Transition Temperature Calculation from Gibbs Free Energy

At the transition temperature between two states $\text{A}$ and $\text{B}$ of a substance ($\text{A} \rightleftharpoons \text{B}$) at a pressure of $1\text{ atm}$, both states are in thermodynamic equilibrium. Therefore, the standard Gibbs free energy change for the phase transition is zero: $\Delta G^0 = 0$

We are given the expression for the standard Gibbs free energy change as: $\Delta G^0 = 105 - 35 \log T$

Substitute $\Delta G^0 = 0$ into the expression: $105 - 35 \log T = 0$

Rearranging the terms to solve for $\log T$: $35 \log T = 105$ $\log T = \frac{105}{35} = 3$

Taking the inverse logarithm (base 10): $T = 10^3\text{ K} = 1000\text{ K}$

To find the transition temperature in degrees Celsius (${}^\circ\text{C}$): $T({}^\circ\text{C}) = T(\text{K}) - 273$ $T({}^\circ\text{C}) = 1000 - 273 = 727^\circ\text{C}$

Hence, the transition temperature in ${}^\circ\text{C}$ is 727.