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Question

One mole of a mixture of N2,NO2 and N2O4 has a mean molar mass of 55.4. On heating to a temperature at which N2O4 is completely dissociated: N2O42NO2, the mean molar mass tends to a lower value of 39.57. What is the mole ratio of N2:NO2:N2O4 in the original mixture?

A
0.4 : 0.2 : 0.4
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B
0.5 : 0.1 : 0.4
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C
0.6 : 0.2 : 0.2
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D
0.4 : 0.4 : 0.2
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Solution

The correct option is B 0.5 : 0.1 : 0.4
Let
nN2=x
nNO2=y
nN2O4=z
Total moles =1
x+y+z=1 (i)
mean molar mass before the reaction:
28x+46y+92zx+y+z=55.4 (ii)
Once the reaction happens, all the `z` moles of `N_2O_4` get converted into `2y` moles of `NO_2`
mean molar mass after the reaction:
28x+46(y+2z)x+y+2z=39.57 (iii)
Using `(ii)` and `(iii)`, we get `z=0.4`
Also, we get
x=0.5
y=0.1

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