Standard Enthalpy of Formation — Revision Notes

⚡ 30-Second Revision

Definition — $\Delta H_f^\circ$ is enthalpy change for forming 1 mole of compound from elements in standard states.
Standard Conditions — $298.15\,\text{K}$ ($25^\circ\text{C}$), $1\,\text{bar}$ pressure.
Standard State of Elements — Most stable form at standard conditions (e.g., $\text{O}_2(\text{g})$, $\text{C}(\text{graphite})$). $\Delta H_f^\circ = 0$ for these.
Hess's Law Formula — $\Delta H_{rxn}^\circ = \sum n_p \Delta H_f^\circ(\text{products}) - \sum n_r \Delta H_f^\circ(\text{reactants})$.
Sign — Negative $\Delta H_f^\circ$ = exothermic, more stable; Positive $\Delta H_f^\circ$ = endothermic, less stable.

2-Minute Revision

Standard Enthalpy of Formation ($\Delta H_f^\circ$) is a key concept in thermochemistry. It quantifies the heat change when one mole of a compound is synthesized directly from its constituent elements, which must be in their most stable physical and allotropic forms (standard states) at standard conditions ($298.

15\,\text{K}$,$1\,\text{bar}$). A crucial convention is that the$\Delta H_f^\circ$ for any element in its standard state is defined as zero. This provides a universal reference point for all compounds.

The primary utility of $\Delta H_f^\circ$ values is in calculating the standard enthalpy change for any chemical reaction ($\Delta H_{rxn}^\circ$) using Hess's Law. The formula is $\Delta H_{rxn}^\circ = \sum n_p \Delta H_f^\circ(\text{products}) - \sum n_r \Delta H_f^\circ(\text{reactants})$, where $n_p$ and $n_r$ are stoichiometric coefficients.

Remember to always write a balanced chemical equation, correctly identify standard states (and thus zero $\Delta H_f^\circ$ values), and pay close attention to signs and stoichiometry during calculations.

A negative $\Delta H_f^\circ$ indicates an exothermic formation and generally a more stable compound, while a positive value suggests an endothermic formation and a less stable compound.

5-Minute Revision

The Standard Enthalpy of Formation ($\Delta H_f^\circ$) is the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states under standard conditions. Standard conditions are typically $298.

15\,\text{K}$($25^\circ\text{C}$) and$1\,\text{bar}$pressure. The 'standard state' for an element is its most stable physical and allotropic form at these conditions (e.g.,$\text{O}_2(\text{g})$,$\text{C}(\text{graphite})$,$\text{Br}_2(\text{l})$).

A fundamental convention is that $\Delta H_f^\circ$ for any element in its standard state is defined as zero.

Key Points for NEET:

1
Definition Precision — A formation reaction must yield exactly one mole of the compound, and reactants must be elements in their standard states. Fractional coefficients for reactants are common and correct.
2
Zero Enthalpy of Elements — Always remember $\Delta H_f^\circ = 0$ for elements like $\text{H}_2(\text{g})$, $\text{N}_2(\text{g})$, $\text{O}_2(\text{g})$, $\text{Cl}_2(\text{g})$, $\text{C}(\text{graphite})$, $\text{Fe}(\text{s})$, etc. Do not assign zero to non-standard states (e.g., $\text{O}_3(\text{g})$, $\text{C}(\text{diamond})$).
3
Hess's Law Application — The most common application is calculating $\Delta H_{rxn}^\circ$ using the formula:

$$\Delta H_{rxn}^\circ = \sum n_p \Delta H_f^\circ(\text{products}) - \sum n_r \Delta H_f^\circ(\text{reactants})$$

Example: For $\text{CO}(\text{g}) + \frac{1}{2}\text{O}_2(\text{g}) \rightarrow \text{CO}_2(\text{g})$ Given: $\Delta H_f^\circ(\text{CO}(\text{g})) = -110.

5\,\text{kJ/mol}$,$\Delta H_f^\circ(\text{CO}_2(\text{g})) = -393.5\,\text{kJ/mol}$.$\Delta H_f^\circ(\text{O}_2(\text{g})) = 0\,\text{kJ/mol}$.$$\Delta H_{rxn}^\circ = [1 \times \Delta H_f^\circ(\text{CO}_2(\text{g}))] - [1 \times \Delta H_f^\circ(\text{CO}(\text{g})) + \frac{1}{2} \times \Delta H_f^\circ(\text{O}_2(\text{g}))]$$$$\Delta H_{rxn}^\circ = [1 \times (-393.

5)] - [1 \times (-110.5) + \frac{1}{2} \times 0]

$$$$

\Delta H_{rxn}^\circ = -393.5 - (-110.5) = -393.5 + 110.5 = -283.

1
Sign Interpretation — A negative $\Delta H_f^\circ$ means the compound's formation is exothermic, indicating it's thermodynamically more stable than its elements. A positive $\Delta H_f^\circ$ means endothermic formation, suggesting less stability.

Common Mistakes to Avoid: Forgetting stoichiometric coefficients, making sign errors, or incorrectly identifying standard states for elements.

Prelims Revision Notes

Standard Enthalpy of Formation ($\Delta H_f^\circ$) - NEET Revision Notes

1. Definition and Key Conditions:

Definition — The enthalpy change when one mole of a compound is formed from its constituent elements in their most stable physical and allotropic forms (standard states) under standard conditions.
Standard Conditions — $298.15\,\text{K}$ ($25^\circ\text{C}$) and $1\,\text{bar}$ pressure. (For solutions, $1\,\text{M}$ concentration).
'One Mole' Rule — The balanced chemical equation for a formation reaction must produce exactly one mole of the target compound. Fractional coefficients for reactants are permissible.

* Example: $\frac{1}{2}\text{N}_2(\text{g}) + \frac{3}{2}\text{H}_2(\text{g}) \rightarrow \text{NH}_3(\text{g})$

2. Standard States of Elements:

Convention — The standard enthalpy of formation for any element in its most stable standard state is defined as zero.
**Examples of Standard States (and $\Delta H_f^\circ = 0$):**

* Gases: $\text{H}_2(\text{g})$, $\text{N}_2(\text{g})$, $\text{O}_2(\text{g})$, $\text{F}_2(\text{g})$, $\text{Cl}_2(\text{g})$ * Liquids: $\text{Br}_2(\text{l})$, $\text{Hg}(\text{l})$ * Solids: $\text{C}(\text{graphite})$, $\text{Fe}(\text{s})$, $\text{Na}(\text{s})$, $\text{S}_8(\text{rhombic})$

**Non-Standard States (and $\Delta H_f^\circ \neq 0$):**

* $\text{O}_3(\text{g})$ (ozone), $\text{C}(\text{diamond})$, $\text{S}(\text{monoclinic})$, $\text{H}(\text{g})$ (atomic hydrogen).

3. Calculation of Standard Enthalpy of Reaction ($\Delta H_{rxn}^\circ$) using Hess's Law:

Formula — For a general reaction $a\text{A} + b\text{B} \rightarrow c\text{C} + d\text{D}$:

$$\Delta H_{rxn}^\circ = \sum n_p \Delta H_f^\circ(\text{products}) - \sum n_r \Delta H_f^\circ(\text{reactants})$$

Where $n_p$ and $n_r$ are the stoichiometric coefficients from the balanced equation.

Steps for Calculation:

1. Write the balanced chemical equation with state symbols. 2. List all $\Delta H_f^\circ$ values for reactants and products. Assign $0$ to elements in their standard states. 3. Substitute values into the Hess's Law formula, multiplying each $\Delta H_f^\circ$ by its stoichiometric coefficient. 4. Perform arithmetic carefully, paying attention to signs.

4. Interpretation of $\Delta H_f^\circ$ Sign:

Negative $\Delta H_f^\circ$ — Exothermic formation. Compound is generally more stable than its constituent elements.
Positive $\Delta H_f^\circ$ — Endothermic formation. Compound is generally less stable than its constituent elements.

5. Common Pitfalls for NEET:

Ignoring Standard States — Forgetting $\Delta H_f^\circ = 0$ for elements or assigning it to non-standard states.
Stoichiometry Errors — Not multiplying $\Delta H_f^\circ$ values by their coefficients.
Sign Errors — Incorrectly subtracting or adding terms in Hess's Law formula.
Confusing Reaction Types — Mistaking a general reaction for a formation reaction (e.g., $\text{CO} + \frac{1}{2}\text{O}_2 \rightarrow \text{CO}_2$ is not $\Delta H_f^\circ$ for $\text{CO}_2$).

Vyyuha Quick Recall

For Every Compound, One Mole From Elements, Standard States, Zero Elemental Heat.

For Every Compound: Refers to the compound whose $\Delta H_f^\circ$ is being defined.
One Mole From Elements: Emphasizes forming exactly one mole from its constituent elements.
Standard States: Highlights that elements must be in their most stable standard states.
Zero Elemental Heat: Reminds that $\Delta H_f^\circ$ for elements in standard states is zero.