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Q.

20 gm of CaCO3 is allowed to dissociate in a 5.6 litre container at 8190 C. If 50% of CaCO3 is dissocitated at equilibrium, the 'Kp' value is

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a

5 atm

b

1.6atm

c

4.8atm

d

10atm

answer is B.

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Detailed Solution

Initial number of  moles of CaCO3  =20100=0.2

Volume of the container = 5 - 6

Degree of decomposition of CaCO3=50100=0.5

moles of CaCO3 decomposed = 0.2 x 0.5 = 0.1

moles of CaCO3 remain at equilibrium = (0.2 - 0.1) = 0.1

1 mole of CaCO3 → 1 mole of CO2

0.1 mole of CaCO3 → -

\large \boxed{{\text{moles of C}}{{\text{O}}_2}{\text{ formed = 0}}{\text{.1}}}
Stoichiometry
\large \mathop {CaC{O_3}}\left( s \right)
\rightleftharpoons
\large \mathop {CaO} \left( s \right)+
\large \mathop {C{O_2}\left( g \right)}
Initial moles       0.2     0    0
Moles at equlibrium  (0.2 - 0.1)   0.1  0.1

 

 

\large {P_{CaC{O_3}}} = {P_{CaO}} = 1\left( {\because CaC{O_3}\,\& CaO\,ax\,solids} \right)
\large {K_P} = {P_{C{O_2}}}
\large {P_{C{O_2}}} = \frac{{nRT}}{V}

n = 0.1

T = (819 + 273) K

V = 5.6 Lit

 

\large \therefore {P_{C{O_2}}} = {K_P} = \frac{{0.1 \times 0.082 \times 1092}}{{5.6}}
\large \boxed{{P_{C{O_2}}} = {K_P} = 1.6atm}

 

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