[oque]

Nitrogen dioxide NO2 is one of a number of oxides of nitrogen found in our atmosphere. It
can dimerize to give N2O4 (g):
2NO2 (g) N 2 O 4 (g)

At 298 K, the ∆G of formation for N2O4 (g) is 98.28 kJ, whereas for NO2 (g) is 51.84
kJ. Starting with one mole of N2O4 (g) at 1.0 atm and 298 K, calculate what fraction
will be decomposed if the total pressure is kept constant at 1.0 atm and the
temperature is maintained at 298 K.

Supposedly the answer is 0.166, but I haven't been able to find the way to solve it correctly, my result was 0.39.

I calculated the constant K with ΔG= -RTlnK. The ΔG for the whole reaction is (according to me) 5.4kJ
The constant I calculated is 0.99782. Then:

(NO₂)²/(N₂O₄)

(2x)²/(1-x)= K

Solve the cuadratic ecuation and it's 0.39,  Where did I go wrong?

[Borek]

The ΔG for the whole reaction is (according to me) 5.4kJ
The constant I calculated is 0.99782.

Check this part.

[oque]

I calculated again and its 0.113. I realized that ΔG it's in kJ, not in J in order to use R.
But again, now I solved the quadratic equation and its 0.15468 not close enough to the right answer.

[mjc123]

I agree with you, but you get the given answer if K = 0.133. Perhaps the book made a transcription error in doing the quadratic equation.

[AWK]

The problem comes from ICHO24 and its solution is given
https://www.alquimicos.com/oq_reg/internacionales/icho_24.pdf

[mjc123]

Ah. Total pressure is 1 atm, for mole fraction must divide by (1+x).