Q.Enthalpy is an extensive property. In general, if enthalpy of an overall reaction A→B along one route is ΔrH and ΔrH1, ΔrH2, ΔrH3 ..... represent enthalpies of intermediate reactions leading to product B. What will be the relation between ΔrH for overall reaction and ΔrH1, ΔrH2 ..... etc. for intermediate reactions.

Concept: Hess’s Law — enthalpy is a state function, so the total enthalpy change for a reaction depends only on the initial and final states, not on the path taken.

Since enthalpy is extensive, the enthalpy change for the overall reaction is simply the sum of the enthalpy changes of the intermediate steps, provided the initial and final states match.

If the intermediate reactions add up exactly to the overall reaction A → B, then:

$\Delta_r H = \Delta_r H_1 + \Delta_r H_2 + \Delta_r H_3 + \dots$ …

The key idea here is that enthalpy is a state function. That means its value depends only on the initial and final states of the system — not on the path taken between them. This is the foundation of Hess’s Law.

Think of it like climbing a mountain. The change in your altitude from base camp to the summit is the same whether you go straight up or take a winding trail with several rest stops. The total vertical gain is just the sum of the gains on each segment. Enthalpy works exactly the same way: the total enthalpy change for a reaction is the sum of the enthalpy changes for any sequence of steps that gets you from the same reactants to the same products.

Now, let’s apply this to your question step by step.

1. Identify the overall process. You have a reaction $A \rightarrow B$ with an overall enthalpy change $\Delta_r H$. This is the enthalpy difference between the initial state (reactants $A$) and the final state (products $B$).

2. Consider the intermediate route. Instead of going directly from $A$ to $B$, suppose the reaction proceeds through a series of intermediate steps: $A \rightarrow X_1$, $X_1 \rightarrow X_2$, $X_2 \rightarrow X_3$, and so on, until finally reaching $B$. Each step has its own enthalpy change: $\Delta_r H_1$, $\Delta_r H_2$, $\Delta_r H_3$, etc.

3. Apply Hess’s Law. Since enthalpy is a state function, the total enthalpy change for the indirect route must equal the enthalpy change for the direct route. The total enthalpy change for the indirect route is simply the sum of the enthalpy changes of each intermediate step.