S5 Chemistry Practice Book · Unit 12: Conductivity of solutions

Unit 12 Conductivity of solutions

Key unit competence: Interpret the electrical conductivity of electrolytic solutions to explain the factors that affect it and use conductivity measurements.

Key ideas

Electrolytic solutions conduct by the movement of ions. Conductance G = 1/R, unit siemens (S = Ω^-1). Specific conductivity (conductivity) κ = G × (l/A); l/A is the cell constant (cm⁻¹). Unit of κ: S cm⁻¹.
Molar conductivity Λ_m = κ ÷ c, or Λ_m = 1000κ ÷ c when κ is in S cm⁻¹ and c in mol dm⁻³; unit S cm² mol⁻¹.
κ falls on dilution (fewer ions per cm³) but Λ_m RISES on dilution. Strong electrolytes: Λ_m = Λ°_m − A√c (a straight line against √c). Weak electrolytes: Λ_m rises steeply at low c because ionisation increases.
Factors: nature of electrolyte (strong or weak), concentration, temperature (higher T, higher conductivity), size and charge of ions, solvent viscosity. H⁺ and OH⁻ conduct exceptionally well (proton hopping).
Kohlrausch's law: at infinite dilution each ion contributes independently: Λ°_m = ν₊λ°₊ + ν₋λ°₋. It gives Λ° of weak electrolytes: Λ°(CH₃COOH) = Λ°(CH₃COONa) + Λ°(HCl) − Λ°(NaCl).
Degree of ionisation α = Λ_m ÷ Λ°_m; for a weak acid K_a = cα^2 ÷ (1 − α) (Ostwald's dilution law). Uses: conductometric titrations and solubility of sparingly soluble salts (s = 1000κ ÷ Λ°_m). Metals conduct by electrons (conductivity falls as T rises, no chemical change); electrolytes by ions (rises with T, chemical change at electrodes).

Common misconceptions

"Molar conductivity falls on dilution like conductivity does." No: κ falls, but Λ_m rises on dilution because ions are freer (strong) or more ionised (weak).
"Metals and electrolytes conduct in the same way." No: Metals conduct by delocalised electrons; electrolytes by moving ions, with chemical change at the electrodes.
"Heating a metal and an electrolyte has the same effect on conduction." No: Heating lowers a metal's conductivity but raises an electrolyte's.

Worked examples

Example 1. Describe how the conductivity of a solution is measured and how Λ_m is calculated.

Solution

A conductivity cell (two platinised Pt electrodes of fixed area and separation) is dipped in the solution and connected to an AC Wheatstone bridge or a conductivity meter (AC prevents electrolysis).

The cell constant l/A is found with a standard KCl solution of known κ.

Measure R; G = 1/R; κ = G × cell constant.

Λ_m = 1000κ ÷ c (c in mol dm⁻³); keep the temperature constant.

Example 2. Explain the shapes of Λ_m against √c for KCl and for ethanoic acid.

Solution

KCl (strong): fully ionised; on dilution interionic attraction falls, so Λ_m rises slightly in a straight line; extrapolate to c = 0 to get Λ°.

Ethanoic acid (weak): only slightly ionised; on dilution the degree of ionisation rises greatly, so Λ_m rises steeply at low c.

The curve cannot be extrapolated; use Kohlrausch's law for Λ°.

Practice questions

Define molar conductivity.
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The conductivity of a solution containing one mole of electrolyte between electrodes 1 cm apart; Λ_m = κ ÷ c.
Common mistake: Confusing it with specific conductivity.
Why is alternating current used to measure conductivity?
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Direct current would electrolyse the solution and change its concentration and the electrodes (polarisation).
Common mistake: Saying AC is cheaper.
State Kohlrausch's law of independent migration of ions.
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At infinite dilution, each ion makes a fixed, independent contribution to the molar conductivity of an electrolyte.
Common mistake: Saying all ions have equal conductivity.
Give two differences between metallic and electrolytic conduction.
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Electrons vs ions; no chemical change vs chemical change at electrodes; conductivity falls vs rises with temperature (any two).
Common mistake: Saying both involve ions.
Why do H⁺ and OH⁻ have very high ionic conductivities?
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They move by proton transfer between water molecules (Grotthuss mechanism), not by the ion physically travelling.
Common mistake: Saying they are the largest ions.
How does the size of an ion affect its conductivity in water?
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Small ions such as Li⁺ are strongly hydrated, so the large hydrated ion moves slowly: Li⁺ conducts less than K⁺.
Common mistake: Thinking the smallest bare ion always moves fastest.
Write Ostwald's dilution law for a weak acid.
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K_a = cα^2 ÷ (1 − α) ≈ cα^2 when α is small.
Common mistake: Writing K_a = cα.
A cell has κ = 0.0129 S cm⁻¹ for 0.100 mol dm⁻³ KCl. Find Λ_m.
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Λ_m = 1000 × 0.0129 ÷ 0.100 = 129 S cm² mol⁻¹.
Common mistake: Forgetting the factor 1000.
Give two uses of conductivity measurements.
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Conductometric titrations; finding solubility and K_sp; finding α and K_a; checking purity of water (any two).
Common mistake: Listing titration with indicators.
Why is the conductivity of distilled water subtracted when finding the solubility of AgCl?
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Water itself conducts slightly; only the conductivity due to dissolved AgCl ions is wanted.
Common mistake: Ignoring the water's own conductivity.

Matching and drag-and-drop

Matching

Match each item in column A with the correct answer in column B. Write the letter next to each number.

Column A	Column B
1. The SI unit of conductance is the:	a. resistance
2. Kohlrausch's law states that at infinite dilution:	b. each ion contributes independently to the molar conductivity
3. The degree of ionisation of a weak electrolyte is given by:	c. Λ_m ÷ Λ°_m
4. Conductance is the reciprocal of:	d. siemens

Show answer

1 → d (siemens) · 2 → b (each ion contributes independently to the molar conductivity) · 3 → c (Λ_m ÷ Λ°_m) · 4 → a (resistance)

1 S = 1 Ω^-1.
Λ° = sum of the ionic contributions.
α = Λ_m/Λ°_m.
G = 1/R.

Drag and drop
Choose the correct word or phrase from the box for each gap. One word in the box is not needed.
ions · S cm⁻¹ · it is only very slightly ionised · mol dm⁻³
1. Electrolytic solutions conduct electricity by the movement of .
2. The conductivity of pure water is very low because .
3. The unit of specific conductivity (κ) is .
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1: ions · 2: it is only very slightly ionised · 3: S cm⁻¹
- Positive and negative ions carry charge through the solution.
- [H⁺] = 10⁻⁷ mol dm⁻³ at 25 °C.
- κ = G × l/A, so S × cm⁻¹.

Matching

Match each item in column A with the correct answer in column B. Write the letter next to each number.

Column A	Column B
1. On dilution, the molar conductivity of a solution:	a. delocalised electrons
2. On dilution, the specific conductivity (κ) of a solution:	b. S cm² mol⁻¹
3. The unit of molar conductivity is:	c. increases
4. In metals, electric current is carried by:	d. decreases

Show answer

1 → c (increases) · 2 → d (decreases) · 3 → b (S cm² mol⁻¹) · 4 → a (delocalised electrons)

Ions move more freely or ionise more.
There are fewer ions per cm³.
Λ_m = 1000κ/c.
No chemical change occurs.

Drag and drop
Choose the correct word or phrase from the box for each gap. One word in the box is not needed.
weak electrolytes · increases its conductivity · 0.020 S · 2.0 S
1. Ostwald's dilution law applies to .
2. A conductivity cell has R = 50 Ω. Its conductance is .
3. Raising the temperature of an electrolyte solution usually .
Show answer
1: weak electrolytes · 2: 0.020 S · 3: increases its conductivity
- K_a = cα^2/(1 − α).
- G = 1/50 = 0.020 S.
- Ions move faster in a less viscous solvent.

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