Acids and Bases — Hard Practice Quiz

A Chemistry cheat sheet for Acids and Bases — every key formula with its symbols defined — plus a hard-level practice quiz to test recall.

Formulas & key concepts

Conjugate Acid-Base Pairs: Proton transfer between acid HX and water.

$$HX(aq) + H_2O(l) \rightleftharpoons X^-(aq) + H_3O^+(aq)$$

Proton Transfer in Water: If \(H_2O\) is a stronger base than \(X^-\), equilibrium favors products.

$$HX(aq) + H_2O(l) \rightleftharpoons X^-(aq) + H_3O^+(aq)$$

Acid Dissociation Constant: Equilibrium constant for weak acid ionization.

$$K_a = \frac{[H_3O^+][A^-]}{[HA]}$$ or $$K_a = \frac{[H^+][A^-]}{[HA]}$$

Where: \(K_a\) = acid dissociation constant

pH Definition: Negative logarithm of hydrogen ion concentration.

$$pH = -\log[H^+]$$

pOH Definition: Negative logarithm of hydroxide ion concentration.

$$pOH = -\log[OH^-]$$

pH-pOH Relationship: Sum of pH and pOH equals 14 at 25°C.

$$pH + pOH = 14.00$$

H+ from pH: Calculate hydrogen ion concentration from pH.

$$[H^+] = 10^{-pH}$$

OH- from pOH: Calculate hydroxide ion concentration from pOH.

$$[OH^-] = 10^{-pOH}$$

Percent Ionization: Fraction of acid molecules that donate protons.

$$\text{Percent ionization} = \frac{[H^+]_{\text{equilibrium}}}{[HA]_{\text{initial}}} \times 100\%$$

Weak Acid Ionization: General equation for weak acid dissociation.

$$HA(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq) + A^-(aq)$$

Weak Acid Ionization Simplified: Simplified form without explicit water.

$$HA(aq) \rightleftharpoons H^+(aq) + A^-(aq)$$

Weak Acid Ka Expression: Equilibrium constant expression for weak acid.

$$K_a = \frac{[H_3O^+][A^-]}{[HA]}$$ or $$K_a = \frac{[H^+][A^-]}{[HA]}$$

Weak Base Ionization: Base accepts proton from water.

$$B(aq) + H_2O(l) \rightleftharpoons HB^+(aq) + OH^-(aq)$$

Base Dissociation Constant: Equilibrium constant for weak base ionization.

$$K_b = \frac{[HB^+][OH^-]}{[B]}$$

Where: \(K_b\) = base dissociation constant

Ka-Kb Relationship: Product of acid and conjugate base constants equals \(K_w\) at 25°C.

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

pKa-pKb Relationship: Sum of pKa and pKb of conjugate pair equals 14 at 25°C.

$$pK_a + pK_b = pK_w = 14.00$$

Conjugate Base Reaction: Weak conjugate base reacts with water to produce weak acid and hydroxide.

$$X^-(aq) + H_2O(l) \rightleftharpoons HX(aq) + OH^-(aq)$$

<strong>Relative Strengths of Conjugate Acid-Base Pairs</strong><br> <table style="width:100%; border-collapse: collapse; font-size: 0.85em; margin-top: 5px;"> <tr style="border-bottom: 1px solid #ccc;"> <th style="text-align: left; padding: 3px;">Acid</th> <th style="text-align: left; padding: 3px;">Base</th> </tr> <tr><td>HCl (strong)</td><td>Cl⁻ (negligible)</td></tr> <tr><td>H₂SO₄ (strong)</td><td>HSO₄⁻ (weak)</td></tr> <tr><td>HNO₃ (strong)</td><td>NO₃⁻ (negligible)</td></tr> <tr><td>H₃O⁺</td><td>H₂O</td></tr> <tr><td>HF (weak)</td><td>F⁻ (weak)</td></tr> <tr><td>CH₃COOH (weak)</td><td>CH₃COO⁻ (weak)</td></tr> <tr><td>NH₄⁺ (weak)</td><td>NH₃ (weak)</td></tr> <tr><td>H₂O</td><td>OH⁻ (strong)</td></tr> </table>

<strong>Polyprotic Acids at 25°C</strong><br> <table style="width:100%; border-collapse: collapse; font-size: 0.85em; margin-top: 5px;"> <tr style="border-bottom: 1px solid #ccc;"> <th style="text-align: left; padding: 3px;">Acid</th> <th style="text-align: left; padding: 3px;">Ka₁</th> <th style="text-align: left; padding: 3px;">Ka₂</th> <th style="text-align: left; padding: 3px;">Ka₃</th> </tr> <tr><td>H₃PO₄ (Phosphoric)</td><td>7.5×10⁻³</td><td>6.2×10⁻⁸</td><td>4.2×10⁻¹³</td></tr> <tr><td>H₂SO₃ (Sulfurous)</td><td>1.7×10⁻²</td><td>6.4×10⁻⁸</td><td>—</td></tr> <tr><td>H₂CO₃ (Carbonic)</td><td>4.3×10⁻⁷</td><td>5.6×10⁻¹¹</td><td>—</td></tr> <tr><td>H₂C₂O₄ (Oxalic)</td><td>5.9×10⁻²</td><td>6.4×10⁻⁵</td><td>—</td></tr> </table>

<strong>Conjugate Acid-Base Pairs (Ka × Kb = Kw)</strong><br> <table style="width:100%; border-collapse: collapse; font-size: 0.85em; margin-top: 5px;"> <tr style="border-bottom: 1px solid #ccc;"> <th style="text-align: left; padding: 3px;">Acid</th> <th style="text-align: left; padding: 3px;">Ka</th> <th style="text-align: left; padding: 3px;">Base</th> <th style="text-align: left; padding: 3px;">Kb</th> </tr> <tr><td>HF</td><td>6.8×10⁻⁴</td><td>F⁻</td><td>1.5×10⁻¹¹</td></tr> <tr><td>HC₂H₃O₂</td><td>1.8×10⁻⁵</td><td>C₂H₃O₂⁻</td><td>5.6×10⁻¹⁰</td></tr> <tr><td>NH₄⁺</td><td>5.6×10⁻¹⁰</td><td>NH₃</td><td>1.8×10⁻⁵</td></tr> <tr><td>HCO₃⁻</td><td>5.6×10⁻¹¹</td><td>CO₃²⁻</td><td>1.8×10⁻⁴</td></tr> </table>

Practice quiz

  1. A $0.10 \text{ M}$ solution of a weak acid $HA$ has a $K_a$ of $1.8 \times 10^{-5}$. Calculate the pH of the solution and the percent ionization of the acid.

    • pH = $2.87$, Percent ionization = $1.34\%$
    • pH = $1.00$, Percent ionization = $18\%$
    • pH = $4.74$, Percent ionization = $0.018\%$
    • pH = $2.87$, Percent ionization = $0.134\%$

    Answer: pH = $2.87$, Percent ionization = $1.34\%$

  2. A $0.25 \text{ M}$ solution of a weak base $B$ has a pH of $11.20$. Determine the $K_b$ for this base.

    • $1.0 \times 10^{-5}$
    • $1.8 \times 10^{-5}$
    • $2.5 \times 10^{-3}$
    • $6.3 \times 10^{-12}$

    Answer: $1.0 \times 10^{-5}$

  3. Acetic acid ($CH_3COOH$) has a $K_a$ of $1.8 \times 10^{-5}$. What is the pH of a $0.15 \text{ M}$ solution of sodium acetate ($CH_3COONa$), which is the conjugate base?

    • $4.74$
    • $7.00$
    • $8.96$
    • $11.26$

    Answer: $8.96$

  4. Calculate the pH of a $0.10 \text{ M}$ solution of phosphoric acid ($H_3PO_4$). Use the provided table for $K_a$ values and assume only the first dissociation is significant.

    • $1.20$
    • $1.62$
    • $2.12$
    • $3.00$

    Answer: $1.62$

  5. A $0.10 \text{ M}$ solution of a weak acid $HA$ is diluted to $0.010 \text{ M}$. How does this dilution affect the percent ionization of the acid and the pH of the solution?

    • Percent ionization decreases, pH decreases.
    • Percent ionization increases, pH increases.
    • Percent ionization increases, pH decreases.
    • Percent ionization decreases, pH increases.

    Answer: Percent ionization increases, pH increases.

  6. A weak acid $HA$ has a $K_a$ of $4.0 \times 10^{-7}$. What is the ratio of the conjugate base concentration to the weak acid concentration, $\frac{[A^-]}{[HA]}$, when the solution has a pH of $6.00$?

    • $0.040$
    • $0.40$
    • $2.5$
    • $4.0$

    Answer: $0.40$

  7. $50.0 \text{ mL}$ of $0.20 \text{ M}$ $HCl$ is mixed with $150.0 \text{ mL}$ of $0.050 \text{ M}$ $NaOH$. What is the pH of the resulting solution?

    • $1.90$
    • $7.00$
    • $12.10$
    • $1.00$

    Answer: $1.90$

  8. Two weak acids, $HA$ and $HB$, are prepared at the same initial concentration of $0.10 \text{ M}$. Solution $HA$ has a pH of $3.00$, while solution $HB$ has a pH of $4.00$. Which statement is true regarding their relative strengths and their conjugate bases?

    • $HA$ is a stronger acid than $HB$, and $A^-$ is a stronger base than $B^-$.
    • $HA$ is a stronger acid than $HB$, and $A^-$ is a weaker base than $B^-$.
    • $HB$ is a stronger acid than $HA$, and $B^-$ is a stronger base than $A^-$.
    • $HB$ is a stronger acid than $HA$, and $B^-$ is a weaker base than $A^-$.

    Answer: $HA$ is a stronger acid than $HB$, and $A^-$ is a weaker base than $B^-$.

  9. A weak acid $HX$ has a $K_a$ of $2.0 \times 10^{-3}$. If the initial concentration of $HX$ is $0.050 \text{ M}$, calculate its percent ionization. Is the approximation that $x$ is negligible compared to the initial concentration valid in this case?

    • $1.0\%$; Approximation is valid.
    • $2.0\%$; Approximation is valid.
    • $18.1\%$; Approximation is not valid.
    • $20.0\%$; Approximation is not valid.

    Answer: $18.1\%$; Approximation is not valid.

  10. A solution contains $0.10 \text{ M}$ acetic acid ($CH_3COOH$) and $0.20 \text{ M}$ sodium acetate ($CH_3COONa$). Given that the $K_a$ for acetic acid is $1.8 \times 10^{-5}$, calculate the pH of this solution.

    • $4.44$
    • $4.74$
    • $5.05$
    • $5.35$

    Answer: $5.05$

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