Question #44304

Elements $P, Q, R,$ and $S$ belong to Group 17 of the periodic table. The magnitude of their standard electron gain enthalpies ($|\Delta_{eg}H^\ominus|$) follows the order $Q > P > R > S$, while their standard reduction potentials ($E^\circ_{X_2/X^-}$) follow the order $P > Q > R > S$.

A student incorrectly hypothesizes that the halogen with the highest magnitude of electron gain enthalpy will form the sodium salt with the highest limiting molar conductivity ($\Lambda_m^\circ$) due to its strong ionic character. In reality, the highest $\Lambda_m^\circ$ belongs to the sodium salt of halogen $X$.

Given the following data at $298 \text{ K}$: $\bullet$ $\Lambda_m^\circ(\ce{NaQ}) = 12.60 \text{ mS m}^2 \text{ mol}^{-1}$ $\bullet$ Transport number of $\ce{Na^+}$ in $\ce{NaQ}$ at infinite dilution is $0.400$. $\bullet$ Absolute ionic mobility of $S^-$ at infinite dilution is $8.00 \times 10^{-8} \text{ m}^2 \text{ V}^{-1} \text{ s}^{-1}$. $\bullet$ Absolute ionic mobility of $P^-$ at infinite dilution is $5.60 \times 10^{-8} \text{ m}^2 \text{ V}^{-1} \text{ s}^{-1}$. $\bullet$ Faraday constant $F = 96500 \text{ C mol}^{-1}$.

Identify halogen $X$ and calculate its $\Lambda_m^\circ(\ce{NaX})$ in $\text{S cm}^2 \text{ mol}^{-1}$.