આપેલ ઉષ્મારાસાયણિક વિગતો પરથી $25\,^o C$ તાપમાને $OH^-$ આયનની સર્જન એન્થાલ્પી .......... $\mathrm{kJ}$ માં ગણો. $(\Delta _fG^oH^+_{(aq)} = 0)$

$H_2O(l) \rightarrow H^+(aq) + OH^-(aq)\,;\,\,\Delta H = 57.32\,kJ$

$H_2(g)+ \frac{1}{2} O_2(g) \rightarrow H_2O(l)\,;\,\, \Delta H=-286.20\,kJ$

Question

આપેલ ઉષ્મારાસાયણિક વિગતો પરથી $25\,^o C$ તાપમાને $OH^-$ આયનની સર્જન એન્થાલ્પી .......... $\mathrm{kJ}$ માં ગણો. $(\Delta _fG^oH^+_{(aq)} = 0)$

$H_2O(l) \rightarrow H^+(aq) + OH^-(aq)\,;\,\,\Delta H = 57.32\,kJ$

$H_2(g)+ \frac{1}{2} O_2(g) \rightarrow H_2O(l)\,;\,\, \Delta H=-286.20\,kJ$

A$-228.88$
B$+228.88$
C$-343.52$
D$-22.88$

AIEEE 2009, Diffcult

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Solution

a
Given, for reaction

$(i)$ $\quad H_{2} O(\ell) \rightarrow H^{+}(a q .)+O H^{-}(a q .)$

$\Delta H_{r}=57.32 \,k J$

$(ii)$ $\quad H_{2}(g)+\frac{1}{2} O_{2}(g) \rightarrow H_{2} O(\ell)$

$\Delta H_{r}=-286.20 \,k J$

For reaction $(i)$

$\Delta {H_r} = \Delta H_f^o\left( {{H^ + },aq} \right) + \Delta H{\mkern 1mu} _f^o\left( {O{H^ - }.aq} \right) - \Delta H{\mkern 1mu} _f^o\left( {{H_2}O,\ell } \right)$

$57.32 - 0 + \Delta H{\mkern 1mu} _f^o\,\left( {O{H^{ - 1}},aq} \right) - \quad \Delta H_f^o\left( {{H_2}O,\ell } \right)\quad \ldots (iii)$

For reaction $(ii)$

$\Delta {H_r} = \Delta H_f^o\left( {{H_2}O,l} \right) + \Delta H_f^o\left( {{H_2}O,\,l} \right) - \Delta H_f^o\left( {{H_2},g} \right) - \frac{1}{2}\Delta H_f^o({O_2},g)$

$ - 286.20 = \Delta H_f^o\,({H_2}O,l)$

On replacing this value in equ. $(iii)$ we have

$57.32 = \Delta H_f^o\left( {O{H^ - },aq} \right) - ( - 286.20)$

$\Delta H_f^o = - 286.20 + 57.32$

$=-228.88 \,k J$

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