A Magic solution was prepared by a Kota Teacher such that:
$A (g) + 10 (a q) ⟶ A \cdot 10 (a q); Δ H = - 10 kJ / mol$
For 1 mole of $H_{2} O$ added to this Magic solution enthalpy of dilution is $- 5 kJ / mol;$ for 2 nd mole it becomes $- \frac{5}{2} kJ / mol$ for 3 rd mole it becomes $- \frac{5}{2^{2}} kJ / mol$ and so on.
To mark the celebration of rank-1 of IIT JEE-2016, 'KOTA CLASSES' asked the top ranker to add a very large amount of water to this Magic solution. The heat energy released is $40 %$ converted to useful work of burning fire crackers for celebration. Find the magnitude of useful work obtained (in kJ/mol) from such Magic solution containing 1 mole of A.

Question

Accepted Answer

A(g)+∞aq⋅⟶A∞aqΔH=−10+5+52+522+…+52n =−10−51+12+122…+12n =−10−511−12 =−20kJ/molEnthalpy of dilution= -10 k.J/molΔG=−0.4×10=−4kJ/mol

Detailed Solution