The molar conductivity of a solution of a weak acid $HX$ $(0.01 \ M)$ is $10$ times smaller than the molar conductivity of a solution of a weak acid $HY$ $(0.10 \ M)$. If $\lambda_{X^{-}}^0 \approx \lambda_{Y^{-}}^0$,the difference in their $pK_a$ values,$pK_a(HX) - pK_a(HY)$,is (consider degree of ionization of both acids to be $\ll 1$)

Consider the following cell reaction:
$Cd_{(s)} + Hg_{2}SO_{4(s)} + \frac{9}{5}H_{2}O_{(l)} \rightleftharpoons CdSO_{4} \cdot \frac{9}{5}H_{2}O_{(s)} + 2Hg_{(l)}$
The value of $E_{\text{cell}}^{0}$ is $4.315 \ V$ at $25^{\circ}C$. If $\Delta H^{\circ} = -825.2 \ kJ \ mol^{-1}$,the standard entropy change $\Delta S^{\circ}$ in $J \ K^{-1} \ mol^{-1}$ is ........ . (Nearest integer) [Given: Faraday constant $= 96487 \ C \ mol^{-1}$]

Column $I$	Column $II$
$(A)$. Kohlrausch law can calculate	$(P)$. $\frac{\Lambda_m^c}{\Lambda_m^o}$
$(B)$. Molar conductance $\Lambda_m$	$(Q)$. $\frac{1}{R} \times \frac{l}{A}$
$(C)$. Specific conductance $\kappa$	$(R)$. $\Lambda_m^o$ of $Ca_3(PO_4)_2$
$(D)$. Degree of ionization of weak electrolyte	$(S)$. $\frac{\kappa \times 1000}{M}$

Which of the following options shows the correct matches?

At $300 \ K$,the $E_{cell}^{\circ}$ of $A_{(s)} + B^{2+}_{(aq)} \rightleftharpoons A^{2+}_{(aq)} + B_{(s)}$ is $1.0 \ V$. If $\Delta_r S^{\circ}$ of this reaction is $100 \ J \ K^{-1} \ mol^{-1}$,what is $\Delta_r H^{\circ}$ (in $kJ \ mol^{-1}$) of this reaction? $(F = 96500 \ C \ mol^{-1})$

If the molar conductivity $(\Lambda_{m})$ of a $0.050 \ mol \ L^{-1}$ solution of a monobasic weak acid is $90 \ S \ cm^{2} \ mol^{-1}$,its extent (degree) of dissociation will be. [Assume $\Lambda_{+}^{\circ} = 349.6 \ S \ cm^{2} \ mol^{-1}$ and $\Lambda_{-}^{\circ} = 50.4 \ S \ cm^{2} \ mol^{-1}$.]

Which of the following is not correct?