IB Chemistry Topic 8 & 18: Acids and Bases Comprehensive Study Guide

Brønsted-Lowry Theory of Acids and Bases

• Definition of Brønsted-Lowry Acid: A substance behaves as an acid when it donates a proton to a base. Therefore, a Brønsted-Lowry acid is a proton donor ($H^+$ donor).

• Definition of Brønsted-Lowry Base: A substance behaves as a base when it accepts a proton from an acid. Therefore, a Brønsted-Lowry base is a proton acceptor ($H^+$ acceptor).

• Composition of Acids: Acids are typically a combination of hydrogen ions ($H^+$) and an anion. Examples include Hydrochloric acid ($HCl$), Nitric acid ($HNO_3$), and Ethanoic acid ($HC_2H_3O_2$).

• Composition of Bases: Bases are typically a combination of hydroxide ions ($OH^-$) and metal cations. Examples include Sodium hydroxide ($NaOH$) and Potassium hydroxide ($KOH$).

• Metals and Hydrogen: In some cases, a hydrogen atom located next to a metal signifies a base, such as Sodium hydride ($NaH$).

• Conjugate Acid-Base Pairs: A conjugate pair consists of two species that differ by exactly one single proton ($H^+$).     * The acid in the reaction will become the conjugate base after donating a proton.     * The base in the reaction will become the conjugate acid after accepting a proton.

• Rules for Finding Conjugates:     * To find the conjugate acid of a species, add one $H^+$.     * To find the conjugate base of a species, subtract (take away) one $H^+$.

• Historical Context: Prior to the Brønsted-Lowry theory, acids were primarily distinguished by their taste, specifically described as tasting sour.

Questions & Discussion: Brønsted-Lowry Theory

• Question: Label the conjugate acid-base pairs in the following reaction: $CH_3COOH + H_2O(g) \rightleftharpoons CH_3COO^- + H_3O^+$     * Conjugate pair 1: $CH_3COOH/CH_3COO^-$         * $CH_3COOH$ is the acid because it donates a proton ($H^+$).         * $CH_3COO^-$ is the conjugate base.     * Conjugate pair 2: $H_2O/H_3O^+$         * $H_2O$ is the base because it accepts a proton ($H^+$).         * $H_3O^+$ is the conjugate acid.

Amphiprotic and Amphoteric Species

• Amphiprotic Definition: A chemical species capable of both accepting and donating protons ($H^+$), thus enabling it to act as either a Brønsted-Lowry acid or a Brønsted-Lowry base depending on the reaction environment.

• Water as an Amphiprotic Species: Water ($H_2O$) is amphiprotic because it can donate a proton to form a hydroxide ion ($OH^-$) or accept a proton to form a hydronium ion ($H_3O^+$).

• Amphoteric Definition: A more general term for a species that can act as an acid or a base, including reactions that do not involve proton transfer.

• Relationship between terms: Amphiprotic specifically relates to the Brønsted-Lowry theory (proton transfer). Amphoteric is broader. While all amphiprotic species are amphoteric, not all amphoteric species are amphiprotic.

Questions & Discussion: Amphiprotic Equations

• Question: Write an equation to show hydrogen phosphate ($HPO_4^{2-}$) acting as an acid and a base in water.     * Acting like an Acid: $HPO_4^{2-} + H_2O(g) \rightleftharpoons PO_4^{3-} + H_3O^+$     * Acting like a Base: $HPO_4^{2-} + H_2O(g) \rightleftharpoons H_2PO_4^- + OH^-$

Properties and Reactions of Acids and Bases

• Exothermic Nature: Neutralization reactions are exothermic, meaning they release heat to the surroundings.

• Neutralization: A chemical reaction where an acid and a base react to form a salt and water. The resulting salt and water are neutral solutions (neither acidic nor basic).

• Definition of a Salt: An ionic compound produced during a neutralization reaction.

• Reaction with Hydroxyl Bases:     * General Equation: $\text{Acid} + \text{Base} \rightarrow \text{Salt} + \text{Water}$     * Procedure to find salt formula: Remove the hydrogen from the acid and the hydroxyl group ($OH^-$) from the base to form water ($H_2O$). Join the remaining terms, ensuring the positive ion (cation) is listed first and the charges balance.

• Reaction with Carbonate Bases:     * General Equation: $\text{Acid} + \text{Carbonate Base} \rightarrow \text{Salt} + \text{Water} + CO_2$     * Metal carbonates include $Na_2CO_3$, $MgCO_3$, and $CaCO_3$.

• Reaction with Metals:     * General Equation: $\text{Acid} + \text{Metal} \rightarrow \text{Salt} + H_2$     * Reactive metals include Calcium ($Ca$), Magnesium ($Mg$), Potassium ($K$), and Zinc ($Zn$).     * Unreactive metals include Copper ($Cu$), Silver ($Ag$), and Gold ($Au$).

Questions & Discussion: Reaction Equations

• Question: Write the equation for the reaction between hydrochloric acid ($HCl$) and a solution of sodium hydroxide ($NaOH$).     * Equation: $HCl + NaOH \rightarrow H_2O + NaCl$     * Explanation: Remove $H^+$ from $HCl$ and $OH^-$ from $NaOH$ to form $H_2O$. Join the remaining sodium ($Na^+$) and chloride ($Cl^-$) ions to form the salt.

• Question: Write the equation for the reaction when zinc is added to hydrochloric acid.     * Equation: $2HCl + Zn \rightarrow ZnCl_2 + H_2$

The pH Scale and Self-Ionization of Water

• Self-Ionization of Water: Water exists in equilibrium between $H_2O$ molecules and its ionized forms: $2H_2O \rightleftharpoons H_3O^+ + OH^-$.

• Ionic Product Constant ($K_w$): At $298\,K$, the ionization constant of water is $K_w = [H^+][OH^-] = (1.0 \times 10^{-7}) \times (1.0 \times 10^{-7}) = 1.0 \times 10^{-14}$.

• The "p" Operator: The prefix "p" represents taking the negative logarithm of a value ($p = -\log$).

• pH Formulas:     * $pH = -\log([H^+])$     * $pOH = -\log([OH^-])$     * $pK_w = pH + pOH = 14$     * $[H^+] = 10^{-pH}$     * $[OH^-] = 10^{-pOH}$

• pH Values and Concentration:     * A change of one pH unit represents a 10-fold change in hydrogen ion concentration ($[H^+]$).     * A two-unit change represents a 100-fold change.     * Acidity measures the concentration of hydrogen ions present. pH has no units.

• Classification of Solutions:     * Acidic: pH < 7 and [H^+] > [OH^-].     * Neutral: $pH = 7$ and $[H^+] = [OH^-]$.     * Basic (Alkaline): pH > 7 and [H^+] < [OH^-].

Acid-Base Indicators

• Definition: Weak acids or bases that change color based on the concentration of $H^+$ in a solution. The undissociated and dissociated forms have different colors.

• Types: Available as liquid dyes or dye-infused paper strips (litmus paper).

• Measurement: Values are determined by comparing the result against a standard pH/color key.

• Common Indicators:     * Litmus: Red in acid, Blue in alkali.     * Methyl Orange: Red in acid, Yellow in alkali.     * Phenolphthalein: Colorless in acid, Pink in alkali.

• Selection: For titrations, choose an indicator that changes color ($pK_{in} = pH$) at the steepest part of the titration curve (the equivalence point).

Strong and Weak Acids and Bases

• Strength vs. Concentration: Strength refers to the extent of ionization/dissociation, not the molarity.

• Strong Acids:     * Fully dissociate in solution ($\approx 100\%$).     * Form strong electrolytes.     * Examples: $HCl$, $HNO_3$, $H_2SO_4$.     * Reaction uses a single forward arrow.

• Weak Acids:     * Partially dissociate in solution ( < 5\%).     * Form weak electrolytes.     * Examples: $CH_3COOH$ (ethanoic acid), $H_2CO_3$ (carbonic acid), $Propanoic\,Acid$, $H_3PO_4$ (phosphoric acid).     * Reaction uses a double equilibrium arrow.

• Strong Bases:     * Fully ionize in solution ($\approx 100\%$).     * Examples: $NaOH$, $KOH$, $Ba(OH)_2$.

• Weak Bases:     * Partially ionize in solution ( < 5\%).     * Examples: $NH_3$ (ammonia), $CH_3CH_2NH_2$ (ethylamine).

• Conjugate Strength: A strong acid has a weak conjugate base. A strong base has a weak conjugate acid.

Experimental Determination of Strength

• Conductivity: Strong acids and bases are better conductors because they contain a higher concentration of mobile ions at the same molar concentration. Conductivity is measured using pH meters or conductivity meters.

• pH Measurement: At equal concentrations, a strong acid will have a lower pH than a weak acid, and a strong base will have a higher pH than a weak base.

• Rates of Reaction: Reaction rates depend on $[H^+]$. Stronger acids will react more vigorously with metals and carbonates.

Acid Deposition

• Natural Rain: Naturally acidic with a pH of $5.6$ due to dissolved $CO_2$ (carbonic acid: $H_2CO_3$).

• Acid Deposition Definition: Precipitation with a pH below $5.6$. It is caused by sulfur and nitrogen oxides dissolving in water to form acids.

• Formation of Pollutants:     * Sulfur Oxides ($SO_x$): Formed by natural processes or burning sulfur-containing fuels. Produces Sulfurous acid ($H_2SO_3$) and Sulfuric acid ($H_2SO_4$).     * Nitrogen Oxides ($NO_x$): Produced during combustion in coal, gas, or oil power stations. Produces Nitrous acid ($HNO_2$) and Nitric acid ($HNO_3$).

• Environmental Effects:     * Buildings: Corrodes marble and limestone statues.     * Soil: Leaching of metal ions, harming plant growth.     * Water: Acidification of lakes, poisoning fish, and damaging aquatic ecosystems.     * Human Health: Irritation of mucous membranes and respiratory illnesses such as asthma.

• Mitigation Strategies:     * NOx/SOx Reduction: Use of catalytic converters, improved engine design, and removing sulfur pre-combustion or post-combustion.     * Alternative Energy: Switching to solar or wind power.     * Liming: Adding calcium oxide or calcium hydroxide (lime) to lakes to neutralize acidity and precipitate aluminum.

Lewis Theory of Acids and Bases

• Lewis Acid: An electron pair acceptor (also known as an electrophile).

• Lewis Base: An electron pair donor (also known as a nucleophile).

• Coordinate Covalent Bond: Formed when a Lewis base reacts with a Lewis acid, as both electrons in the shared pair come from the base.

• Relation to Brønsted-Lowry: A Lewis base is also a Brønsted-Lowry base. However, the term Lewis acid is often reserved for species that act as electron acceptors but do not donate $H^+$ions (e.g., transition metal ions acting as Lewis acids with ligands).

Calculations and Dissociation Constants

• Acid Dissociation Constant ($K_a$): For the reaction $HA + H_2O \rightleftharpoons H^+ + A^-$, the expression is $K_a = \frac{[H^+][A^-]}{[HA]}$.

• Base Dissociation Constant ($K_b$): For the reaction $A^- + H_2O \rightleftharpoons OH^- + HA$, the expression is $K_b = \frac{[OH^-][HA]}{[A^-]}$.

• Relationship for Conjugate Pairs:     * $K_a \times K_b = K_w$     * $K_a \times K_b = 10^{-14}$     * $pK_a + pKb = 14$     * $pK_a = -\log(K_a)$     * $pK_b = -\log(K_b)$

pH Curves and Titrations

• Titration: Analytical technique used to determine the concentration of an unknown acid or base by adding a solution of known concentration until a color change or specific pH is reached.

• Equivalence Point: Also called the point of inflection or end point. It is where the amount of base added is stoichiometrically equal to the amount of acid.

• Strong Acid - Strong Base Curve: Initial slow rise; equivalence point resides at exactly $pH = 7$.

• Weak Acid - Strong Base Curve:     * Starts with a buffer region where the slope levels out.     * Buffer Region: Small additions of acid or base result in little pH change.     * Half-equivalence Point: Occurs halfway through the buffer region where $[H^+] = K_a$, therefore $pH = pK_a$.     * Equivalence point is pH > 7.

• Strong Acid - Weak Base Curve: Equivalence point is pH < 7.

• Indicator Equilibrium: Indicators follow the equilibrium $HIn \rightleftharpoons H^+ + In^-$. Color change occurs when $[HIn] = [In^-]$, which implies $K_{in} = [H^+]$ and $pK_{in} = pH$.

• Indicator Data:     * Methyl Orange: $pK_{in} = 3.7$, range $3.1-4.4$. Used for strong acids.     * Phenolphthalein: $pK_{in} = 9.3$, range $8.2-10.0$. Used for strong bases.     * Bromophenol Blue: $pK_{in} = 9.3$, range $3.0-4.6$.

Salt Hydrolysis and Buffers

• Salt Hydrolysis: The process where a salt reacts with water to reconstruct the parent acid and base: $\text{Salt} + \text{Water} \rightarrow \text{Acid} + \text{Base}$.

• Predicting Salt pH:     * Strong Acid + Strong Base = Neutral Salt.     * Strong Acid + Weak Base = Acidic Salt.     * Weak Acid + Strong Base = Basic Salt.

• Buffer Preparation:     1. Mixing a weak acid/base with a salt containing its conjugate (e.g., ethanoic acid and sodium ethanoate).     2. Partial neutralization of a weak acid/base with a strong acid/base.