If the conductivity of mercury at 0°C is 1.07 × 10⁶ S m⁻¹ and the resistance of a cell containing mercury is 0.243Ω, then the cell constant of the cell is x × 10⁴ m⁻¹. The value of x is ____________. (Nearest integer)

Solution

Chemistry ma’am · 3 steps

Cell constant is conductivity times resistance. Multiply, then match the power of ten they ask for.

1. Link the quantities. Resistance is R = ρ l/A and conductivity is κ = 1/ρ. So R = 1/κ × l/A, where l/A is the cell constant G^*.

   G^* = l/A = κ × R

2. Put in numbers. G^* = 1.07 × 10⁶ S m⁻¹ × 0.243 Ω = 2.6 × 10⁵ m⁻¹, since 1.07 × 0.243 = 0.26 and S × Ω = 1.
3. So. 2.6 × 10⁵ m⁻¹ = 26 × 10⁴ m⁻¹, so x = 26.

The common slip: 440. Dividing conductivity by resistance instead of multiplying gives 4.4 × 10⁶ m⁻¹, that is 440, not 26.

The idea to keep. Remember κ = G^*/R, so the cell constant is always κ × R. Check units: S m⁻¹ times Ω leaves m⁻¹, exactly what a cell constant should have.

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