Question: 54. In which of the following equilibria, \mathrm{K}_{\mathrm{p}} and \mathrm{K}_{\mathrm{c}} are NOT equal ?
(1) \mathrm{PCl}_{5(\mathrm{~g})} \rightleftharpoons \mathrm{PCl}_{3(\mathrm{~g})}+\mathrm{Cl}_{2(\mathrm{~g})}
(2) \mathrm{H}_{2(\mathrm{~g})}+\mathrm{I}_{2(\mathrm{~g})} \rightleftharpoons 2 \mathrm{HI}_{(\mathrm{g})}
(3) \mathrm{CO}_{(\mathrm{g})}+\mathrm{H}_{2} \mathrm{O}_{(\mathrm{g})} \rightleftharpoons \mathrm{CO}_{2(\mathrm{~g})}+\mathrm{H}_{2(\mathrm{~g})}
(4) 2 \mathrm{BrCl}_{(\mathrm{g})} \rightleftharpoons \mathrm{Br}_{2(\mathrm{~g})}+\mathrm{Cl}_{2(\mathrm{~g})}
Answer: Option (1)
Explanation:
The relation between equilibrium constants \mathrm{K}_{\mathrm{p}} and \mathrm{K}_{\mathrm{c}} is given by:
\mathrm{K}_{\mathrm{p}} = \mathrm{K}_{\mathrm{c}}(\mathrm{RT})^{\Delta n}Here, \Delta n is the difference between the total number of moles of gaseous products and gaseous reactants.
If \Delta n = 0, then \mathrm{K}_{\mathrm{p}} = \mathrm{K}_{\mathrm{c}}.
For option (1):
\mathrm{PCl}_{5(\mathrm{g})} \rightleftharpoons \mathrm{PCl}_{3(\mathrm{g})} + \mathrm{Cl}_{2(\mathrm{g})}Number of moles of gaseous reactants = 1
Number of moles of gaseous products = 2
\Delta n = 2 - 1 = 1 \neq 0Therefore, \mathrm{K}_{\mathrm{p}} \neq \mathrm{K}_{\mathrm{c}}.
For option (2):
\Delta n = 2 - (1 + 1) = 0For option (3):
\Delta n = (1 + 1) - (1 + 1) = 0For option (4):
\Delta n = (1 + 1) - 2 = 0Thus, only in option (1),
\mathrm{K}_{\mathrm{p}} and \mathrm{K}_{\mathrm{c}} are not equal.