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Q.

At a certain temperature, the degree of dissociation of PCl5 was found to be 0.25 under a total pressure of 15 atm. The value of Kp for the dissociation of PCl5 in the reaction, PCl5gPCl3g+Cl2g 

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a

1

b

0.25

c

0.5

d

0.75

answer is A.

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Detailed Solution

\large PC{l_5}\left( g \right) \rightleftharpoons PC{l_3}\left( g \right) + C{l_2}\left( g \right)

Initial moles of PCl5 = 1

Degree of decomposition of PCl5 = 0.25

Equilibrium presssure 15 atm

Moles of PCl5 at equilibrium = (1 - 0.25) = 0.75

1 mole of PCl5 gives 1 mole of PCl3 and 1 mole of Cl2

0.25 moles of PCl5 gives _______ and _______.

Question Image

 

 

\large PC{l_5}\left( g \right) \rightleftharpoons PC{l_3}\left( g \right) + C{l_2}\left( g \right)
 
\large PC{l_5}\left( g \right)
\large \rightleftharpoons
\large PC{l_3}\left( g \right) +
\large C{l_2}\left( g \right)
Initial moles      1      -   -
Moles at equilibrium(1 - 0.25)   0.25 0.25

Total moles at equilibrium = 1 - 0.25 + 0.25 +0.25 = 1.25

\large {X_{PC{l_3}}} = \frac{{0.75}}{{1.25}} = \frac{3}{5}
\large {X_{PC{l_3}}} = {X_{C{l_2}}}\frac{{0.25}}{{1.25}} = \frac{1}{5}
\large {K_P} = \frac{{{P_{PC{l_3}}}.{P_{C{l_2}}}}}{{{P_{PC{l_5}}}}}
\large {K_P} = \frac{{\left( {\frac{1}{5} \times 15} \right)\left( {\frac{1}{5} \times 15} \right)}}{{\left( {\frac{3}{5} \times 15} \right)}}
\large \boxed{{K_P} = 1atm}

 

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