Find the concentration of M, (M), in kgmol/m^3, that is to be used in Reactions

Question

Find the concentration of M, (M), in kgmol/m^3, that is to be used in Reactions (1) and (2)

Problem 2. A gaseous mixture of argon (Ar) along with a small concentration of nitrogen (N2), passes through a normal shock wave. Conditions just downstream of the shock wave are as follows: static temperature of 5000 K, static pressure of 10 KPa, and velocity relative to the shock wave of 150 m/s. The N2 begins to dissociate to N downstream of the shock wave according to the following reaction: where M is any molecule in the system and the reverse reaction is not important for these conditions because N2 will be almost fully dissociated to N when reaction is complete. Furthermore, the concentration of N2 is small enough so that changes of the static temperature and pressure, and the velocity relative to the shock wave, are negligible as the reaction proceeds. Finally, transport is negligible during the reaction process. Tables of the reaction rate constants give k2 = 2.0 x 10^7 m^6/(kgmol^2s) for the present conditions. Furthermore, the equilibrium constant in terms of molal concentrations, Kc, for the following stoichiometry: is Kc = 20.0 kgmol/m^3. Please do the following:

Explanation / Answer

As per the given data here, intermediate is N

so d[N] / dt = K1[N2][M] + K2[N][N][M] = 0

K1 = -K2[N][N][M] / [N2][M] = -K2[N][N] / [N2] .......................1

Also d[N2] /dt = 0 at equilibrium so

d[N2]/ dt = Kc[N2] + Kc' [N]^2 = 0

Or

Kc[N2] = Kc'[N]^2 .............(2)

[N][N] / [N2] = Kc / Kc' ....(3)

On putting values from table and equation 1 and 3 we can calcualte the value of Kc

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