Question

For reaction $A \rightleftharpoons B$, $\Delta G^{\circ} = 105 - 35 \log T$. Find the transition temperature (in $^{\circ} C$) of the above reaction at 1 bar.

Answer 1

The transition temperature is the temperature at which the system is at equilibrium between two states, which implies $\Delta G^{\circ} = 0$.
1. Set equilibrium condition:
At transition temperature, $\Delta G^{\circ} = 0$.

2. Solve for T:
$105 - 35 \log T = 0$
$35 \log T = 105$
$\log T = \frac{105}{35} = 3$
$T = 10^3 = 1000 \text{ K}$

3. Convert to Celsius:
$t = T - 273$
$t = 1000 - 273 = 727^{\circ} C$

The transition temperature is 727 $^{\circ} C$.