The standard molar enthalpy of formation (ΔH_f^°) is defined as the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states at 298 K (25°C). By convention, the standard enthalpy of formation for any element in its most stable form at 298 K is assigned a value of zero.

Let's analyze each option:

Br₂(g): Bromine's most stable state at 298 K is liquid (Br₂(l)), not gas. Therefore, ΔH_f^° for Br₂(g) is not zero.

CH₄(g): Methane is a compound, not an element. Its formation from carbon (graphite) and hydrogen (H₂(g)) has a significant enthalpy change (ΔH_f^° = -74.8 kJ/mol).

H₂O(g): Water vapor is a compound. Its formation from hydrogen (H₂(g)) and oxygen (O₂(g)) also has a non-zero enthalpy (ΔH_f^° = -241.8 kJ/mol).

Cl₂(g): Chlorine's most stable form at 298 K is indeed diatomic gas. Therefore, by definition, its standard molar enthalpy of formation is zero.

The key concept is that for any element in its standard state (the most stable physical form at 298 K and 1 atm pressure), ΔH_f^° = 0. For chlorine, the standard state is Cl₂(g).

Related Topics and Formulae

Standard State: The reference state for an element is its most stable form under standard conditions (1 atm pressure and specified temperature, usually 298 K). Examples include:

• H₂(g) for hydrogen
• O₂(g) for oxygen
• C(s, graphite) for carbon
• Br₂(l) for bromine
• Cl₂(g) for chlorine

Enthalpy of Formation Equation: The standard enthalpy change for a reaction can be calculated using: $\Delta H^{°}=\sum \Delta H_f^{°}\left(\mathrm{products}\right)-\sum \Delta H_f^{°}\left(\mathrm{reactants}\right)$

Key Theory: This convention simplifies thermochemical calculations because elements in their standard states serve as a baseline (zero energy) for measuring the energy stored in chemical bonds when compounds are formed.