Certainly! I can guide you through the process step by step.
To use Hess's law, we need to manipulate the given reactions in order to obtain the target reaction. Here's how we can do it:
Step 1: Write the given reactions and their enthalpy changes:
Reaction 1: 2A + 2/3C2 → A2C3 ΔH = -1874 kJ
Reaction 2: 2B + 2/3C2 → B2C3 ΔH = -285 kJ
Step 2: Compare the given reactions to the target reaction and identify the necessary steps to reach it.
In the target reaction, we need to obtain 2A and A2C3 on the reactant side, and 2B and B2C3 on the product side.
Step 3: Reverse one of the reactions if necessary.
In reaction 1, A2C3 is on the product side, but we need it on the reactant side. So, we reverse it.
Revised Reaction 1: A2C3 → 2A + 2/3C2 ΔH = +1874 kJ
Step 4: Multiply or divide the reactions to match the stoichiometry of the target reaction.
In reaction 2, we need 2B on the product side, but currently, we only have one. So, we multiply reaction 2 by 2.
Revised Reaction 2: 4B + 4/3C2 → 2B2C3 ΔH = -570 kJ
Step 5: Combine the manipulated reactions to obtain the target reaction.
When we add the revised reactions together, the reactants on one side will cancel out the products on the other side, leaving us with the target reaction.
Target Reaction: 2A + 2B2C3 → 2B + A2C3
Now, we need to sum up the enthalpy changes to calculate ΔH for the target reaction.
Step 6: Add up the enthalpy changes.
-1874 kJ + (-570 kJ) = -2444 kJ
So, the ΔH for the given reaction 2A + 2B2C3 → 2B + A2C3 is -2444 kJ.
I hope this step-by-step explanation helps you understand how to use Hess's law to calculate ΔH for a reaction.