Using the given relationship and the stoichiometry of the reaction, we can apply the thermodynamic calculations to find the change in enthalpy for \( B + D \rightarrow E + 2C \). Substituting into the equation, we get \( \Delta H = -175 \, \text{kJ/mol} \).
Step 2: Conclusion.
The enthalpy change for the reaction is \( -175 \, \text{kJ/mol} \), corresponding to option (b).