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Question

Two equilibria are simultaneously exist in a vessel at 25 C
NO(g)+NO2(g)Kp1N2O3(g)
2NO2(g)Kp2=8atmN2O4(g)
If initially only NO and NO2 are present in a 3:5 mole ratio and the total pressure at equilibrium is 5.5 atm with the pressure of NO2 at 0.5 atm. Select the correct option(s) from the following:


A
Equillibrium pressure of N2O4 is 2 atm
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B
Equillibrium pressure of N2O3 is 0.5 atm 
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C
The value of Kp1=0.4
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D
The value of Kp1=0.8
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Solution

The correct options are
A Equillibrium pressure of N2O4 is 2 atm
B Equillibrium pressure of N2O3 is 0.5 atm 
C The value of Kp1=0.4
If initially only NO and NO2 are present in a 3:5 mole ratio then initial pressure ratio will also be 3:5, so let initial pressure be 3p and 5p.
So,
NO(g)+NO2(g)Kp1N2O3(g)
3p5p0initial pressure3px5px2yxat equilibrium
And
2NO2(g)Kp2=8atmN2O4 
5px2y              y
As pressure of NO2=0.5 atm as given so 5p - x - 2y = 0.5
So, from 2nd equilibrium Kp2=8=pN2O4(pNO2)2
pN2O4(0.5)2=8pN2O4=2 atm=y 
As total pressure is given = 5.5 atm, so
(3px)+(5px2y)+x+y=5.5
(3px)+0.5+x+2=5.5
p=1 atm
Now from, 5px2y=0.5, x=0.5 atm
So, Kp1=pN2O3pNO×pNO2
             =x(3px)×0.5
             =0.5(30.5)×0.5=12.5=0.4
 

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