Q.Given $N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)$; $\Delta_r H = -92.4$ kJ mol$^{-1}$. What is the standard enthalpy of formation of $NH_3$ gas?

Standard Enthalpy of Formation: From Intuition to Definition

Imagine you're building a house. You don't start from a finished house — you start from raw materials: bricks, cement, wood, steel. The cost of assembling those raw materials into the final house is a useful number. In chemistry, we do the same thing with compounds.

Every chemical compound is made from elements in their natural, most stable forms. The standard enthalpy of formation ($\Delta_f H^\circ$) is the energy change when you build one mole of a compound from its elements, with everything in their standard states.

The Intuition First

Think of it as the "birth certificate" energy of a compound. It tells you:

• How much energy is released or absorbed when the compound is formed from scratch.
• Whether the compound is more stable (lower energy) or less stable (higher energy) than the elements it came from.

If $\Delta_f H^\circ$ is negative, the compound is more stable than its elements — energy was released during formation. If positive, the compound is less stable — energy had to be absorbed to force the elements together.

The Precise Definition

Key points to lock in:

1. Exactly 1 mole of the compound is formed — not 2, not 0.5.
2. Elements in their standard states — this means the most stable physical form of the element at 1 bar and the given temperature. For example:
   • Carbon: graphite (not diamond)
   • Oxygen: $O_2(g)$ (not $O_3$)
   • Hydrogen: $H_2(g)$
   • Bromine: $Br_2(l)$ (liquid at room temperature)
3. Standard conditions: 1 bar pressure (not 1 atm — slight difference, but in most exams they treat them as equivalent unless specified). Temperature is usually 298 K (25°C), but can be any specified temperature.

The Critical Rule: Elements Have Zero Formation Enthalpy

This is not a measurement — it's a convention. We set the zero point of the energy scale at the most stable form of each element. So:

• $\Delta_f H^\circ$ of $O_2(g)$ = 0
• $\Delta_f H^\circ$ of $C(graphite)$ = 0
• $\Delta_f H^\circ$ of $Br_2(l)$ = 0

But $\Delta_f H^\circ$ of $O_3(g)$ is not zero — ozone is not the standard state of oxygen.

Worked Example: Water

Write the formation reaction for liquid water:

The $\Delta_f H^\circ$ for $H_2O(l)$ is $-285.8 \text{ kJ/mol}$.

What does this tell you? When 1 mole of water is formed from hydrogen gas and oxygen gas (both in their standard states), 285.8 kJ of heat is released. The water molecule is more stable than the separate elements.

Common Mistake to Avoid …