JEE Main 2022 · 25 July · evening · Single correct · +4 / −1
The molar conductivity of a conductivity cell filled with 10 moles of 20 mL NaCl solution is Λ ₘ₁ and that of 20 moles another identical cell heaving 80 mL NaCl solution is Λ ₘ₂. The conductivities exhibited by these two cells are same. The relationship between Λ ₘ₂ and Λ ₘ₁ is
- (a) Λ ₘ₂ = 2Λ ₘ₁
- (b) Λ ₘ₂ = Λ ₘ₁ / 2
- (c) Λ ₘ₂ = Λ ₘ₁
- (d) Λ ₘ₂ = 4Λ ₘ₁
Answer and solution
Answer (a) Λ ₘ₂ = 2Λ ₘ₁
Solution
Chemistry ma’am · 4 steps
Same conductivity in both cells, so molar conductivity depends only on concentration: work out each c.
- Link the two. Molar conductivity is conductivity divided by molar concentration. With κ in S cm⁻¹ and c in mol L⁻¹, the factor 1000 converts litres to cm³.
Λₘ = (κ × 1000)/c
- Find each concentration. Cell 1 has c₁ = (10 mol)/(0.020 L) = 500 mol L⁻¹. Cell 2 has c₂ = (20 mol)/(0.080 L) = 250 mol L⁻¹.
- Take the ratio. κ is the same in both cells, so it cancels: Λₘ₂/Λₘ₁ = c₁/c₂ = 500/250 = 2.
- So. Λₘ₂ = 2Λₘ₁, which is option (a). The more dilute solution has the larger molar conductivity.
The idea to keep. At fixed κ, molar conductivity is inversely proportional to concentration. Always find c from moles and volume together, never from either one alone.
Answer from the NTA final answer key. Solution by PrepWiser.