Discussion
The resistance of 0.10 M KCl solution when measured with a conductivity cell at 298 K is 100 Ω. If the conductivity of 0.10 M KCl solution is 1.29 Sm-1 , what is the value of cell constant of the same solution at 298 K?
Answer: D
The cell constant is \(1.29\ \text{cm}^{-1}\).
Conductivity \(\kappa\) is related to the measured resistance \(R\) through the cell constant \(G^{*} = l/A\): \(\kappa = G^{*}/R\), so \(G^{*} = \kappa R\).
\[ \begin{aligned} G^{*} &= 1.29\ \text{S m}^{-1} \times 100\ \Omega \\ &= 129\ \text{m}^{-1} \\ &= 1.29\ \text{cm}^{-1} \end{aligned} \]
The last step uses 1 m = 100 cm, so 129 per metre is 1.29 per centimetre. \(1.29\ \text{m}^{-1}\) is the conductivity's number without multiplying by the resistance, \(1.29 \times 10^{-2}\ \text{m}^{-1}\) comes from dividing by 100 instead of multiplying, and the two 0.129 values are slips of a power of ten.
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