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I'm looking for the dissociation constant of molecular dinitrogen ($\ce{N2}$) as a function of temperature,

$$\ce{N2 <=>[$K$] 2N} \quad K=\frac{[\ce{N}]^2}{[\ce{N2}]}$$

Casas & Bermelo (1978) reported three data points for nitrogen (I couldn't access their references):

$$K_{298}=2\cdot 10^{-160},\ K_{2000}=10^{-3},\ K_{20000}=1.29\cdot 10^5$$

  1. Are these the accepted values today? Is there a more complete database online?
  2. Would it be correct to fit an exponential function using these data points to extract $K$ for other temperatures?
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Update: If you plot the $\log(K_p)$ vs temperature it does not give a straight line over such a large temperature range so you are unlikely to be successful.

However, you can estimate $K_p$ as the molecular properties of dinitrogen are known so you can calculate the partition functions Z and so the equilibrium constant at any temperature. You need the vibrational frequency (and possibly anharmonicity), rotational constant and dissociation energy. Work out the partition functions for translation, rotation & vibration for dinitrogen and translation for N atoms and that is all you need.

The equations needed are given in most phys. chem. textbooks and specialist books on statistical mechanics. At a standard state of $1$ bar pressure $$k_P= \frac{Z_{trans}(N)^2}{NZ_{trans}(N_2)Z_{rot}(N_2)Z_{vib}(N_2)}\exp(-E_0/(kT))$$

The experimental values at low temperature are likely to have the biggest error since dinitrogen is such a stable molecule, and it probably does not matter much how small the $K_p$ is its always tiny at low temperatures. Using the method above I calculated values as $2.4 10^{-160}, ~ 8.4 10^{-19}$ and $ 62400$ at the three temperatures you quote (using the dissociation energy as 9.756 eV).

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  • $\begingroup$ did you get the constants from NIST? $\endgroup$ – Sparkler Apr 5 '17 at 17:49
  • $\begingroup$ There are also NIST records of ~e-33 at room temperature. $\endgroup$ – Sparkler Apr 5 '17 at 17:55
  • $\begingroup$ No I looked them up in Herzberg spectroscopy books. The constants are well known, however. I'm sure that the room temp values are difficulty to measure accurately as so little dissociates. It may not matter as the amount is so small, it will depend on what you need the number for. There seems to be uncertainty as to the dissociation constant. It is not hard to write code to do the calculation, I knocked together a Python version quite easily. $\endgroup$ – porphyrin Apr 6 '17 at 12:55
  • $\begingroup$ The NIST data is for the rate constant not the equilibrium constant. When calculating values the atom Z has to be multiplied by its multiplicity, 4 in the case of N atoms ($^4S_{3/2}$) and the rotational Z divided by 2 due to symmetry. $\endgroup$ – porphyrin Apr 6 '17 at 19:59

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