JEE Main 2023 Chemistry Question Paper with Answer and Solution

(A) Given: $\Delta H = 20 \ kJ \ mol^{-1}$,$E_{a,f} = 300 \ kJ \ mol^{-1}$.
For the same rate,the activation energy $E_{a}$ is proportional to temperature $T$ (assuming the pre-exponential factor $A$ remains constant).
$\frac{E_{a,f}}{T_{uncat}} = \frac{E_{a,f}^{\prime}}{T_{cat}}$
$T_{uncat} = 327 + 273 = 600 \ K$
$T_{cat} = 27 + 273 = 300 \ K$
$\frac{300}{600} = \frac{E_{a,f}^{\prime}}{300} \implies E_{a,f}^{\prime} = 150 \ kJ \ mol^{-1}$.
We know $\Delta H = E_{a,f}^{\prime} - E_{a,b}^{\prime}$.
$20 = 150 - E_{a,b}^{\prime}$.
$E_{a,b}^{\prime} = 150 - 20 = 130 \ kJ \ mol^{-1}$.

(B) Conductivity $(\kappa)$ decreases with dilution because the number of ions per unit volume decreases. This is true for both strong and weak electrolytes. Statement $(A)$ is correct.
$(B)$ On dilution,the volume of the solution increases,so the number of ions per unit volume decreases. Statement $(B)$ is incorrect.
$(C)$ Molar conductivity $(\Lambda_m)$ increases with decrease in concentration (dilution) because the total volume containing one mole of electrolyte increases. Statement $(C)$ is correct.
$(D)$ For strong electrolytes,$\Lambda_m$ increases slowly with dilution,whereas for weak electrolytes,it increases sharply due to an increase in the degree of dissociation. Statement $(D)$ is correct.
$(E)$ For weak electrolytes,the change in molar conductivity with dilution is due to an increase in the degree of dissociation $(\alpha)$,not a decrease. Statement $(E)$ is incorrect.
The correct statements are $(A)$,$(C)$,and $(D)$. Therefore,the total number of correct statements is $3$.