Q:

Finding the value of pressure equilibrium constant

Question:

A rigid vessel containing only $\ce{NO2(g)}$ is heated to $\pu{337^{ \circ}C}$  and allowed to come to equilibrium according to the following reaction: 
  $$\ce{2NO2 <=> 2NO + O2}$$ 
The density of the resulting mixture is measured to be $\pu{0.52 g/L}$ at a total pressure of $\pu{ 0.75 atm}$. What is the value of $K_\mathrm p$? 

The answer key says it should be $\pu{0.65 atm}$, but I can't get that number. I first tried to find mols using the given density and molar masses, and then finding the partial pressure of each component using the mol fractions, but it doesn't work out.

A:

The density is given.From here you will get a relation between initial concentration and volume.From $K_c$ you will get relation between volume,extent of dissociation and initial concentration.From $K_p$ you will get relation between pressure,extent of dissociation and initial concentration.After that use the formulas that Klaus Warzecha gave.I think that will be enough to solve this.

