To determine the temperature [tex]\( T_{eq} \)[/tex] at which the forward and reverse corrosion reactions occur in equilibrium, we need to use the Gibbs free energy equation at equilibrium. The Gibbs free energy [tex]\( G \)[/tex] is given by:
[tex]\[ G = H - T S \][/tex]
At equilibrium, the Gibbs free energy change [tex]\( \Delta G \)[/tex] for the reaction is zero:
[tex]\[ \Delta G = \Delta H - T_{eq} \Delta S = 0 \][/tex]
We can rearrange this equation to solve for the equilibrium temperature [tex]\( T_{eq} \)[/tex]:
[tex]\[ T_{eq} = \frac{\Delta H}{\Delta S} \][/tex]
Let's use the given values for the enthalpy change [tex]\( \Delta H \)[/tex] and entropy change [tex]\( \Delta S \)[/tex] to find [tex]\( T_{eq} \)[/tex]. We need to ensure the units are consistent, so we first convert the enthalpy change from kJ to J (since [tex]\( 1 \, \text{kJ} = 1000 \, \text{J} \)[/tex]):
[tex]\[ \Delta H = -3352 \, \text{kJ} = -3352 \times 1000 \, \text{J} \][/tex]
[tex]\[ \Delta H = -3352000 \, \text{J} \][/tex]
Now, we can substitute the values into the equation:
[tex]\[ T_{eq} = \frac{\Delta H}{\Delta S} \][/tex]
[tex]\[ T_{eq} = \frac{-3352000 \, \text{J}}{-625.1 \, \text{J/K}} \][/tex]
Evaluating this expression gives the equilibrium temperature:
[tex]\[ T_{eq} = 5362.342025275956 \, \text{K} \][/tex]
Therefore, the temperature [tex]\( T_{eq} \)[/tex] at which the forward and reverse corrosion reactions occur in equilibrium is approximately:
[tex]\[ \begin{array}{|c|c|}
\hline
5362 & \text{K} \\
\hline
\end{array} \][/tex]
This can be expressed as:
[tex]\[ \boxed{5362 \, \text{K}} \][/tex]
