Numerical/Formula

1. TITLE

How to solve Limiting Molar Conductivity numericals in NEET — Step-by-step

2. PROBLEM TYPE INTRO

This numerical falls under the category of Electrochemistry, specifically dealing with Kohlrausch’s Law of independent migration of ions. You will need the formula $\Lambda_{m}^\circ = v_{+}\lambda_{+}^\circ + v_{-}\lambda_{-}^\circ$ to indirectly calculate the limiting molar conductivity of weak electrolytes using data from strong electrolytes. The most typical mistake students make is adding all given values together or subtracting the wrong strong electrolyte.

3. MCQ

Question: The limiting molar conductivities ($\Lambda_m^\circ$) for $NaCl$, $HCl$, and $NaAc$ (sodium acetate) are $126.4\text{ S cm}^2\text{ mol}^{-1}$, $425.9\text{ S cm}^2\text{ mol}^{-1}$, and $91.0\text{ S cm}^2\text{ mol}^{-1}$ respectively. Calculate the limiting molar conductivity ($\Lambda_m^\circ$) for $HAc$ (acetic acid).

(a) $643.3\text{ S cm}^2\text{ mol}^{-1}$
(b) $390.5\text{ S cm}^2\text{ mol}^{-1}$
(c) $461.3\text{ S cm}^2\text{ mol}^{-1}$
(d) $208.5\text{ S cm}^2\text{ mol}^{-1}$

4. STEP-BY-STEP SOLUTION

SOLUTION
Given:
* $\Lambda_{m(NaCl)}^\circ = 126.4\text{ S cm}^2\text{ mol}^{-1}$
* $\Lambda_{m(HCl)}^\circ = 425.9\text{ S cm}^2\text{ mol}^{-1}$
* $\Lambda_{m(NaAc)}^\circ = 91.0\text{ S cm}^2\text{ mol}^{-1}$

To Find:
$\Lambda_{m(HAc)}^\circ$ (Limiting molar conductivity of acetic acid)

Formula:
$\Lambda_{m(HAc)}^\circ = \Lambda_{m(HCl)}^\circ + \Lambda_{m(NaAc)}^\circ - \Lambda_{m(NaCl)}^\circ$
Explain when to use this formula: Use this application of Kohlrausch's law when you need to find the limiting molar conductivity of a weak electrolyte (like acetic acid) that cannot be determined directly by extrapolating a graph to zero concentration. You use the known values of strong electrolytes and algebraically manipulate them.

Step 1: Break down the required weak electrolyte into its constituent ions based on Kohlrausch’s Law.
$\Lambda_{m(HAc)}^\circ = \lambda_{H^+}^\circ + \lambda_{Ac^-}^\circ$

Step 2: Arrange the given strong electrolytes to isolate the required ions ($H^+$ and $Ac^-$) while canceling out the "spectator" ions ($Na^+$ and $Cl^-$).
We need to add $HCl$ (provides $H^+$) and $NaAc$ (provides $Ac^-$), and then subtract $NaCl$ (removes the unwanted $Na^+$ and $Cl^-$).
Equation: $\lambda_{H^+}^\circ + \lambda_{Cl^-}^\circ + \lambda_{Na^+}^\circ + \lambda_{Ac^-}^\circ - \lambda_{Na^+}^\circ - \lambda_{Cl^-}^\circ$

Step 3: Substitute the given numerical values into the arranged equation and solve.
Calculation: $\Lambda_{m(HAc)}^\circ = 425.9 + 91.0 - 126.4$
Calculation: $\Lambda_{m(HAc)}^\circ = 516.9 - 126.4 = 390.5$

Answer: $390.5\text{ S cm}^2\text{ mol}^{-1}$ (Option b)

5. WHERE STUDENTS GO WRONG

  • ❌ Mistake 1: Adding all the provided values together ($425.9 + 91.0 + 126.4 = 643.3$) instead of subtracting the compound that contains the spectator ions.
  • ❌ Mistake 2: Subtracting the wrong strong electrolyte (e.g., subtracting $NaAc$ instead of $NaCl$), which leaves you with the wrong combination of ions and an incorrect result of $461.3\text{ S cm}^2\text{ mol}^{-1}$.
  • ❌ Mistake 3: Failing to multiply the molar conductivity by the correct stoichiometric coefficient ($v_+$ or $v_-$) when dealing with electrolytes like $CaCl_2$ or $MgCl_2$.

6. QUICK FORMULA REFERENCE

Formulas Used:
* Formula 1 — $\Lambda_m^\circ = v_{+}\lambda_{+}^\circ + v_{-}\lambda_{-}^\circ$ — Use when the limiting molar conductivities of individual cations and anions are given.
* Formula 2 — $\Lambda_{m(\text{weak})}^\circ = \Sigma\Lambda_{m(\text{strong to add})}^\circ - \Sigma\Lambda_{m(\text{strong to subtract})}^\circ$ — Use when calculating the limiting molar conductivity of a weak electrolyte from three given strong electrolytes.

7. SIMILAR PROBLEM HINT

"If NEET changes the values, the method stays the same. Practice with: Finding $\Lambda_{m}^\circ$ for $NH_4OH$ (ammonium hydroxide) using the given $\Lambda_{m}^\circ$ values for $NH_4Cl$, $NaOH$, and $NaCl$."

8. NCERT REFERENCE

Based on: NCERT Class 12, Unit 2 (Electrochemistry), Example 2.8.

9. CTA

More solved numericals → Redox Reactions & Electrochemistry Complete Guide
Practice problems → Mock exams