For the gas phase reaction, $\mathrm{PCl}_5(g) \rightleftharpoons \mathrm{PCl}_3(g)+\mathrm{Cl}_2(g)$ which…

For the gas phase reaction, $\mathrm{PCl}_5(g) \rightleftharpoons \mathrm{PCl}_3(g)+\mathrm{Cl}_2(g)$ which of the following conditions are correct?
  1. $\Delta H = 0$ and $\Delta S < 0$
  2. $\Delta H > 0$ and $\Delta S > 0$
  3. $\Delta H < 0$ and $\Delta S < 0$
  4. $\Delta H > 0$ and $\Delta S < 0$

Solution

Key Idea : $\Delta H=\Delta E+\Delta n R T$
$\Delta n=$ number of moles of product - number of moles of reactants
$\Delta G=\Delta H-T \Delta S$
For a spontaneous process $\Delta G$ must be negative.
$\mathrm{PCl}_5(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_3(\mathrm{~g})+\mathrm{Cl}_2(\mathrm{~g})$
In this reaction
$\Delta n=2-1=1$
Thus, $\Delta H$ is positive, $i e, > 0$
If $\Delta H$ is positive, then to maintain the value of $\Delta G$ negative, $\Delta S$ should be positive, $i e, \Delta S > 0$.

Asked in: NEET 2008 (Screening)

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