GATE 2026 MT – Question 53
20 g of gold (Au) and 20 g of silver (Ag) are mixed to form a single-phase solid solution (assume ideal mixing). The atomic weight of Au is 197 g/mol and the atomic weight of Ag is 108 g/mol. The value of universal gas constant R is 8.314 J/mol-K. The total entropy of mixing (rounded off to two decimal places) is ___________ J/K.
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Correct answer: 1.50 to 1.60
Explanation
The amounts are $n_{Au}=20/197=0.101523\ \mathrm{mol}$ and $n_{Ag}=20/108=0.185185\ \mathrm{mol}$. Their mole fractions are approximately 0.35410 and 0.64590.
For ideal mixing, the total entropy increase is $\Delta S=-R(n_{Au}\ln x_{Au}+n_{Ag}\ln x_{Ag})$. Substituting $R=8.314$ gives **1.55 J/K**. This is the total entropy for the supplied masses, rather than molar mixing entropy.