: 0-14 (Acidic < 7, Basic > 7)
$pH = -log[H_3O^+]$

pH Scale Classifications

Acidic: pH < 7, H_3O^+ > 1 x 10^{-7} M
Neutral: pH = 7, $H_3O^+ = 1 x 10^{-7} M$
Basic: pH > 7, H_3O^+ < 1 x 10^{-7} M