The temperature at which the following process reaches equilibrium at 1.0 atm is the normal melting point for phosphoric acid. H₃PO₄(s) ⇄ H₃PO₄(l)
Use the following thermodynamic information at 298 K to determine this temperature.

Question

The temperature at which the following process reaches equilibrium at 1.0 atm is the normal melting point for phosphoric acid. H<sub>3</sub>PO<sub>4</sub>(s) ⇄ H<sub>3</sub>PO<sub>4</sub>(l) Use the following thermodynamic information at 298 K to determine this temperature. A) 286 K B) 305 K C) 315 K D) 347 K E) 3170 K

Quizplus · Accepted Answer

The melting point corresponds to the temperature at which the Gibbs free energy change ($\Delta G$) of the process becomes zero. At equilibrium, $\Delta G = 0$ and we can use the equation $\Delta G = \Delta H - T\Delta S$ to solve for the temperature. 
\begin{align*}
0 &= \Delta H - T\Delta S\
T &= \frac{\Delta H}{\Delta S}
\end{align*}
Using the given thermodynamic data, we find that $\Delta H = 17.9$ kJ/mol and $\Delta S = 48.7$ J/(mol K). Substituting these values into the equation above, we get:
\begin{align*}
T &= \frac{\Delta H}{\Delta S}\
&= \frac{17.9 	imes 10^3	ext{ J/mol}}{48.7	ext{ J/(mol K)}}\
&\approx \boxed{	extbf{(C) }315	ext{ K}}
\end{align*}

The Temperature at Which the Following Process Reaches Equilibrium at 1.0