Question

The pH of pure water at $25^{\circ }C$ and $35^{\circ }C$ are $7$ and $6$ respectively. The heat of formation of water from $H^{+}$ and $O{H}^{-}$ is_____.

Answer 1

Answer: 84.55

At $25^{\circ }C;\left[H^{+}\right]=10^{-7}$

$\therefore K_w=10^{-14}$

At $35^{\circ }C;\left[H^{+}\right]=10^{-6}$

$\therefore K_w=10^{-12}$

Now using

$2.303\log \frac{K_{w_2}}{K_{w_1}}=\frac{\Delta H}{R}\left[\frac{T_2-T_1}{T_1\times T_2}\right]$

$2.303\log \frac{10^{-12}}{10^{-14}}=\frac{\Delta H}{2}\left[\frac{10}{298\times 308}\right]$

$\therefore \Delta H=84551.4cal/mol$

$=84.551kcal/mol$

Thus, $H_{2}O\rightleftharpoons H^{+}+O{H}^{-}$

$\Delta H=-84.551kcal/mol$