DAT Organic Chemistry: pKa and the Acidity Scale

DAT High-Yield Concept

Logarithmic Scale: $pK_a = -\log K_a$ . A smaller or negative $pK_a$ indicates a stronger acid. Each 1-unit decrease in $pK_a$ represents a 10-fold increase in acid strength.
Conjugate Relationship: For any acid-base conjugate pair in water at $\pu{25 degC}$ , $pK_a + pK_b = 14$ . Stronger acids (lower $pK_a$ ) form weaker conjugate bases (higher $pK_b$ ).
Equilibrium Direction: Acid-base equilibria always favor the formation of the weaker acid (the species with the higher $pK_a$ ) and weaker base.
Core Benchmarks: Rapid DAT problem solving requires committing key benchmark $pK_a$ values to memory (mineral acids < 0, carboxylic acids ~4–5, phenols ~10, alcohols ~15–17, alkynes ~25, amines ~35, alkanes ~50).

Acid Dissociation Constant ( $K_a$ ) and the $pK_a$ Scale

Quantitative acid strength is governed by the acid dissociation constant, $K_a$ . For a neutral acid $\ce{HA}$ dissociating in water:

\ce{HA + H2O <=> A^- + H3O^+}

K_a = \frac{[\ce{A^-}][\ce{H3O^+}]}{[\ce{HA}]}

Because equilibrium constants range over many orders of magnitude, organic chemists use the logarithmic scale:

pK_a = -\log_{10} K_a

Key Concept: Inverse Relationship
Because of the negative logarithm, a larger

K_a

yields a smaller (or more negative)

pK_a

. Stronger acids dissociate more completely, giving lower

pK_a

values. Weak acids hold their protons tightly, giving higher

pK_a

values.

Worked Example: Evaluating Acid Strength from $K_a$

Problem: Acetic acid ( $\ce{CH3COOH}$ ) has $K_a = \pu{1.8 x 10^{-5}}$ . Calculate its $pK_a$ and compare its strength to hydrocyanic acid ( $\ce{HCN}$ , $pK_a = 9.2$ ).

Reasoning: Apply the logarithmic equation $pK_a = -\log(K_a)$ : $pK_a = -\log(\pu{1.8 x 10^{-5}}) = 5 - \log(1.8) \approx 4.74$ Comparing $pK_a$ values: $\ce{CH3COOH}$ ( $pK_a = 4.74$ ) < $\ce{HCN}$ ( $pK_a = 9.2$ ).

Answer: Acetic acid has a $pK_a$ of 4.74 and is a significantly stronger acid than hydrocyanic acid (by over 4 orders of magnitude).

DAT Exam Trap: Do not confuse the magnitude of $K_a$ with $pK_a$ . A larger exponent in $K_a$ means a smaller $pK_a$ value and a stronger acid.

Base Dissociation Constant ( $K_b$ ) and $pK_b$ Relationship

Base strength is measured by the equilibrium constant $K_b$ for proton abstraction from water (covered alongside Brønsted-Lowry concepts in dedicated acid-base lessons):

\ce{B + H2O <=> BH^+ + OH^-}

K_b = \frac{[\ce{BH^+}][\ce{OH^-}]}{[\ce{B}]}

pK_b = -\log_{10} K_b

In aqueous solution at $\pu{25 degC}$ , the self-ionization constant of water links conjugate acid-base pairs:

K_a \cdot K_b = K_w = 1.0 \times 10^{-14}

pK_a + pK_b = 14

Worked Example: Calculating Conjugate Base Basicity

Problem: Phenol ( $\ce{C6H5OH}$ ) has a $pK_a$ of $\approx 10.0$ . Calculate the $pK_b$ of the phenoxide ion ( $\ce{C6H5O^-}$ ) and compare its base strength to the acetate ion ( $\ce{CH3COO^-}$ , conjugate base of acetic acid with $pK_a = 4.74$ ).

Reasoning: For phenoxide: $pK_b(\ce{C6H5O^-}) = 14 - pK_a(\ce{C6H5OH}) = 14 - 10.0 = 4.0$ . For acetate: $pK_b(\ce{CH3COO^-}) = 14 - pK_a(\ce{CH3COOH}) = 14 - 4.74 = 9.26$ . A smaller $pK_b$ indicates a stronger base: $pK_b(\ce{C6H5O^-})$ < $pK_b(\ce{CH3COO^-})$ .

Answer: Phenoxide ( $pK_b = 4.0$ ) is a stronger base than acetate ( $pK_b = 9.26$ ) because its conjugate acid (phenol) is weaker than acetic acid.

DAT Exam Trap: The identity $pK_a + pK_b = 14$ applies only between an acid and its own conjugate base. Never combine the $pK_a$ of one compound with the $pK_b$ of an unrelated base.

Benchmark $pK_a$ Values for Common Functional Groups

DAT questions routinely require ranking acidities or predicting reaction viability using organic chemical structure benchmarks.

The pKa numbers worth memorizing, on one ladder — pKa is a logarithmic scale, so each rung down the ladder is another factor of ten in acid strength: acetic acid is not twice as acidic as ethanol but about ten billion times. Notice how tightly water and a simple alcohol sit together near 16 - for DAT purposes they are interchangeable - while the jump from a terminal alkyne at 25 to an alkane at 50 spans twenty-five orders of magnitude. Anything above about 30 is not an acid in any practical sense; it is a hydrocarbon that only the harshest bases can touch.

Functional Group / Species	Representative Formula	Approximate $pK_a$	Relative Strength
Strong Mineral Acids	$\ce{HCl}$ , $\ce{H2SO4}$	< 0 (-7 to -3)	Very Strong Acid
Hydronium Ion	$\ce{H3O^+}$	-1.7	Strong Acid
Carboxylic Acids	$\ce{RCOOH}$	4 – 5	Moderate Acid
Pyridinium / Protonated Aniline	$\ce{C5H5NH^+}$ / $\ce{C6H5NH3^+}$	5.0	Moderate Acid
Phenols	$\ce{ArOH}$	10.0	Weak Acid
Ammonium Ions (Aliphatic)	$\ce{RNH3^+}$	9 – 11	Weak Acid
Alcohols & Water	$\ce{ROH}$ , $\ce{H2O}$	15 – 17	Very Weak Acid
$\alpha$ -Protons (Ketones/Esters)	$\ce{RCOCH3}$	19 – 20	Extremely Weak Acid
Terminal Alkynes	$\ce{RC#CH}$	25	Extremely Weak Acid
Amines (Neutral)	$\ce{RNH2}$	35 – 38	Negligible Acid
Alkanes	$\ce{RH}$	50	Non-acidic

pKa and the Acidity Scale

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