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GATE 2022 MT – Question 12

Metallurgical Thermodynamics · Reaction equilibria and Ellingham diagrams · 1 mark · Multiple choice

By Sieverts’ law, the equilibrium solubility of nitrogen gas in molten steel is proportional to ______. Its equilibrium partial pressure is $p_{N_2}$.

  1. $p_{N_2}$
  2. $\sqrt{p_{N_2}}$
  3. $1/p_{N_2}$
  4. $p_{N_2}^2$

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Correct answer: (B) $\sqrt{p_{N_2}}$

Explanation

Dissolution obeys $\tfrac12N_2(g)\rightleftharpoons[N]$. At equilibrium, $K=a_N/p_{N_2}^{1/2}$. In the dilute limit, nitrogen concentration is proportional to $\sqrt{p_{N_2}}$, **B**.