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  • The pH of pure water at 250C and 450C are 7 and 5.5 respectively. Calculate the heat of dissociation of H2O into H+ and OH- ions.

The pH of pure water at 250C and 450C are 7 and 5.5 respectively. Calculate the heat of dissociation of H2O into H+ and OH- ions.

Option: 1

65.5 kcal/mol


Option: 2

98.5 kcal/mol


Option: 3

10 kcal/mol


Option: 4

Data inadequate


Answers (1)

best_answer

We have given,

\begin{array}{ll}{\text { At } 25^{\circ} \mathrm{C} ;} & {\left[\mathrm{H}^{+}\right]=10^{-7} \quad \therefore K_{w}=10^{-14}} \\ {\text { At } 45^{\circ} \mathrm{C} ;} & {\left[\mathrm{H}^{+}\right]=10^{-5.5} \quad \therefore K_{w}=10^{-11}}\end{array}

Now using the van't Hoff's equation for the dependance of Keq on the Temperature,

\mathrm{2.303 \log _{10} \frac{K_{w_{2}}}{K_{w_{1}}}=\frac{\Delta H}{R}\left [ \frac{1}{T_1}-\frac{1}{T_2} \right ]}

Here, R = 2cal /mol.K

T1 = 25 0C = 298 K

T2 = 45 0C = 318 K

putting this values in the above equation.

2.303 \log _{10} \frac{10^{-11}}{10^{-14}}=\frac{\Delta H}{2}\left[\frac{318-298}{318 \times 298}\right]

\Rightarrow \Delta H = 65472.45\; cal/mol

\Rightarrow \Delta H = 65.5\; kcal/mol

Hence, the correct answer is Option (1)

Posted by

Kuldeep Maurya

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