Synthesis gas, a mixture of carbon monoxide and hydrogen gas, is produced industrially by reacting solid carbon with steam according to the following equation:

\[ \text{C}(s) + \text{H}_2\text{O}(g) \rightarrow \text{CO}(g) + \text{H}_2(g) \]

The standard enthalpy changes for three related thermochemical equations are given in the table below.

Equation	Reaction	\(\Delta H^\circ\) (\(\text{kJ/mol}_{rxn}\))
(1)	\(\text{C}(s) + \text{O}_2(g) \rightarrow \text{CO}_2(g)\)	\(-394\)
(2)	\(2\,\text{CO}(g) + \text{O}_2(g) \rightarrow 2\,\text{CO}_2(g)\)	\(-566\)
(3)	\(2\,\text{H}_2(g) + \text{O}_2(g) \rightarrow 2\,\text{H}_2\text{O}(g)\)	\(-484\)

Based on the information provided, what is the value of \(\Delta H^\circ\) for the reaction \(\text{C}(s) + \text{H}_2\text{O}(g) \rightarrow \text{CO}(g) + \text{H}_2(g)\)?