Enthalpy — Revision Notes

⚡ 30-Second Revision

Definition: — $H = U + PV$
Change in Enthalpy: — $\Delta H = \Delta U + P\Delta V$
Constant Pressure: — $\Delta H = Q_p$
Gaseous Reactions: — $\Delta H = \Delta U + \Delta n_g RT$
Exothermic: — $\Delta H < 0$ (Heat released)
Endothermic: — $\Delta H > 0$ (Heat absorbed)
Hess's Law: — $\Delta H_{rxn} = \sum \Delta H_{steps}$
From Formation Enthalpies: — $\Delta H_{rxn}^\circ = \sum n_p \Delta H_f^\circ (products) - \sum n_r \Delta H_f^\circ (reactants)$
Standard State: — 1 bar, 298 K; $\Delta H_f^\circ (element) = 0$
Units: — $R = 8.314\,\text{J mol}^{-1}\text{K}^{-1}$, $T$ in Kelvin, $\Delta H/\Delta U$ in Joules or kJ.

2-Minute Revision

Enthalpy ($H$) is a thermodynamic state function defined as $H = U + PV$. Its change, $\Delta H$, is crucial because it represents the heat exchanged ($Q_p$) during a process at constant pressure, which is common for chemical reactions.

Remember the sign convention: negative $\Delta H$ means an exothermic reaction (releases heat), while positive $\Delta H$ means an endothermic reaction (absorbs heat). The relationship between $\Delta H$ and internal energy change ($\Delta U$) is given by $\Delta H = \Delta U + P\Delta V$.

For reactions involving gases, this simplifies to $\Delta H = \Delta U + \Delta n_g RT$, where $\Delta n_g$ is the change in moles of gaseous products minus reactants. Be meticulous with units (Joules for $R$, Kelvin for $T$).

Hess's Law is vital for calculating $\Delta H$ for complex reactions by summing the $\Delta H$ values of simpler, known steps. This also applies to calculating reaction enthalpies from standard enthalpies of formation, where $\Delta H_{rxn}^\circ = \sum n_p \Delta H_f^\circ (products) - \sum n_r \Delta H_f^\circ (reactants)$.

Always remember that $\Delta H_f^\circ$ for elements in their standard state is zero.

5-Minute Revision

Enthalpy ($H$) is a fundamental thermodynamic property, a state function defined as $H = U + PV$. Its significance in chemistry stems from the fact that the change in enthalpy, $\Delta H$, directly quantifies the heat absorbed or released ($Q_p$) by a system undergoing a process at constant pressure.

This makes it incredibly useful for studying most chemical reactions. A negative $\Delta H$ indicates an exothermic reaction, where heat is released to the surroundings (e.g., combustion), while a positive $\Delta H$ signifies an endothermic reaction, where heat is absorbed from the surroundings (e.

g., melting ice).\n\nThe relationship between $\Delta H$ and the change in internal energy ($\Delta U$) is given by $\Delta H = \Delta U + P\Delta V$. For reactions involving gases, assuming ideal behavior, this can be expressed as $\Delta H = \Delta U + \Delta n_g RT$.

Here, $\Delta n_g$ is the difference between the sum of stoichiometric coefficients of gaseous products and gaseous reactants. It's crucial to use the correct units: $R$ in $\text{J mol}^{-1}\text{K}^{-1}$, $T$ in Kelvin, and ensure $\Delta H$ and $\Delta U$ are in consistent units (Joules or kJ).

For reactions with no gaseous components (only solids and liquids), $\Delta V$ is negligible, so $\Delta H \approx \Delta U$.\n\nHess's Law of Constant Heat Summation is a powerful tool. It states that because enthalpy is a state function, the total enthalpy change for a reaction is independent of the pathway.

This allows us to calculate $\Delta H$ for a reaction by algebraically summing the $\Delta H$ values of a series of steps that add up to the overall reaction. A common application is calculating $\Delta H_{rxn}^\circ$ from standard enthalpies of formation ($\Delta H_f^\circ$) using the formula: $\Delta H_{rxn}^\circ = \sum n_p \Delta H_f^\circ (products) - \sum n_r \Delta H_f^\circ (reactants)$.

Remember that $\Delta H_f^\circ$ for elements in their standard state (e.g., $O_2(g)$, $C(graphite)$) is defined as zero. Practice manipulating equations and their $\Delta H$ values (reversing changes sign, multiplying by a factor multiplies $\Delta H$) to master Hess's Law problems.

Prelims Revision Notes

1
Enthalpy Definition: — $H = U + PV$. It's a state function. \n2. Change in Enthalpy: $\Delta H = H_{final} - H_{initial}$. \n3. Constant Pressure Heat: $\Delta H = Q_p$. This is the heat exchanged at constant pressure. \n4. Exothermic Reactions: Release heat, $\Delta H < 0$. Products have lower enthalpy than reactants. \n5. Endothermic Reactions: Absorb heat, $\Delta H > 0$. Products have higher enthalpy than reactants. \n6. Relationship with Internal Energy: $\Delta H = \Delta U + P\Delta V$. \n * For reactions involving gases: $\Delta H = \Delta U + \Delta n_g RT$. \n * $\Delta n_g = (\text{moles of gaseous products}) - (\text{moles of gaseous reactants})$. \n * Units: $R = 8.314\,\text{J mol}^{-1}\text{K}^{-1}$, $T$ in Kelvin. Convert $\Delta H/\Delta U$ to Joules if $R$ is in Joules. \n * If $\Delta n_g = 0$, then $\Delta H = \Delta U$. \n * If $\Delta n_g > 0$, then $\Delta H > \Delta U$. \n * If $\Delta n_g < 0$, then $\Delta H < \Delta U$. \n * For reactions with only solids/liquids, $\Delta V \approx 0$, so $\Delta H \approx \Delta U$. \n7. Standard State: 1 bar pressure, 298 K (25 \text{°C}). \n8. **Standard Enthalpy of Formation ($\Delta H_f^\circ$):** Enthalpy change when 1 mole of a compound is formed from its elements in their standard states. $\Delta H_f^\circ (element, standard state) = 0$. \n9. **Standard Enthalpy of Combustion ($\Delta H_c^\circ$): Enthalpy change when 1 mole of a substance is completely burnt in oxygen. \n10. Hess's Law:** $\Delta H_{overall} = \sum \Delta H_{steps}$. Independent of path. \n11. **Calculating $\Delta H_{rxn}^\circ$ from $\Delta H_f^\circ$:** $\Delta H_{rxn}^\circ = \sum n_p \Delta H_f^\circ (products) - \sum n_r \Delta H_f^\circ (reactants)$. \n12. Bond Enthalpy (approximate): $\Delta H_{rxn}^\circ \approx \sum (\text{bond enthalpies of reactants}) - \sum (\text{bond enthalpies of products})$.

Vyyuha Quick Recall

To remember the relation $\Delta H = \Delta U + \Delta n_g RT$ and its implications:\nHappy Uncles Play Volleyball (H = U + PV)\nHe Usually Neglects Really Tiny things ($\Delta H = \Delta U + \Delta n_g RT$)\n\nFor $\Delta n_g$ sign:\nGas Products More: $\Delta n_g > 0 \Rightarrow \Delta H > \Delta U$ (Gas products make more volume, so $\Delta H$ is 'more' than $\Delta U$)\nGas Reactants More: $\Delta n_g < 0 \Rightarrow \Delta H < \Delta U$ (Gas reactants take up more volume, so $\Delta H$ is 'less' than $\Delta U$)