Question

At the transition temperature \(T\), \(A \rightleftharpoons B\) and \(\Delta G^\circ = 105 - 35\log T\), where \(A\) and \(B\) are two states of substance \(X\). The transition temperature in \(^{\circ}C\) when pressure is 1 atm is ______.

Answer 1

Correct Answer: 727

Step 1: Understanding the Concept:
Transition temperature is the temperature at which two phases or states of a substance are in equilibrium.
At equilibrium, the change in Gibbs free energy (\(\Delta G^0\)) is zero.
Step 2: Detailed Explanation:
Set \(\Delta G^0 = 0\) to find the transition temperature:
\[ 0 = 105 - 35 \log T \]
\[ 35 \log T = 105 \]
Divide both sides by 35:
\[ \log T = \frac{105}{35} = 3 \]
The logarithm is base 10:
\[ T = 10^3 = 1000 \text{ K} \]
Convert temperature from Kelvin to Celsius:
\[ T(^{\circ}C) = 1000 - 273 = 727^{\circ}C \].
Step 3: Final Answer:
The transition temperature is 727 \(^{\circ}C\).