JEE Chemistry Thermodynamics Notes Set 04

Enthalpy of Reaction, Formation and Combustion

1. The standard enthalpy of formation \(\Delta_fH^\circ\) is the enthalpy change when one mole of a compound forms from its elements in their standard states (most stable form at 1 bar). It is zero for elements in the standard state. Graphite, rhombic sulphur and white phosphorus are the reference forms.
2. The enthalpy of combustion \(\Delta_cH^\circ\) is the heat change when one mole of a substance burns completely in oxygen. Burning an element to its stable oxide is also the formation of that oxide, for example C(graphite) to \(\ce{CO2}\).
3. \(\Delta_rH^\circ=\sum\Delta_fH^\circ(\text{products})-\sum\Delta_fH^\circ(\text{reactants})\). With combustion data the order is reversed: \(\Delta_rH^\circ=\sum\Delta_cH^\circ(\text{reactants})-\sum\Delta_cH^\circ(\text{products})\).
4. Hess's law: the enthalpy change of a reaction is the same whether it takes place in one step or several. Multiply a reaction and its enthalpy by the same factor; reverse a reaction and change the sign of \(\Delta H\).

Relation of \(\Delta H\) and \(\Delta U\)

1. \(\Delta H=\Delta U+\Delta n_gRT\), where \(\Delta n_g\) is gaseous moles of products minus reactants.
2. A bomb calorimeter works at constant volume and measures \(\Delta U=-C_{cal}\Delta T/n\). Convert to \(\Delta H\) with \(\Delta n_gRT\).
3. For solids, liquids and reactions with \(\Delta n_g=0\), \(\Delta H\approx\Delta U\).

Other Enthalpy Changes

Calorimetry

1. Heat evolved \(q=C_{cal}\Delta T\) (or \(m s\Delta T\) for a solution).
2. Per mole: \(\Delta H=-q/n\), using the limiting reagent for n.
3. Kirchhoff's law: \(\Delta H_{T_2}-\Delta H_{T_1}=\Delta C_P(T_2-T_1)\).