For reaction A⇌ B ΔG° = 105 – 35 log T Find the transition temperature (in °C) of the above reaction at 1 bar

The correct answer is 727.

Step-by-step Explanation:

For the given reaction:
A ⇌ B

The standard Gibbs free energy change ($\Delta G^{\circ }$) as a function of temperature ($T$ in Kelvin) is given by the relation:
$\Delta G^{\circ }=105-35\log T$

The transition temperature is the temperature at which the reaction is in a state of equilibrium under standard conditions (1 bar). At equilibrium, the change in standard Gibbs free energy is zero:
$\Delta G^{\circ }=0$

Substituting this condition into the given equation:
$105-35\log T=0$

Rearranging the equation to solve for $\log T$:
$35\log T=105$

$\log T=\frac{105}{35}$

$\log T=3$

Assuming the logarithm is base 10 (common logarithm), we solve for $T$:
$T={10}^3$

$T=1000\text{K}$

To find the transition temperature in degrees Celsius ($°\text{C}$), we convert the temperature from Kelvin using the relation:
$T(°\text{C})=T\left(\text{K}\right)-273$

$T(°\text{C})=1000-273$

$T(°\text{C})=727°\text{C}$

Thus, the transition temperature of the reaction at 1 bar is 727 °C.