Question

The pH of pure water at 300 K and 310 K are 7 and 6 respectively. Calculate the heat of formation of water from $H^{+}$ and $O{H}^{-}$ ions.
(Take R = 2 cal/Kmol)

• A. 85.56 kcal
• B. 42.78 kcal
• C. 0
• D. -85.56 kcal

Answer 1

The correct option is D -85.56 kcal

$K_{w\left(310K\right)}={10}^{-12}$ and $K_{w\left(300K\right)}={10}^{-14}$
Using the arhenious equation
$ln\frac{{10}^{-12}}{{10}^{-14}}=\frac{\Delta H}{R}\frac{(T_2-T_1)}{T_1{T}_2}$

$\Delta H=\frac{2.3\times 2\times 300\times 310}{310-300}=85.56kcal$

Now this enthalpy change is for dissociation of water since we have taken $K_w$ values.
$\therefore \Delta H_f=-85.56kcal$