Final answer:
To find the enthalpy change for 2B → C, we apply Hess's Law by reversing the first reaction A → 2B and combining it with the second reaction A → C. This gives a total enthalpy change of -478.8 kJ for the 2B → C process.
Step-by-step explanation:
To calculate the enthalpy change for the process 2B → C, we need to use the concept of Hess's Law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps into which a reaction can be divided. The first given reaction is A → 2B with an enthalpy change (ΔH°rxn) of +456.7 kJ/mol. The second reaction is A → C with an enthalpy change of -22.1 kJ/mol.
We know that enthalpy is a state function, meaning that it does not depend on the path taken from reactants to products, only the initial and final states. So, to get from 2B → C, we can reverse the first reaction to get B from A, and then use the second reaction to get to C from A. When we reverse the first reaction, we change the sign of the enthalpy, making it -456.7 kJ/mol for A → 2B. Adding it to the enthalpy for the second reaction, we get:
(-456.7 kJ/mol) + (-22.1 kJ/mol) = -478.8 kJ/mol for 2B → C.
The standard enthalpy change for the reaction 2B → C is therefore ΔH° = -478.8 kJ.