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Q#1 GATE CH 2021 NAT +2 marks -0.66 marks

A binary liquid mixture consists of two species 1 and 2. Let ๐œธย and ๐’™ย represent the activity coefficient and the mole fraction of the species, respectively. Using a molar excess Gibbs free energy model, ๐ฅ๐งย ๐œธ๐Ÿย ๐’—๐’”. ๐’™๐Ÿย and ๐ฅ๐งย ๐œธ๐Ÿย ๐’—๐’”. ๐’™๐Ÿย are plotted. A tangent drawn to the ๐ฅ๐งย ๐œธ๐Ÿย ๐’—๐’”. ๐’™๐Ÿ curve at a mole fraction of ๐’™๐Ÿย = ๐ŸŽ. ๐Ÿย has a slope = โˆ’1.728.

The slope of the tangent drawn to the ๐ฅ๐งย ๐œธ๐Ÿย ๐’—๐’”. ๐’™๐Ÿย curve at the same mole fraction is________(correct to 3 decimal places).

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