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GATE 2025 MT – Question 34

Metallurgical Thermodynamics · Reaction equilibria and Ellingham diagrams · 1 mark · Numerical answer

For the gas-phase reaction $\mathrm{CO}+\tfrac12\mathrm O_2\rightleftharpoons\mathrm{CO}_2$, equilibrium partial pressures at a particular temperature are $p_{CO}=10^{-6}$ atm, $p_{O_2}=10^{-6}$ atm, and $p_{CO_2}=16$ atm. The equilibrium constant is ______ $\times10^{10}$ (rounded to one decimal place).

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Show answer and explanation

Correct answer: 1.6 to 1.6

Explanation

The equilibrium expression is $K_p=p_{CO_2}/(p_{CO}\sqrt{p_{O_2}})$, using pressures relative to the 1 atm standard state.

Substitute: $K_p=16/(10^{-6}\times10^{-3})=1.6\times10^{10}$. The requested coefficient is **1.6**.