The Heat of Solution of.... | JEE Main 2024 | Thermodynamics

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JEE MAIN 2024

04-04-24 S1

Question

The heat of solution of anhydrous $\mathrm{CuSO}_4$ and $\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}$ are $-70 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $+12 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively.
The heat of hydration of $\mathrm{CuSO}_4$ to $\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}$ is $-\mathrm{x} k \mathrm{~K}$. The value of x is $\_\_\_\_$ .

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Solution

(1) $\mathrm{CuSO}_4(\mathrm{~s})+5 \mathrm{H}_2 \mathrm{O} \xrightarrow{\mathrm{x}} \mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}$
(2) $\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}+\mathrm{H}_2 \mathrm{O} \xrightarrow{12} \mathrm{CuSO}_4(\mathrm{aq})$
$ \mathrm{CuSO}_4+\mathrm{H}_2 \mathrm{O} \xrightarrow{-70} \mathrm{CuSO}_4(\mathrm{aq})
$ from (1) & (2)
$ -70=x+12
$ $ x=-82 $

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