The resistivity of a 0.8 M solution of an electrolyte is 5 × 10⁻³ Ω cm.
Its molar conductivity is _________ × 10⁴ Ω⁻¹ cm² mol⁻¹. (Nearest integer)

Solution

Chemistry ma’am · 4 steps

Flip resistivity to get conductivity, then multiply by 1000 over molarity for molar conductivity.

1. Conductivity first. Conductivity is the reciprocal of resistivity: κ = 1/ρ = 1/(5 × 10⁻³) = 200 Ω⁻¹ cm⁻¹.

   Λₘ = (κ × 1000)/M

2. Why 1000. Molarity counts moles per litre, but κ is in cm⁻¹. Since 1 L = 1000 cm³, the factor 1000 converts the volume to cm³.
3. Put in numbers. Λₘ = (200 × 1000)/0.8 = 2.5 × 10⁵ = 25 × 10⁴ Ω⁻¹ cm² mol⁻¹.
4. So. The blank already carries × 10⁴, so the answer is 25.

The common slip: 250000. Entering the full value 2.5 × 10⁵ gives 250000. The blank is already multiplied by 10⁴, so only 25 goes in.

The idea to keep. Resistivity is the reciprocal of conductivity. Then use Λₘ = κ × 1000 / M with κ in Ω⁻¹ cm⁻¹, because the 1000 turns litres into cm³.

Answer from the NTA final answer key. Solution by PrepWiser.