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Question

Two solid compounds X and Y dissociates at a certain temperature as follows:
X(s)A(g)+2B(g);KP1=9×103atm3
Y(s)2B(g)+C(g);KP2=4.5×103atm3
The total pressure of gases over a mixture of X and Y is:

A
4.5 atm
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B
0.45 atm
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C
0.6 atm
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D
None of these
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Solution

The correct option is B 0.45 atm
X(s)A(g)+2B(g);KP1=9×103atm3 ......(1)
Y(s)2B(g)+C(g);KP2=4.5×103atm3 ......(2)
Add reactions (1) and (2)
X(s)+Y(s)A(g)+4B(g)+C(g)
KP=KP1×KP2=9×103atm3×4.5×103atm3
Let P be the pressure of A.
The pressures of B and C will be 4P and P respectively.
Hence, the expression for the equilibrium constant will be KP=PA×P4B×PC
Substitute values in the above expression.
P×(4P)4×P=9×4.5×103×103
P=0.0735
6P=6×0.0735=0.45atm
Hence, the total pressure of gases over a mixture of X and Y is 0.45 atm.

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