At the transition temperature T, A ⇌ B and ΔG$$^0$$ = 105 − 35 log T where A and B are two states of substance X. The transition temperature in °C when pressure is 1 atm is __________. (Nearest integer)

For the one-component equilibrium $$A \rightleftharpoons B$$, the criterion for equilibrium at pressure $$1\,$$atm is

$$\Delta G = 0.$$

When the substances are taken in their standard states, $$\Delta G = \Delta G^{0}$$, so at the transition temperature $$T_{t}$$ we must have

$$\Delta G^{0}(T_{t}) = 0.$$

The temperature-dependence of the standard Gibbs free-energy change is given as

$$\Delta G^{0} = 105 - 35 \log T \qquad (\text{units consistent; } \log \text{ is base }10).$$

Setting $$\Delta G^{0}=0$$ for the transition:

$$0 = 105 - 35 \log T_{t}$$

$$35 \log T_{t} = 105$$

$$\log T_{t} = \frac{105}{35} = 3$$

$$T_{t} = 10^{3} = 1000 \text{ K}.$$

Convert the Kelvin temperature to Celsius:

$$T_{(\!^{\circ}\!C)} = T_{(\!K)} - 273 \approx 1000 - 273 = 727^{\circ}\!C.$$

Hence, the transition temperature is approximately 727 °C.