Condition for Carbon monoxide to be produced

Chemistry Level pending

Carbon monoxide (CO) is a colorless, odorless, and tasteless gas that is slightly less dense than air. It is toxic to humans and animals when encountered in higher concentrations. In the atmosphere, it is spatially variable and short lived, having a role in the formation of ground-level ozone. Carbon and water vapor can react to produce carbon monoxide and hydrogen gas as follows: \begin{align} \text{C}(s)+\text{H}_2\text{O}(g) \to \text{CO}(g)+\text{H}_2(g), \\ \Delta H=131 \text{ kJ}, \quad \Delta S=134 \text{ J/K}. \end{align} Carbon and water vapor do not react at room temperature. What is the temperature condition for this reaction to occur spontaneously?

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