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GATE 2019 MT – Question 50

Metallurgical Thermodynamics · Solutions and chemical potential · 2 marks · Numerical answer

Find the zinc partial pressure in torr in equilibrium with liquid lead containing 0.03 mole% zinc at 900 K. Pure-zinc vapour pressure is 0.027 atm; the infinite-dilution Raoult-scale activity coefficient is 8.55. Use 1 torr=1.316×10⁻³ atm (two decimal places).

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Correct answer: 0.04 to 0.06

Explanation

Mole fraction is 0.03/100=0.0003. In the dilute limit, $p_{Zn}=\gamma^\infty x_{Zn}p_{Zn}^\circ=8.55(0.0003)(0.027)=6.9255\times10^{-5}$ atm. Dividing by 0.001316 atm/torr gives 0.05263 torr, or 0.05.

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