GATE 2025 MT – Question 51

Metallurgical Thermodynamics · Reaction equilibria and Ellingham diagrams · 2 marks · Numerical answer

Molten steel at 1900 K containing dissolved hydrogen must be vacuum degassed. The equilibrium hydrogen partial pressure needed to achieve 1 ppm (mass basis) dissolved hydrogen is ______ Torr (rounded to two decimal places). For $\tfrac12\mathrm H_2(g)=[H]$, the equilibrium constant expressed using ppm dissolved H satisfies $\log_{10}K_{eq}=-1900/T+2.4$. Given: 1 atm = 760 Torr.

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Correct answer: 1.19 to 1.22

Explanation

At 1900 K, $\log_{10}K_{eq}=-1+2.4=1.4$, so $K_{eq}=10^{1.4}$.

For hydrogen dissolution, $[H]=K_{eq}\sqrt{p_{H_2}}$, with pressure in atm. Setting $[H]=1$ ppm gives $p_{H_2}=10^{-2.8}=0.00158489\ldots$ atm.

Convert to Torr: $760\times0.00158489=1.2045\ldots$. The answer is **1.20 Torr**.