## explain what assumptions were x2 made in the derivation of Krichevsky-Kasarnovsky equation.

The Krichevsky-Kasarnovsky (K-K) equation is valid for a solution of hydrogen (2) in liquid nitrogen (1) at high pressure:
Ln (f2G vr(P — Nat) —) = In H2,1 (Plat) + X2 RT
(1)
fc Write out the EXACT equation for In (IL) at high pressure P. Then explain what assumptions were x2 made in the derivation of Krichevsky-Kasarnovsky equation. (b) Use the Krichevsky-Kasarnovsky (K-K) equation [eqn. (1)] to calculate the solubility x2 of hydrogen (2) in liquid nitrogen (1) at 77 K and 100 bar. Assume the vapor is pure hydrogen. The following parameters have been reported for this system at those conditions:
og = 0.88 Plat = 1 bar H21 (Plat) = 467 bar V2° = 31.3 cm3.mor1
(c) The solubility, X2, of hydrogen (2) in liquid nitrogen (1) at 77K and 100 bar using the Krichevsky-Ilinskaya (K-I) equation below [eqn. (2)] is around 0.17,
In ()f26A _ = In H2,1 (Plat) + )7- . (x2 — 1) +1700(p RT plat) T
2
where A is a constant for the system. Compare the result of X2 obtained by the Krichevsky-Kasarnovsky equation (in part b) and by the Krichevsky-Ilinskaya equation (x2=0.17). Which result do you think is closer to the experimental value? Explain the reason.

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