Ionic Equilibrium Numerical Problems

JEE Main and Advanced

1. Calculation of pH or pOH of a Solution:

• Problem: Determine the pH of a 0.1 M solution of HCl.

• Shortcut Method: pH = -log[H3O+] = -log(0.1) = 1.

• Problem: Find the pOH of a 0.001 M solution of NaOH.

• Shortcut Method: pOH = -log[OH-] = -log(0.001) = 3.

2. Weak Acid Dissociation Constant (Ka):

• Problem: Calculate the Ka of a weak acid (HA) from the given pH or pOH value.

• Shortcut Method: $$Ka = \frac{[H3O+][A-]}{[HA]}$$

  where [H3O+], [A-], and [HA] represent the equilibrium concentrations of hydronium ions, conjugate base, and weak acid, respectively.

  If pH is given: [H3O+] = 10^(-pH), and [A-] = [HA]

  If pOH is given: [OH-] = 10^(-pOH), and [A-] = [HA][OH-]/[H3O+]

• Problem: Determine the equilibrium concentration of H3O+, A-, and HA in a solution of a weak acid with a known Ka value.

• Shortcut Method: Set up an ICE table to show the initial concentrations, changes, and equilibrium concentrations of the species involved in the dissociation of the weak acid. Ka expression can then be used to solve for the equilibrium concentrations.

3. Weak Base Dissociation Constant (Kb):

• Problem: Calculate the Kb of a weak base (B) from the given pH or pOH value.

• Shortcut Method: $$Kb = \frac{[BH+][OH-]}{[B]}$$

  where [BH+], [OH-], and [B] represent the equilibrium concentrations of conjugate acid, hydroxide ions, and weak base, respectively.

  If pH is given: [H3O+] = 10^(-pH), and [BH+] = [B]

  If pOH is given: [OH-] = 10^(-pOH), and [BH+] = [B][H3O+]/[OH-]

• Problem: Determine the equilibrium concentration of OH-, BH+, and B in a solution of a weak base with a known Kb value.

• Shortcut Method: Set up an ICE table to show the initial concentrations, changes, and equilibrium concentrations of the species involved in the dissociation of the weak base. Kb expression can then be used to solve for the equilibrium concentrations.

4. Salt Hydrolysis:

• Problem: Calculate the pH of a solution formed by dissolving an ammonium salt (NH4Cl) in water.

• Shortcut Method: Ammonium salts undergo hydrolysis in water, producing H3O+ ions. The pH can be determined using the concentration of H3O+ ions produced.

• Problem: Determine the hydrolysis constant (Kw) of water from the pH of a salt solution.

• Shortcut Method: Kw can be calculated using the expression Kw = [H3O+][OH-] at a specific temperature. If the pH of the salt solution is known, [H3O+] can be determined, and Kw can then be calculated.

5. Buffer Solutions:

• Problem: Calculate the pH of a buffer solution prepared by mixing a weak acid and its conjugate base or a weak base and its conjugate acid.

• Shortcut Method: The Henderson-Hasselbalch equation can be used to calculate the pH of a buffer solution: $$pH = pKa + log\frac{[A-]}{[HA]}$$ For a weak acid-base pair. pH = pKb + log\frac{[B]}{[BH+] for a weak base-conjugate acid pair.

• Problem: Determine the composition (concentration of weak acid and conjugate base) of a buffer solution with a desired pH value.

• Shortcut Method: Use the Henderson-Hasselbalch equation to determine the ratio of [A-]/[HA] (or [B]/[BH+]) required for the desired pH value. The concentrations of weak acid and conjugate base can then be calculated based on this ratio.

6. Common Ion Effect:

• Problem: Predict the effect of adding a common ion (either anion or cation) on the equilibrium of a weak acid or weak base solution.

• Shortcut Method: The addition of a common ion shifts the equilibrium of a weak acid or weak base solution according to Le Chatelier’s principle. The shift is towards the formation of the less dissociated species.

• Problem: Calculate the change in pH or pOH upon addition of a common ion.

• Shortcut Method: The change in pH or pOH can be estimated by considering the shift in the equilibrium of the weak acid or weak base solution due to the addition of a common ion. The extent of the pH or pOH change depends on the initial concentration of the weak acid or weak base and the concentration of the added common ion.

7. Solubility Equilibrium:

• Problem: Determine the solubility of a sparingly soluble salt (e.g., CaCO3) from its solubility product (Ksp).

• Shortcut Method: The solubility of a sparingly soluble salt can be calculated using the Ksp expression: Ksp = [Ca2+][CO32-], where [Ca2+] and [CO32-] represent the equilibrium concentrations of calcium and carbonate ions. Solubility is expressed as the concentration of the dissolved salt in moles per liter.

• Problem: Calculate the concentration of dissolved ions ([Ca2+] and [CO32-]) in a saturated solution of a sparingly soluble salt.

• Shortcut Method: Set up an ICE table to show the initial concentrations, changes, and equilibrium concentrations of the dissolved ions. Ksp expression can be used to solve for the equilibrium concentrations.

8. Redox Equilibrium:

• Problem: Balance and analyze redox reactions involving ionic species in solution.

• Shortcut Method: Use oxidation states to balance redox reactions. Identify the species undergoing oxidation and reduction and ensure that the net change in oxidation states is zero.

• Problem: Calculate the electrode potential (E) of a redox reaction involving ions under non-standard conditions.

• Shortcut Method: Use the Nernst equation to calculate the electrode potential under non-standard conditions: E = E° - (0.0592 V/n) x log(Q), where E° is the standard electrode potential, n is the number of moles of electrons transferred in the reaction, and Q is the reaction quotient.

CBSE Board Exams

1. Determination of pH Using Universal Indicator:

• Shortcut Method: Immerse a strip of universal indicator paper in the solution and compare the resulting color with the color chart provided to determine the approximate pH value.

2. Buffer Solutions:

• Shortcut Method: Buffers are solutions that resist changes in pH when small amounts of acid or base are added. They consist of a weak acid and its conjugate base or a weak base and its conjugate acid.

3. Hydrolysis:

• Shortcut Method: Hydrolysis is the reaction of an ion with water to produce an acid or base. Salts of weak acids or weak bases undergo hydrolysis. The nature of the solution (acidic, basic, or neutral) formed by a salt depends on the relative strengths of the acid and base components of the salt.

4. Redox Reactions:

• Shortcut Method: Redox reactions are chemical reactions that involve the transfer of electrons between species. Common redox reactions in ionic solutions include those involving metal ions undergoing oxidation or reduction.

5. Solubility and Ksp:

• Shortcut Method: The solubility product (Ksp) of a sparingly soluble salt is a constant value that represents the maximum concentration of dissolved ions of the salt in equilibrium with the solid salt at a given temperature.

6. Electrochemistry:

• Shortcut Method: Electrochemistry deals with the relationship between chemical changes and electrical changes. In solutions, electrolytes conduct electricity due to the movement of ions. Electrolysis involves the decomposition of ionic compounds by passing an electric current.