More practice questions

4. Q4. A conductivity cell filled with 0.010 mol L⁻¹ KCl has a resistance of 200 Ω at 298 K. Using NCERT Table 2.3, find its cell constant.

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   κ = 0.141 S m⁻¹ (NCERT Table 2.3, page 44), so G* = κR = 0.141 × 200 = 28.2 m⁻¹, which is 0.282 cm⁻¹ (NCERT Eq. (2.18), page 44).

5. Q5. From NCERT Table 2.3, 0.100 mol L⁻¹ KCl has κ = 1.29 S m⁻¹. Find Λ_m in both sets of units.

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   c = 100 mol m⁻³, so Λ_m = 1.29/100 = 0.0129 S m² mol⁻¹ = 129 × 10⁻⁴ S m² mol⁻¹ = 129 S cm² mol⁻¹, as the table lists (NCERT page 45).

6. Q6. Using NCERT Table 2.4, find Λ°_m for K₂SO₄ and for KOH.

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   K₂SO₄: 2(73.5) + 160.0 = 307.0 S cm² mol⁻¹. KOH: 73.5 + 199.1 = 272.6 S cm² mol⁻¹ (NCERT Eq. (2.25) and Table 2.4, page 49).

7. Q7. Arrange HCl, KCl and NaCl in order of increasing Λ°_m, using NCERT Table 2.4.

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   NaCl (50.1 + 76.3 = 126.4) < KCl (73.5 + 76.3 = 149.8) < HCl (349.6 + 76.3 = 425.9), in S cm² mol⁻¹. The anion is the same, so the order is that of the cations; H⁺ is by far the fastest (NCERT Table 2.4, page 49).

8. Q8. Assertion: Λ°_m of acetic acid cannot reliably be found by a straight-line extrapolation of a plot of Λ_m against c^1/2 to zero. Reason: its Λ_m rises steeply at low concentration. Are both true, and does the reason explain the assertion?

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   Both are true, and the reason explains the assertion: the curve is strongly curved and solvent/background conductance becomes important near zero, so Λ°_m comes from Kohlrausch’s law instead (NCERT page 49).

9. Q9. NCERT Table 2.2 gives κ = 0.016 S m⁻¹ for 0.01 M acetic acid. With Λ°_m = 390.5 S cm² mol⁻¹, estimate its degree of dissociation and K_a.

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   c = 10 mol m⁻³, so Λ_m = 0.016/10 = 0.0016 S m² mol⁻¹ = 16 S cm² mol⁻¹. α = 16/390.5 = 0.041, and K_a = 0.01 × 0.041²/(1 − 0.041) ≈ 1.8 × 10⁻⁵ mol L⁻¹, close to NCERT Example 2.9’s 1.78 × 10⁻⁵ (NCERT Eqs. (2.26)–(2.27)).

10. Q10. How does a rise in temperature affect the conductance of a metal wire and of a salt solution?

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    For ordinary metals and dilute salt solutions near room temperature, the metal’s conductance usually decreases while the solution’s conductance usually increases (NCERT pages 42–43).

11. Q11. Beyond the NCERT text: after the water’s own conductivity is subtracted, saturated Mg(OH)₂ at 298 K has κ = 5.55 × 10⁻⁵ S cm⁻¹. Taking Λ_m ≈ Λ°_m, find its solubility from NCERT Table 2.4.

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    Λ°_m = 106.0 + 2(199.1) = 504.2 S cm² mol⁻¹; s = 1000κ/Λ°_m = 1.10 × 10⁻⁴ mol L⁻¹ (reasoned from NCERT Eqs. (2.21) and (2.25)).