[plu]

The equilibrium constant for the reaction N₂O₄ <-> 2NO₂ is 0.113.  If one were to start with 1 mole of N₂O₄ at 1 atm pressure and 298 K, what fraction of it would decompose if pressure and temperature are both maintained at 1 atm and 298 K?

By doing a simple equilibrium calculation:
0.113 = (P_NO2)² / (P_N2O4)
          = (2x)² / (1 - x)
I get a value of 0.155 for x.

However, the solution my instructor gives:
0.113 = (P_NO2)² / (P_N2O4)
          = (2x / 1 + x)² / ( (1 - x) / (1 + x))
Where (1 + x) represents the total pressure of the system at equilibirum, results in an x value of 0.166.  Which solution is correct and why?

[Borek]

Which solution is correct and why?

Both. One is for constant volume, one is for constant pressure. Unless I am wrong 

[plu]

Which solution is correct and why?

Both. One is for constant volume, one is for constant pressure. Unless I am wrong 

Assuming that you are right ( ), which is which?

[Borek]

I was wrong.

You were wrong.

Your instructor is right.

Use definition of partial pressure.

[plu]

Use definition of partial pressure.

I don't understand.  The way my instructor solved the problem, he used pressure/mole fractions instead of actual partial pressures (which are simply the individual pressures of the gases)...

[Borek]

I don't understand.  The way my instructor solved the problem, he used pressure/mole fractions instead of actual partial pressures (which are simply the individual pressures of the gases)...

What's a difference then between partial pressure and pressure fraction?

[plu]

What's a difference then between partial pressure and pressure fraction?

Pressure fractions are equivalent to mole fractions (assuming ideal gases): the pressure of the individual gases divided by the total pressure of the system.  Partial pressures are simply the individual pressures of the gases.

[Borek]

Pressure fractions are equivalent to mole fractions (assuming ideal gases): the pressure of the individual gases divided by the total pressure of the system.  Partial pressures are simply the individual pressures of the gases.

1. How are they related to each other?

2. Which should be used in the reaction quotient?

[plu]

1. How are they related to each other?

2. Which should be used in the reaction quotient?

The partial pressures should be used in the reaction quotient...

[Borek]

OK, try to express partial pressure in terms of amounts of both substances (and in terms of x).

p_NO2 = ...

p_N2O4 = ...

[plu]

P_NO2 = 2x

P_N2O4 = 1 - x

Where x is the amount of N₂O₄ that has decomposed...

[Borek]

Use definition of partial pressure for ideal gases:

p_A = n_A/(n_A + n_B + ...) * p_total

[plu]

Use definition of partial pressure for ideal gases:

p_A = n_A/(n_A + n_B + ...) * p_total

A-ha!  My understanding of the definition of partial pressure was flawed.  Many thanks, Borek