A conductivity cell with two electrodes (dark side) are half filled with infinitely dilute aqueous solution of a weak…

Strategy: Analyze the behavior of conductivity in the limit of infinite dilution for weak electrolytes.

Con\ceptual Analysis:

1. Infinite Dilution: By definition, at infinite dilution, the \degree of dissociation ($\alpha$) has already reached its maximum value ($1$).
2. Conductivity ($\kappa$) vs. Molar Conductivity ($\Lambda_m$): Further adding water decreases the number of ions per unit volume, making $\kappa$ approach zero.
3. Molar Conductivity: $\Lambda_m^0$ is a constant for a given pair of ions. Doubling the volume from an already "infinite" state doesn't change $\alpha$ or the ion speed.

Special Case (Half-filled cell): If a cell with fixed electrodes is only half filled, the geometric cell constant $G^*$ is undefined or doubled in the empty region. Adding water to fill the cell changes the cross-sectional area of the conductor (the solution) between the electrodes, but doesn't change the substan\ce's intrinsic $\Lambda_m^0$. Measurement at such low concentrations is extremely difficult.

$\boxed{\text{Answer: (c) remain same or cannot be measured accurately}}$